{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Clustering and the k-means Algorithm\n", "\n", "Copyright 2020 Allen B. Downey\n", "\n", "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "This notebook introduces [cluster analysis](https://en.wikipedia.org/wiki/Cluster_analysis) and one of the most common algorithms for it, [k-means](https://en.wikipedia.org/wiki/K-means_clustering).\n", "\n", "It also introduces \n", "\n", "* Jupyter, which is a tool for creating notebooks like this one;\n", "\n", "* NumPy, which we'll use to perform array operations;\n", "\n", "* Pandas, which we'll use to read and clean the data; and\n", "\n", "* scikit-learn, which provides an implementation of k-means.\n", "\n", "We'll proceed \"top-down\"; that is, we'll use scikit-learn first, then we'll open the hood and see how it works.\n", "\n", "If you want to follow along:\n", "\n", "* Use this link to run this notebook and do the exercises: [tinyurl.com/DowPen20](https://tinyurl.com/DowPen20)\n", "\n", "* Use this link to run the same notebook with solutions: [tinyurl.com/DowPenSoln20](https://tinyurl.com/DowPenSoln20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bio\n", "\n", "I am a professor at [Olin College](http://www.olin.edu/), which is a small engineering school near Boston, Massachusetts, USA.\n", "\n", "Olin was created in 1999 with the mission to transform engineering education." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Classes and books\n", "\n", "I have been at Olin since 2003. I teach classes related to software, data science, Bayesian statistics, and physical modeling.\n", "\n", "I have written several books on these topics, including *Think Python* and *Think Stats*. Most are published by O'Reilly Media, which is famous for putting animals on their covers:\n", "\n", "\n", "\n", "But all of them are freely available from [Green Tea Press](https://greenteapress.com/wp/).\n", "\n", "Finally, I write a blog about Data Science and related topics, called [Probably Overthinking It](https://www.allendowney.com/blog/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Jupyter and Colab\n", "\n", "Jupyter is a tool for writing notebooks that contain text, code, and results.\n", "\n", "You can install Jupyter on your own computer, but can also use services like Colab that run the notebook for you.\n", "In that case, you don't have to install anything; you just need a browser.\n", "\n", "A notebook contains:\n", "\n", "* Text cells, which contain text in Markdown or HTML, and\n", "\n", "* Code cells, which contain code in Python or one of about 100 other languages.\n", "\n", "This is a text cell; the one below is a code cell." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hello, Jupyter\n" ] } ], "source": [ "print('Hello, Jupyter')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On Colab, code cells have a triangle \"Play\" icon on the left side. You can press it to run the code in the cell.\n", "\n", "Or if you select a cell by clicking on it, you can run it by pressing Shift-Enter.\n", "\n", "As an exercise:\n", "\n", "1. Run the `print` statement in the previous cell.\n", "2. Modify the code in that cell and run it again.\n", "3. Run the next cell, which imports the Python modules we'll use later." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Also run the following cell, which defines a function we'll use." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def decorate(**options):\n", " \"\"\"Decorate the current axes.\n", " \n", " Call decorate with keyword arguments like\n", " decorate(title='Title',\n", " xlabel='x',\n", " ylabel='y')\n", " \n", " The keyword arguments can be any of the axis properties\n", " https://matplotlib.org/api/axes_api.html\n", " \"\"\"\n", " ax = plt.gca()\n", " ax.set(**options)\n", " \n", " handles, labels = ax.get_legend_handles_labels()\n", " if handles:\n", " ax.legend(handles, labels)\n", "\n", " plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Clustering\n", "\n", "Cluster analysis is a set of tools for looking at data and \n", "\n", "* Discovering groups, species, or categories,\n", "\n", "* Defining boundaries between groups.\n", "\n", "It is a form of \"unsupervised\" learning, which means that the only input is the dataset itself; the algorithm is not given any correct examples to learn from.\n", "\n", "As an example, I'll used data collected and made available by Dr. Kristen Gorman at the Palmer Long-Term Ecological Research Station in Antarctica.\n", "\n", "This dataset was published to support this article: Gorman, Williams, and Fraser, [\"Ecological Sexual Dimorphism and Environmental Variability within a Community of Antarctic Penguins (Genus *Pygoscelis*)\"](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0090081), March 2014.\n", "\n", "The following cell downloads the raw data." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Load the data files from https://github.com/allisonhorst/palmerpenguins\n", "# With gratitude to Allison Horst (@allison_horst)\n", "\n", "import os\n", "\n", "if not os.path.exists('penguins_raw.csv'):\n", " !wget https://github.com/allisonhorst/palmerpenguins/raw/master/inst/extdata/penguins_raw.csv" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dataset is stored in a CSV file, which contains one row for each penguin and one column for each variable.\n", "\n", "I'll use Pandas to read the CSV file and put the results in a `DataFrame`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(344, 17)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv('penguins_raw.csv')\n", "df.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A `DataFrame` is like a 2-D array, but it also contains names for the columns and labels for the rows.\n", "\n", "The `shape` of the `DataFrame` is the number of rows and columns.\n", "\n", "The `head` method displays the first few rows." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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studyNameSample NumberSpeciesRegionIslandStageIndividual IDClutch CompletionDate EggCulmen Length (mm)Culmen Depth (mm)Flipper Length (mm)Body Mass (g)SexDelta 15 N (o/oo)Delta 13 C (o/oo)Comments
0PAL07081Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN1A1Yes2007-11-1139.118.7181.03750.0MALENaNNaNNot enough blood for isotopes.
1PAL07082Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN1A2Yes2007-11-1139.517.4186.03800.0FEMALE8.94956-24.69454NaN
2PAL07083Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN2A1Yes2007-11-1640.318.0195.03250.0FEMALE8.36821-25.33302NaN
3PAL07084Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN2A2Yes2007-11-16NaNNaNNaNNaNNaNNaNNaNAdult not sampled.
4PAL07085Adelie Penguin (Pygoscelis adeliae)AnversTorgersenAdult, 1 Egg StageN3A1Yes2007-11-1636.719.3193.03450.0FEMALE8.76651-25.32426NaN
\n", "
" ], "text/plain": [ " studyName Sample Number Species Region \\\n", "0 PAL0708 1 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "1 PAL0708 2 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "2 PAL0708 3 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "3 PAL0708 4 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "4 PAL0708 5 Adelie Penguin (Pygoscelis adeliae) Anvers \n", "\n", " Island Stage Individual ID Clutch Completion Date Egg \\\n", "0 Torgersen Adult, 1 Egg Stage N1A1 Yes 2007-11-11 \n", "1 Torgersen Adult, 1 Egg Stage N1A2 Yes 2007-11-11 \n", "2 Torgersen Adult, 1 Egg Stage N2A1 Yes 2007-11-16 \n", "3 Torgersen Adult, 1 Egg Stage N2A2 Yes 2007-11-16 \n", "4 Torgersen Adult, 1 Egg Stage N3A1 Yes 2007-11-16 \n", "\n", " Culmen Length (mm) Culmen Depth (mm) Flipper Length (mm) Body Mass (g) \\\n", "0 39.1 18.7 181.0 3750.0 \n", "1 39.5 17.4 186.0 3800.0 \n", "2 40.3 18.0 195.0 3250.0 \n", "3 NaN NaN NaN NaN \n", "4 36.7 19.3 193.0 3450.0 \n", "\n", " Sex Delta 15 N (o/oo) Delta 13 C (o/oo) \\\n", "0 MALE NaN NaN \n", "1 FEMALE 8.94956 -24.69454 \n", "2 FEMALE 8.36821 -25.33302 \n", "3 NaN NaN NaN \n", "4 FEMALE 8.76651 -25.32426 \n", "\n", " Comments \n", "0 Not enough blood for isotopes. \n", "1 NaN \n", "2 NaN \n", "3 Adult not sampled. \n", "4 NaN " ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Three species of penguins are represented in the dataset: Adelie, Chinstrap and Gentoo, as shown in this illustration (by Allison Horst, available under the [CC-BY](https://creativecommons.org/licenses/by/2.0/) license):\n", "\n", "\n", "\n", "In this dataset we are told that there are three species, and we are told which species each penguin belongs to.\n", "But for purposes of clustering, we'll pretend we don't have this information and we'll see whether the algorithm \"discovers\" the different species." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The measurements we'll use are:\n", "\n", "* Body Mass in grams (g).\n", "\n", "* Flipper Length in millimeters (mm).\n", "\n", "* Culmen Length in millimeters. \n", "\n", "* Culmen Depth in millimeters.\n", "\n", "If you are not familiar with the word \"culmen\", it refers to the [top margin of the beak](https://en.wikipedia.org/wiki/Bird_measurement#Culmen), as shown in the following illustration (also by Allison Horst):\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This might seem like an artificial exercise. If we already know that there are three species, why are we trying to discover them?\n", "\n", "For now, I'll just say that it's a learning example. But let's come back to this question: what is unsupervised clustering good for?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Distributions of measurements\n", "\n", "The measurements we have will be most useful for clustering if there are substantial differences between species and small variation within species. To see whether that is true, and to what degree, I will plot distributions of measurements for each species. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For convenience, I'll create a new column, called `Species2`, that contains a shorter version of the species names." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def shorten(species):\n", " \"\"\"Select the first word from a string.\"\"\"\n", " return species.split()[0]\n", "\n", "df['Species2'] = df['Species'].apply(shorten)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll use the `groupby` method to divide the dataset by species." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "pandas.core.groupby.generic.DataFrameGroupBy" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grouped = df.groupby('Species2')\n", "type(grouped)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a `GroupBy` object that contains the three groups and their names. The following loop prints the group names and the number of penguins in each group." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Adelie 152\n", "Chinstrap 68\n", "Gentoo 124\n" ] } ], "source": [ "for name, group in grouped:\n", " print(name, len(group))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the `GroupBy` object to extract a column, like flipper length, from each group and compute its mean." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Adelie 189.95364238410596\n", "Chinstrap 195.8235294117647\n", "Gentoo 217.1869918699187\n" ] } ], "source": [ "varname = 'Flipper Length (mm)'\n", "\n", "for name, group in grouped:\n", " print(name, group[varname].mean())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also use it to display the distribution of values in each group." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for name, group in grouped:\n", " sns.kdeplot(group[varname], label=name)\n", " \n", "decorate(xlabel=varname,\n", " ylabel='PDF',\n", " title='Distributions of features')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`kdeplot` uses [kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) to make a smooth histogram of the values.\n", "\n", "It looks like we can use flipper length to identify Gentoo penguins, but not to distinguish the other two species.\n", "\n", "To make these steps easier to reuse, I'll wrap them a function." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def make_kdeplots(df, varname):\n", " \"\"\"Make a KDE plot for each species.\n", " \n", " df: DataFrame\n", " varname: string column name\n", " by: string column name\n", " \n", " returns: dictionary from species name to Cdf\n", " \"\"\"\n", " grouped = df.groupby('Species2')\n", " for name, group in grouped:\n", " sns.kdeplot(group[varname], label=name)\n", " \n", " decorate(xlabel=varname,\n", " ylabel='PDF',\n", " title='Distributions of features')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can use it to explore other features, like culmen length." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "make_kdeplots(df, 'Culmen Length (mm)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks like we can use culmen length to identify Adelie penguins." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Use `make_kdeplots` to display the distributions of one of the other two features:\n", "\n", "* `'Body Mass (g)'`\n", "* `'Culmen Depth (mm)'`" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "make_kdeplots(df, 'Body Mass (g)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Scatter plot\n", "\n", "If we can identify Gentoo penguins by flipper length and Adelie penguins by culmen length, maybe we can combine these variables to identify all three species. \n", "\n", "I'll start by making a scatter plot of the data." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "var1 = 'Flipper Length (mm)'\n", "var2 = 'Culmen Length (mm)'\n", "var3 = 'Culmen Depth (mm)'\n", "var4 = 'Body Mass (g)'" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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kE7oKOUBXrffSlZdI59IcGTnCoYuHODJyhC5vFxPJiapVdvVW5ZmlmjWocSnltxczuBCiH4ii/avLSSn3CCFagQNo3n79wG9JKRuoiK5YVmqxqF4rd4SWDbDxzrmspWWD5sOnl531PwOb7q5+rUUvs/C1gsOliTpSYfAEtUaIkUv66ziT5xpHOWlEg6g7zWYKfcN95GWeU5OniGaiBFwBOnwdNcm45Mx/C4/5nD7dMuG3z32bdC5dMpdNwU0kcgkOjxwm5A4RcAVI59Ocnj7NjtYds9ZFV1s7W4wqr6EbFgJ/KYT4IvATSlV8/6fKa+yTUl6Z9/xjwE+klH8rhPjYzPM/qXbCilVGLRbVa3FTNOtGIdEUg/3Pzkm+27dp2Y4eekHUvwZ87dC2pTSwelv0s63ocOMoJytRgzku9aZoVsRwZuoMg9FBvE4vQVeQVD7F6cnTJLNJw/lVu8b1mvbX8OLoi1r2ZPeQyqeIZCK8rvN1umVCu7CXBaLDI4cRUsz64Il5hnjNnmYeuP6Bqj8bo9Kk0bqX3vrZQzc+1DBWR78LXA84gWJzQglUG6AW8uvAG2b+/BXgKVSAunap1aK62ZviwjWe2Lg5N4q2XrjwtPaaosDhwtOw2cDlXC+IFvc7LQys5w41xDpOvaiFY4LZTCGcCWMTNjwODwAeh4d0Lk04E9Y938wa1/1b7mc8Oc5kapJwOozL7mJTcBP3b7n/qu9jfiCSSPZ27eVC5AKRTISAK8BtXbeRLWSv/oFcBaPPPJFJ6K6fPXn+ST548weXfN2rUU2Aeq2Uctcix5fAD4UQEviclPLzQKeUchhASjkshNDNuYUQDwMPA2zYsGGRl1c0PLVaVDezOVQvWzr/U+h9Y+k83AEtI9LLzn7xtbnz5ldvKvWXNgqiesesNHRtcOohhQ46g0QyEVK5FG67m3Q+TYECQae+aY4ZNdzG0EYe2vlQ1RlhXua5reu2skD0i/FfEM/FS86N5+L0NPXojmMGo8/80MVDbA5tLgncSG1dbTmoyotPCLFDSvnqIsa/U0p5eSYI/UgIcbLaF84Es88D7NmzR7lYrFZqsX5kdh1Lr6zoXwOjv4TAfXPnVXKjkDltDWrizNz60aa7teOV5llNEG2QdZx6UQsptJG026g0ta11Gz6nj7Hk2Oy6z/qm9fQE9G/+Zte4zEjYO3wdDEWHSo7Fs3E2BDZwbPQYQVeQoCtIJB1hKDrE7V23VzVuJcYSYzhtTo5MHpl9/5uDm8kUMrrrZ8tFNQHqLuC9QogLaGtQRbPYq8rMpZSXZx7HhBAHgVuBUSFE90z21A0sT+9gRWNSi5ux2XUsvbJi92vh7I9n5NtVBMpAt5ZdbZpX0kuFNb8/PcwGUaNsawXaCJmlFlJoI2n3k+ef5P4t95dlM3u793IwfpDtrdtL1qwqqeHMrHGZYX3Ter597ttlgWhn6052d+yeDaJBd5CtzVsZjA0u+Zp2YeeFkRdmP69UPsULIy/Q5esikonorp8tB9UEqLcsZmAhhB+wSSmjM39+E/BXwLeB9wJ/O/P4rcWMr1hFLHVR3ew6VqAbpvrn9hN5Qtrrt947Zyx7tUBpNvOrhRhkhdoImaUWN//50m6YK029MPICmUJGd33LzJqV0RoXYMoXT4/B2CC7O3czlpgXiFq2cnbqLPs27GNDaG7JQ0pZ80228zOk65qvIyuzi1o/qwWGAUoI0SSljEkpDTcCFM8x+HUnWpuO4nX+TUr5fSHEi8DXhBDvBy4C71z89BUKzK9jtfbCLx7TvPeKm3Kn+rV9T1ur3K9jNvOrhRikgWyEaoWRWm+pBqVG0u5wOmy4vvXA9Q8saY3rUvQSh0cPL7kdxlhijPWB9WwIlgais1Nna7LJVu8zz8s8t3bdSn+kf7bEd2vXreQKOX6t99caUmb+LSHEcbQM56iUMg4ghNgC7AN+C/gC8ITei6WU54HX6hyfAJaeBysURcxmM5PnYMPtWnBIRbQg1XG9dhwTG0rNZH61EIM0iI3QVamyDDkQHuDgS18mGBmlM5Mk5vJy8Mqr7N/1viUblL6m/TU8c+kZsoUs+UIeu82O0+Yk5ArpbuBdjAv5QtXbI68+wvaW7UsWdxiVOHe175rdyLvYzNJIreeyuXA73Ozp2jN7bjQTpdXRWlezWEMnCSnlG9H2Pn0AeEUIERZCTAD/AnQB75VS6gYnhWJZKWYz1fZ9ig5rFkGb7oLr36o9tm4218vJLLVwWKiFY4bVmOhZ1Xf23wmOnSYACF8LASA4dpq+s/++5GnctOYmsvksOZlDIsnJHNl8lu0t24llS4s+i8lC9Hoz5WWe0URpoCu6VwyEBzhw8gCfPfZZDpw8UNGhwsjt4f4t97N/6/7ZTbl+h990dmbUUwpoSIeJimtQUsrvAt9dprkoFItnubMZs9RCDFIrxwyTmNo0e+4QA3YbffELjIXjdDj87HW2slGnDDk2fIxOd1BzcQdweGlyS0aHjy15zoOxQW5fe3uJKq/D24HX4V1yFgL6SsM2TxuTqcmSY0Vvvfku5Genz3Jy8iQP7dRXFF6txLmUbMZIIRnPxOva98mIakQSCsXyY6VarU43+iWLQeogPze7aXZg8jQHc+ME7V46HU3EChkOJvrZn42z8OyOfJ6Yy818z4yYzUZHJr/keY8lxlgfXK8rKKiF1U+Hr4PByGBJAPQ4PNiFnWgmWhL8ktkk/RFNURhyh0jlU/RHKm92taqsVkkhacZhohHWoBSK+mC1Wm0F7zMacDjoCwYYcyTp8AXY63CU3fhridlNs30iSVBCwO7Wzre7IZekj2TZPPe23sjByePgEjTZXMQKGSKZCG9svWnJN8XF3Ij1MArQG5s28rPLPyNHbrYFhgMH777+3WRkpiT4/c3hvyHoCpYoCqWUy7bZdT6L6WO1VFePpaAClKLxWA612krwtFtAPW4WZjfNjjWtoXNsGuxJcHggl6Ipl2O0dU3ZuRt3/Cb7XximrxBnNB+lQzh4o7MTNuxd8vus1T4lowD9o4s/wml3QkFzfrALTYQxnBguy4rEzH8Lj9UDswrJejc4rCpACSHsaLLx+f2gLlo1KcU1zkpRqy0z9bhZmN0029G2ncF8hrGJE0QjEQLuIB1tN9DTtr385LZeNt72IW19KjaiZbK9+zgwfmTJ77MWUnUwDtAXIhfY1rINb7G7MZDMJnlh+AXavG0lmd+u9l28OPoiCGZtlMKZ8LJtdl2ImQyy3g0Oq2lY+GHgL4FRSs1iVcNChTU0SNO7RWPR+lk9bhaVMhG9MtysC0JTB8HWrUQyEYaiF7h9y1v1L6CTyY4NfLcm77MW6zhGAdplc5VlQYlsgrHE2GxPqWLmd2vnrYwnxpnMTBLJRLTNroHl2+y6FOrd4LCahoV/CGyXUu6UUu6a+VHBSWEdDdL0blGYkFmbpXizmI/VN4tiJrJQ2gzoNvg7Pn6c3Z27CbqDRLOaC8Luzt2m7Hjq8T6NMJJ839Z1G+FMmFQuhZSSVC7F5fhlegI9ZRLuwdggD934EHd038GO1h3c0X3HsrWrWCr1bnBYTYlvEND3nFcorGAFixisXD+z0v+tEnqZyIGTB3TLcC8Ov6jZ8QQXb8ezmPdpldKskqVR0Yy2mBX57D5u6byl5PXFzK+em12XQq1KpYulktXRH8/88TzwlBDiSUobFn7a4rkprmWsFjFYJWO3cP2s3jeL+RiVG4Ell4TMvs+B8IDuPqP7NtzHYGxwyUHLKLg8dGNpC42J5glcDlfJOfXK/GpJPYNrpQyq+H/YxZkf18wPsIx+6wpFrbFSxm5kRNtcm3/gjfJNvMPXwWB0cNbQtNgi3awdj1HmY+Z9Pnn+ybJ9RicmTnB2WjNXrVYJaDYLWzjHosqy2veuuDqGAUpK+d8BhBDvlFJ+ff7vhBDK4FWxcrFSxm5kRLvl3qWN22AYtYT40Gs/xLrAuqqyH6PMx8hhwYhfXvll2T6jbCFLPBuvWglYjy6+iqtTzRrUnwJfr+KYQrEysFLGXisj2gZnMDZo2Jvojp47qrop62U+V3NY0ENvn1EmnyFfyHNkZK4B36bgJuKZuO4YtZLwN6Ibw0qm0hrUrwJvBdYJIf7XvF8FgQptQxWKBsdKGXvRiHZ+JiYLq24PVyUroWrRy3yu5rCgd6Pf1b6Lp4eeJidz5Ao5HDYH0UwUt0PbcxRwBUjn0xweOWy498hKCX+93RhWMpUyqMvAEeDXgKPzjkeBP7JyUoo6cg10bLXUi2+l7+GqklrsjzHrsFDJdihXyGm2Q0BOao9+p/+qY9by/RhRbzeGlUylNahfAL8QQvyblDK7jHNS1IuV0LG1FgHUShl7vYxol5laSN7NOiwY3eifH3me29fdXiLYGHIM0exqxm13E8lECLgC3NZ1G9mC/q3MSgn/WGIMh83BqclTVZUbFXNUswZ1TAixULUXRsuuPjHTgFCxGrDaA2+pwcWKACprLEhdyXu4TFALQcD9W+435bBQqQznxMmxsWPEs3H8Tj9tnjZShRRv6HrD7LnRTJQWR4vp97PU9SO7sHN45DAhd6iqcqNijmoC1PeAPPBvM89/GxBoQeoRYHV9NbyWsVI8UIvgUimAFh+rCX7L4Za+ygKSHksVBGwMbSzbS1Tp5m9UhsvkM/x06Ke4HW6aHE2kC2nOh8/T5esqa31RKSPSez+1Xj+ql0nsSqWaAHWnlPLOec9fEkI8J6W8UwjxO1ZNTFEHrFw/qUV2Fh0Guwv6n53bY9S+DcKD2k+1AWc53NKvUcxKx80EOaMyXDQTxS7smj+eELiki5wtR17mZy2a5mdEzw89z8FzBxmNj9Lp72R/737u6LlD9/3UYv0oL/Pc1nUbFyIXqio3KuaoJkA1CSFuk1K+ACCEuBVomvmdUvOtJqxcP6mUnemV/qD8mN0BF57Wgou3GbIp7bnLBxvvrD7gKLd0y6iFdLxS1qJXhvvOue/Q4esgkUuQLWRx2px0+DqYSk2Vjf380PP84y/+kaArSLe/m0gmwj/+4h8BdIOUWXWfUXPDeC7Onq49s+dVKjcq5qgmQP0e8GUhRBNaaS8C/J4Qwg/8jZWTUywzZtdPzKwpGWVnNnt5ue3ZvwchNLn2/IwonZh77fylo1RUCzDzqRRwrhGlndXo3YwXIx1fSKWsRc+ktM3bxnR6uuRYJB0BQZmz+KnJUziEg+nMNCOJETwODy7h4uC5g7oByoy6r5Ll0uHRw4BymDDLVQOUlPJFYJcQIgQIKeX8/xO+ZtnMViMrQcJd7fqJ2XUco+zM7ikvtyWvaAFo7U1zxwBGXoZNd8PEmZkSX1B7fulFcwHnGlHaWYlRlpPMJvHYPSXnCgSJXIIDJw9UtdZklLWcmjjFcHy47Jq3rLmFr539GgKBHTt58mQLWW7tvLUsyJ2ZOoPf6cdld+Gxe8jlcyTyCZK5pO5czKj7jLLH4+PHlcPEIqmmH5QbeAewCXAIoS3ySSn/ytKZrTZWgoTbDGbXcYyys+P/Vp795NKwcDG5eI7TA5vumjueCsPaPVqAKZ43L+BcGI/x7LkJRsMpOkMe7uptY/OaXtj8Bvj5o5pnXnAt3LxC/x7qhFGW43P6CGfCJdLx0eQoDhxl2YyR0MAoa4lkI6wLriu75pHJI3R6O5lMT86W+JzCidPmLBm3ydlEXuYpyILWDRdw2p2kcimK97WFmFErVsoeP3jzB1VAWgTVlPi+habYO8o8N3OFSVbbwvxi1nH0sjM9c9VCDmY2Wc6SjsJ6g0C0+0Ht2ILgd6HQyYEjQzR7nXSFPMRSOQ4cGeLdWzOs738Kul+rBbt0FC48BS0bdP8u9INcU9l51xJGWc66pnVMp6a5EL1AMpvE6/Rikzb2rN1TtdDAKGsJuUKzjunzr9kf6WdbyzY8zrnM7ezkWS5GS5t+x7IxOn2dTKWntEzP4SGVS5EpZNgR3LHkz6SRWruvFqoJUD1SyrdYPpPVzmpbmK/VOo6euWpsHNpbtYBVRSCirXeuIeC8fU3Pnpug2esk6NW+LRcfL/3826wP5WHkpbmgGOjW/bJwYTymG+Qe2NNzTQcpoyyn1dNKXubpkT1k8hlcdheXo5fxOX0lr68kNDDKWm0c+xcAACAASURBVPqG+3Qd1J02J3JBg4VmTzOXopfKZOb39NzDSHyE09OnCafDBN1BdrXvYmf7Tt25mJGZN1pr99VANQHqeSHELill9aucinJW28J8rdZxDMxVJ7JOzlzOIMMvI0LdrLv5HawvBo+FWY5B+TQdv4uuJjdrB17Amx4j6e7gcuttuK+cgPS0lqV5miGXgrFXIJsom55RkHv23MQ1HaCMshyXzcX64Hp2tM9lJM8OPcvJqZPc5ZsrzV7NRkhPfn4peknXQf2GlhsYTY0ihMBj95DKp8jLPHevu7tMZg5aJ+A3Nb+pZN5GHWLNyMzNbjxWXJ1qAtRdwENCiAtoJT4BSNX23SSrbWG+Vo4JOuaqV6JJTg2c5qVtv0PTBgexVI6nzmZ5oDmmHxQMyqe3jPwYOZECbwsJdyfOXIwNA9+grTAGeMHp1c53ejXJ+vQgHP5iiYhlNJyjK1S66N/kcTASTpl7n6sMoyzn2+e+TTqXLrH16fZ18/Lky7qbZs24NAzGBult7uX01GkGIgME3UG2tWyjy9eF1+VlMjVJOB3WAkNwE+/e8W7dscwIFirJzPXmbmbjseLqVBOgftXyWVwLrEYLHCPF3xLl5wPDY+T9ndVnLQbl023ZQ7zATuz4cAtBFB95MlzvzIJ0QTapiS6yKW0OuQRkYiVZ2Fb7GxlJrZudA0AslaNzQdBazZhpKmgXdp4eeppsITvrLO60OdkU2MSJiRMlm2MBUy4NZ6bOMBofpcvfxabgJlL5FKPxUVw2Fw/trD4wmGmGaFTKtAu74dwfuP6Baj9axVWoRmY+IIS4C7hOSvnPQog1zG3UVZjhWrDAqYH8PBebIN11B1sHDpSU5s6GO8tfD4blU7/TwWt6ejh7JUkkmSXodbK1uwffpVPQsWNOmOEOgssDTW1lWdidmZf4UlIrRTV5tGxuOpnlzTs7V8a2gSVi1uonnA5zJXmFJmcTXoeXVC7FRHKCfCHPW7a8hdd1vY5YNsbh0cO4xl3kC/mSbKvD22EonghnwtiErUQll85p6zyXopc4MnpkNgCub1pfk8ylUimzFg7lqk9UZWxXO0EI8ZfAn6A1KQRwAv9i5aQUK5j55TZh0x69LXN+eQspZpauJu1G72oi0nUHbeN9OHJxEu5OHLk4Gwa+wVa7QW+e3n1auTQV1novpcLa8/V7aHdm2Lu5lTft6GTv5lbanRlNli5s0LULtr1Fe8wkoHNB1dodYA1TPLCnB/9MWc/vcWgCCduoFliLGVcmpj0vijVWIAPhAQ6cPMBnj32WAycPzN48izdiIQQBV4CgO0jfcJ/+GNEBOr2dxLNxhmJDxLNxXDYXyXxSd4zT06dLejadnj7N6cnTumMHnUEKFEjlUkgpSeVSFCgQT8X59NFPc2bqDJF0hDNTZ/j00U/z/NDzS/5MiqXM4lqW3+Fn/9b95GVeV1E4lhireuxi8C/K7+O5OAfPHmQgPLDkea8Wqinx7QduBo4BSCkvCyEClV8yhxDCjuZ8fklK+TYhxCPA69Gk6wAPSSmPm5q1onGpgfz8pp/+Iy+N+8tKc3faXgLu0X+9XvkU9Nf99NSAW+7Vyn3zmRGxbF7TVF5aPPz4qto2YJQpxTIxtrVuKzm3kgIvmU0ynZkm5A7RZmsjV8hxOXaZoC1YNkY4rWVEkXSEVD6Fx+7R2mNkI7qZxbbWbficvtkuvgFXgPVN63lm6BlS+RQBdwCncJKVWaLpKP9y4l8MPfbMoFcS7PB16CoKe5p6qh5X9Ym6OtUEqIyUUhZbbsxYHJnhD4ETaJ14i/xXKeUTJsdRrARqoFZcIyd5zZby0ly7nDR+kVH5tNK63/zzi6VJqE7Essq2DRjdLC/FLplq5Od3+hlNjM7tsxZgEzYcttJbTSwbw+PwMBwfxufwze5JmkxN0uRs0g2Wt3beynB8mO2t20vKbfFsnKA7OLsx1ymc+J1++iP9tf2Q5rG+ab2uovD2rturHsPKLr6rhWoC1NeEEJ8DmoUQvw+8D/hiNYMLIXqA+4G/Bv540bNUrBxqoVYMdNOeidG+uXXuWCoMrkVI8qtd9zMrYlll2waMbpZBp3bzLT6/mo/c2qa1xDIxEoUEqXwKu81Ot78biSxT8bV52vA6vKTzaS2DcngIuUOMJ8fZ3bW7LFgOxgZ1FXiHLh4iL/Ml88jLfJmTRC0ZjA2yu2P3bDYXdAfZ2ryVwdhg1WNY2cV3tVCNSOKTQoj70ExitwN/IaX8UZXjfwb4b8DCkuBfCyH+AvgJ8DEpZZlDhRDiYeBhgA0bNlR5OUXdqYVasV6SfDMillW2bcDoZrmtdRt7u/dWLcu+ruU6vE5vWenLa/eW7Ul69JVHGYoP0expnt3YmswlSWQTuus7o/FR3XLbbV23cWjoEAjw2DykCini2Tj7evbV/oOaYSwxxvrgejaE5u5NUkpT2Y+VXXxXC0IuoqNosR/UVc55G/BWKeUHhRBvAP7LzBpUNzACuIDPA+eu5uu3Z88eeeTIEdPzVKxgigq52IgW5BpRIbcS5lgl89eg5t8szTbmMzPOgZMHGIoOlawpdXg7GEmMcEPbDSXBMpqJ4nf4Z4Pl/LUpgM8e+2yJvdLmwGZ+87rfZDA2WKaQM6uc0zu/b7iPeC6uO0czMnOl4tMQQhyVUu4pO77IADUopVx/lXP+BngPWs8oD9oa1P+RUv7OvHPewEzgqjSWClAKhfXU6mZZ7ThGwezWzls5PHq46uP7t2p7quZfc33TetNj1GKOi+20e61T6wB1UUpZdd1tYQYlpRwWmn3w3wEpKeXHKr1eBSiFYnViFMyWmrUcOHlA99wTEycMszO9zMdoHKNsTgWnxWEUoAzXoIQQv2n0K8C7hLn868xmXwEcB/6vJYylUNQM5Vquj9nMysznaOTqoHf82+e+XbXqrZJC7nVdr9M9rkelccw4UigWR6WNum83+Hkb8B0zF5FSPlUs40kp75VS7pJS3iil/B0pZWxxU1coakfRtTye0rz34jOu5RfGr+3/Pc1uJrXycywKOeZjpHozOrcoW69mDLPXVNQewwxKSvm7yzkRhaKeKNdyffqG+0zZEVn5OZpRvRmdu793v6n260ppV1+uanWkUFwLjIZTNHlKv681eRyMXuOu5acnT5uyI7LyczSyHTIqEeqde0fPHVWPYfaaitpTzUZdhWLV0znTjLBhXMsbxIg2ko1go9ygNZKN6J5fq8/RjIO6EbVaIzIaR0nErUdlUAoFcFdvG9PJLJFkloKURJJZppNZ7uptW/7JFG2XGsCINuQKUZCaQSsSzaBVFgi5Qrrn1+JztNJEtdLYema59ZijYo6qMighxB3ApvnnSykftWhOCsWys3lNEw/s6eHZcxOMzKjP3ryzsz7rTwYNGOthRHtdy3VkChlOT50mko7MNgm8ruU63Qxi85qNS/4crTRRNRr7yfNPkilkqm4rooxel4erBighxFeBXjRJeNHwSgIqQF3r1KEMZaUUXNe13OJr6tJARrTrm9bz9VNfJ0cOl91FKp/i1SuvcnP7zYZ9ojav2bikz8dKE1WjsV8cfpHXdb+u6oCjjF6Xh2pKfHuAO6WUH5RSfnjm5yNWT0zR4NShDFUPKfiF8Rife/o8z5we5+VLYZ45Pc7nnj5vrfy8aEQ7nzoZ0R4fP47T7sQhHAgEDuHAaXfyo4s/MtUnygxWSruNxpZIU/2dlPx8eagmQL0MrEyLZoV1mG1MWAPmS5htQhD0Omn2Onn23ERNxr8wHuOrfQN88gen+GrfABfGY3zz+CX6r8QRQhDyOhFC0H8lzjePX6rJNXUxasDYa535qRG/vPJLOnwdbG3Zyva27Wxt2UqHr4P+SP+SG/YZsbd7L5F0hGgmipSaC3okHZn13dOj2vUjo7Ff0/4aUwFnMXNUmKeaNah24FUhxGFg1nVcSvlrls1K0fjUoQw1Gk7RtUAN1jTT6dYsC8t2m1q8PHd+kmavk64ZJdqBI0McG5ik2e/C67QD4HXakT4nxwena/KedKmFI3yNEDP/LTzmtDkZjAyWGb32BKpv2GdEUdpdrYO6mbb0RmMDpvY7mZ2jYnFUE6A+bvUkFCuQOvRDqpWEuVgqnB+MPvfMBdaG3FyeThJJZQl6nHQF3EzGs7T4XCWvn2ndWYN3VAEzrT8sZFf7Lp65/AzZWJZcIYfDppX4drTu4NjYsfKGfd3VN+yrFWYFC0aycbMBR1kdWU81/aD+QwixEbhOSvljIYQPsFs/NUVD07sPfvxXMHkW0jFwN0HrVviVv7Dsknf1tnHgyBCgZU6xVI7pZJY37+y8yitL0XM7iKWyHA0n2doRIORxksoVODEaxeO0MRJJkc0XyOYlTrvAabexb/uamr+/RuSmNTfxk4s/IVfIIYQgm88ipSTgCrC7c/ds36egO8jWFnMN+4wwkxFB7QQLKuA0HtWo+H4frXFgK5qabx3wvwHl9VEPGmQDJ1MXteCUz4HDoz1OntWOWzSfWknB9UqFuYIkm8+XlPLS2Tw+l41oKk+uUAAJ2bxESrhlQ0vN3lcjMxgb5I61d5SV8s5On2Xfhn1sCC6+YZ8RZjMi1Zl29VJNie9DwK3ACwBSyjNCCPU3Xw+Kyjlvi7b+k45qz3c/uPxB6uePQlM3+ObdqBNT2vGtS1/MN5J2G0nBzaBXKtQyIzupbB6300Y6WyBfkEgEd29tZySaJprKEpgp/fVPJbl7qW9yBWDUOfbs9FnLgoLZjEj55a1eqglQaSllRmvfBEIIB9o+KIWF6N6gLzTOBk4ilyG0YEHcG4LI0JKH1lsjOnBkiAf29NRk/9FdvW187unzTMYzZHIFXA4bNiHYs7GZZE4STmYJep1saA1wajSKz22H6Nz/9D63/Zrx6DPKTna17yKS1uyOah0UzGZESrCweqkmQP2HEOLPAK8Q4j7gg8C/WzutaxujG/QHchdp6Vrwj65OGzgJroVkuDSDSoYhsNb4NQYsDMYT0ZTlzuJCAAIkEgR0hTzYbDZ2dPlL1rc2tvroOz9JyOeaXZvqOz/JbVtal/w+V0K/KUNX8HldbBcGhaV61C0mI1LrR6uTagLUx4D3Ay8BHwC+C3zRykld6xi1LDg11sTeZVbOGXLzg3DoE9qfvSEtOKWm4PYPmRpGLxg/feYKr9/WDsyV4BYrJ9fj2XMTbGz1s2td8+yxSDJLMpvDP3Od4vrWt45fQjKj2RPa4+xzE1idFVrF1bKThUHBrMBhMddUXDtUo+IrAF+Y+VEsA0b7fV523cze5LPaAXdAC07JKW2PzHJTXGf6+aNaWS+wVgtOJtef9IJxe5ObV4ajvCEw17i5ls7iRp9vLJ3jPXtLb4K5AtzR28q5K4nZ0t8dva1k8+YyopXcb8pMdmK2f1QtrqlYvVSj4nsb8D+AjTPnC0BKKYMWz+2axWi/j79rG1y3pSE2cAJaMFqiIEIvWOzoDvD06StEktkyOXktymRm9lN1zlgq7d0858YdSWaRMmcqI6rlJuNG5vTkaYbiQ3gd3pL+UYlsot5TU6xAqinxfQb4TeAlKaUSRywDFff7tDU1xAbOWqEXLDxOB3dvay8rtwE1KZPpiSRa/S4+cM8W3XP1/i7cDmEqIzIKinYbfLVvYEWtS1XCbP8ohaIS1XjxDQIvq+C0fBT3+xRv0H6Po+HXKhaLUf+gPTr7jGrpxbdQJCEMFpWM/i7yBUx1jtV7n/0TccaiaV3zWz1fwJWA2f5RCkUlqsmg/hvwXSHEf1Dqxfdpy2alqMl+n5WA3ubbnd0BXV+8WCrL9d2lleWrlcn0SoLPnpsg4HYQz+TJ5Ap4nHYCbodh9qP3d2HWdknvfXYF3XicjrIs7FvHL5HKyRUnqACtf5TX6WUsMUYkEyHgCrA+sJ6epqV79CmuPaoJUH8NxAAP4LrKuYo68cypMQ4cHWI4nKQ75OWBW3q4e3t99lMbrRNVu3505OKUbvlsaCrBxYk4I9E0kRnBQlfAzfo2v+E89EqCw1MJJhNZ/G4HIa+TdLbAieEoyUxedxw9FmO7tDDQffIHp3SzsJ+dn+D2LW01EVQst7S9KBHf3rq9RCKuXL4Vi6GaANUqpXyT5TNRLJpnTo3xqR+fodnrZF2zl0gyx6d+fAZg2YOUUVC4c0urblakd/yZ01e4Z1t7SXbS5HEgpORwfzF4OYgkslycSHD31nbduRgq587EaW9y45mxNfI4NQeJqWS26vdZC9sloywMpG7gGgmnTAWcekjblURcUUuqCVA/FkK8SUr5Q8tno1gUB45qN6HmGdft4uOBo0OGAaom36x1fAGfPefQDQoHjg5x49pQVcfbg26OXJiiNZAocRaXQnDrxpZZ26Gg18m2jiZD2yEj5ZyUklg6y2g0RS5fwGG34XfZWdfs1RnFmKWWYY2ysJvWN+sGLofNnEikVtJ2s/+vWCkRX+omYMXKohqRxIeA7wshkkKIiBAiKoRQkpwGYjicJOgt/a4R9BqvzdSkM61BR930yGndb//D4aTh8VQ2R9/5CX746gh95yfwOwWnx2NaGc/jIJLMcnhgChuSDe1+9m5p474dXezd0saGdr+hMKGYocwnlsrREXSTyRUQcqbbkRRkcgXWBJa3gm0kwPiNm9bpCkckmBKJjIZTpoQcetSji7ERxU3A8VycTn8n8Vycg2cPGjYnVKx8qtmoG7jaOYr60h3SynrN8/oWRZLaDcVIJLDkb9bnDjFZ8HN6OE8kOa5lM0E/N2Z+zvHUlrJv/90hr25WEHA7yqyETo1G6Gn2EPQ5tSDlc7Kts4nL4ZShMEHvfRplKOtbfCQzBUI+Fx6HjVSuQDiRqZnBpJmMwygL0ysffuPYJcPSnx616J/VSBuMzbqcK1Y+hgFKCLG70gullMdqPx1FETM3uQdu6Zldcwp6HUSS2o34/hs7dUtCi1HDLWRq9CJPDTuJZ/Pk8gVGozYuT9m5pTnBUzNrOfODwgO39PDc+cmy4xtbfZwcjZVYCWWyBUJtzpLNsQUpSWbyTOuMvbM7YFj6MrrR793SyvkrWgkx4HGyd0sruULVb9+QWq371EI5WIv+WY20wbhWfZ8UK4dKGdSnKvxOAvfWeC6KGcze5IrrTAeODnF5WruhvP/OTfRPJQ3VcEv9Zn1syk0iegXhacbrcpDLSxLRSc562nlgn754oKfVpxssFloJbe9qIp0rzWdiqRzbuoOzGeD8MSp9y3/P3o26N/rBifjMPihAQCKTx+uyL3nTrJUZh9mAY6WQo1a2U2ZQfZ+uPQwDlJRy6U19VjlWSXgXc5O7e3tHmSDihR+c0v32G/I4dTMRM9+sv5+4gXttPyCDk5T0EyCOy5bg+4kb+P8MylZGWcFCK6H+KzFeHY7qWh3pjfGNY5dw2ODV4cisqGJLu49YunT9qcimFi/fmBGWFNWAp0cibF3ThNfpWFLmUynjWOr/L4sJOFYJOcx2Ma4Fqu/TtUc1XnwP6h2XUj5azQWEEHbgCHBJSvk2IcRm4HG0Dr3HgPdIKTPVT7kxsFLCW6uyitG33+vX6mciZuY95lrHs85f5bWZ4zTnxgk72jkcvIMx0W3qRqx3A7TZbHzg7s30TyWrmp/dhqmWGP1TyTI1YC5XIFOQS858KlkaWVX6s5JadTGuBUrCfu1Rjcz8dfP+7EFr9X4MqCpAAX8InACKix7/D/B3UsrHhRD/G62Vxz9VOVbDYGUpp1ZllUrffpd6o7tpfTMvnC9wpentJUKDbZ0+UzfiSjfAajvWlrTAqKIlxmg4xYZ2P5vmzeeHr4yQzpZu1F3MlwKjz9xj0ruvkWgkVxPlcn5tUY2K78PznwshQsBXqxlcCNED3I/mRvHHQmvLey/wn2dO+QrwcVZggLJy8bhWZZVKN/+llpt+46Z1jEbSTMYzhJNZXA4bm9r9tPpduvY9lW7ES70BVmqJoYfeFwCXw1YW0RbzpcDoMzerwFMoFNVlUAtJANdVee5n0Lz8iquabcC0lLK4ODAErFvEHOqOlYvHtSyr6N38L4zHSty8T49GeeVSmA/cs6Xqa2xe08QH7tlSFuQWcyNearDsDHl4eWiKC+NxwskMIa8Lr0NwY0+54SzofwFo9bsQAt11L7PUQoGnUCiqW4P6d5jdImIDdgBfq+J1bwPGpJRHhRBvKB7WOVV3+4kQ4mHgYYANGzZc7XLLjtWLx1aWVb55/BL9V+Lamo1XW7PpvxLnm8cv8Uf3bS8738jnrxY34gvjMT7/zHkm4hnS2Tynx+y8ejnMW3d20T+VrCpoeWxw6NQVmlx2Ql4n8VSWQ6eu6Dqig/4XgA/cs4WhyQQHjg4xMpMdP3BL7SyBGklsoFCsFMTVumgIIV4/72kOGJBSDl11YCH+BnjPzGs8aGtQB4E3A11SypwQ4nbg41LKN1caa8+ePfLIkSNXu+SyY/ab/3Ibdxrx3i+/gNtpx+ec+36SyOZIZ/N85X23lZz7zKkx/uf3TpIrFJBSa0vhsNn4s1+9XtdGaWHAcTvttPldPHy3fnb2mR+d4mfnJ2nxuXA7baSzBS5PJ3A5bPzKDV2le6kM1rH+4N+OMRZOkcoXSGXyeFx2PHYbHSEP//CfK27nK5l3ce2smmsuhkb5+1coGg0hxFEp5Z6Fxytt1N0KdEop/2PB8buFEG4p5blKF5RS/inwpzOveQPwX6SU7xZCfB34T2hKvvcC3zL7ZhoFM1lOPYw7jRGIBd9LRHFD0AK+/PwFYuksQY8Lh12Qy0siqQxffv6Coc+flKC1WdI2GlX6DvTzwTBOG1wOJ0ll83icdmLpHDJF1etYw+Ek65q92MScc1dBFrg8Xf36znI4JjSS2EChWAlUKvF9BvgznePJmd+9fZHX/BPgcSHEJ4CfA19a5DgrikayjLl5fYifnZ9ECDGbtUwns9yuI8s+Nx6nye3Aaddu/k67oMnt4Nx4XHfsZ89NsKnNz2t6mmePRZJZw/eZzOQYmkxQQFCQEpvIEUtlaGtyl5xXaR2rktWTEQuzmVPDEdYEXPRdiMy28uht9xEL6++lUigU1lMpQG2SUv5y4UEp5REhxCYzF5FSPgU8NfPn88CtZl6/GqiV6q8WZaJfv2kdo9E0E/EM04kMbqedLWv8/PpN68rGB0kikyOSypPNF3DabThsEpfDXpv3KSXRdA6vy4HTJsgWJNmCJJXRDGTnu5mvb9fv+2Rk9fT+Ozfpnq+XzZ4YjvDSJUl3yDvbI+r5c5O6QVuhUCwPlQJUJXmRub4EipqouGqhvgOt1PTw3eUKPCjfTOq22xmcSuB3O3E7BKlsnlQ2z6/c0Kw7ttn3KRF4Z/oxxQoSh03gcQiimfxMJqO5mV+cTHD3dfp9n4ysnoxKkHrZrMdp41I4RVfIq5UlmdtPpVAo6kOlAPWiEOL3pZRfmH9QCPF+4Ki101p9mFVx6WVKZtV3ldBbD/lq30DZjbsz6CaczGKzCVLZAi6HjTa/l83t1TtDVFSrCTm38iW1sJAvgNdlZyKe4fyVGCGvix3dxn2fQN/qyQi9LM9pt7PG78LtsNXcQFahUCyOSgHqo8BBIcS7mQtIe9Davu+3emKrDTN7m4wEFUf7J2hpcuOd6QTrddqRPifHB6drMke9G7fdbmNzu5/OZm/J2ozRJlize7hsCBK5PF6nA6fHSTZfYDKew2YTrGv2smWNf0bZl8Zlr00bss6Qh4tXZlrHz5QQc7kCLU1u9m6Z8wSMJLP4PYvZKqhQKGpBJbPYUeAOIcQ+4MaZw09KKX+6LDNbhVSr4jISVEwlc7T6S8UDRuq7xaBXnnM77bgd9hIz10gyS2tTbW7cBQk+p51ENkc0JXHYBXYhyBcKJco+j8NmqiV7JcrMYpNZriTSbPU7a7JRV8nJFYracNWOulLKQ1LKz878qOC0DBh1Qm31aS7kqWweiSSV1foj3bw+VJPr3tXbVtbJtc3votXvKuvuWlyzWoj5DqwSu13gdzkJuJ34XU4EkkxWanuaHDZSmTyXp1PYa7Qi1D+V5NZNLVpDxFSOoM/JPdetobejqay7rdnA0kgdaBWKlY6qXzQgRkKDO3rbDNV3tUCvPPfw3VsAqi7ZVZLTFx/nZxZ+jwN7RNDsd+G0C7J5yXQyg9cp8Ljssxtvm71O8jXKFEfDKTa0+dk0bx2tICUj4RTv2bs0I9JG2k6gUKx0VIBqQIyEBg/s6Zm145mIpQl4nLx1Z5flNz6j0qReKctIZn5qOMKlmQaK89fVQm4nbruNwakE2VwBp8OGU0j8bifdIe+sU3oikyPkcZbNYTHUyhfPzPtXprAKhXmuWuJTLD/FTGZhuQngufOT3Lg2xP6be7hxbYjnzk/WrHxkpjxldK7dpt3s5xNL5ZhKZmczC5sQBL1Omr1OhiMpwqkcXqeNgMeB12lDChstXuesos7tsHFDZ4Dr1wbL5rEY9EqZlcqWeph9/8oUVqEwz6rPoFbqgnW1MnCoXfnITHnK6NxUNqfbrTfkceq7nEeSeJx2gh4nDpsgV5BMxNNEUjl2dAdLxqgUQMz8PdfCLd7s+1emsAqFeVZ1gFqM/12jBLR6lI8qlee+2jdQ1Vxi6Zzuzf/ZcxO6ZTUQrA25GZxOza43bWz1ksgUZjPIqwWQxWxgXqovntn3vxK+FCkUjcaqDlBmF6wbxdDV6IbbFXRzcWJm/87MnqSugJv1bfoWQMWxqg24evuDPA7B5XCadS2+ks/E4xCG6zhGN3+9dbXuoIfL4STNXhfOJk0kcTmcorejqWrBQqUNzL9x0zpLvnDofVZFOyZlCqtQ1IZVHaDMZhz1UmAtDCJnRiK6N9xkJsvAZGpu/04iy8WJBHdv1bcAMhtw9fYHHRuLcceW1rLPJGmylGVUVkumNRujXL6Aw2Yjly+Qy0s2tviq/vyOD04T9DnLNjD/7NwE6Zy05AuH3mdVtGNqlCxcNGu6XgAAHfdJREFUoVjprOoAZVatVQ8Fll4QOXRqnA1t3rIb7ivDUe7d1sFINE00pWVQ2zqMLYDMBtzi/qDZDM3npL3JTXKB389iS1l6mUXA6+LNOzs5OjjNdCJLyOfkjt5Omjwug1H00G8fMpnIWvaFQ++z2tbZxJGLUzx3frLuWbhCsRpY1QHKrC+c1W259b5Z6wURh00wGcuypmnOk1dIyOQKbGj3s2lN+f4dPSoFXKM1roX7g6SUTMQyJWNcrZRnhs6Qhya3g3d1zW02jiSzpLK5snWvzWuadOdt1D6kxWsgzKjBFw6jvVQ/enWE7Z0BXh2JlJRh1T4ohcI8qzpAmVVrWdmW26jcFktlub67VD69ud3HyZEYqWy+5Ibbu8ZvKoAaBVyHrdy1/MCRIdw660rdQQ9T8WxNLID00PvMBybjSAkep6NkfnduadXNTu7c0qq7gbkj4LbsC4fRZ5vM5DgxHMXvdsy27TgxHCWZMTAvVDQ02WyWoaEhUim1j60WeDweenp6cDqr29O4qgMUmFNr1UJ+bIRRuW1oKlF2o9vaESCSylFAltxw37qzi+fOTwLVBVCjgOt2CEOJ9EuXpjk3HieRyeFzOehd4+cDd2+mfyppiSpN7zPvCLjxOh1l8ztwdIgb14bKjvdPJSu2D6n28zKD0WfrcztACjwz5VnPTCuRWvkIKpaXoaEhAoEAmzZtQojaOJlcq0gpmZiYYGhoiM2bN1f1mlUfoMxilQLLqNwW8jjLxAY2m40/vPc6+qeSZSWunlZf1QHUKOB+49gl3dLXicvTnB+Pky8UcNtt5AsFzs90zl2qBRAYKwoXfuaf/MEp3fkNh5MlbuPF4yPhlOHfm1VfOIw+2y8+k+XiVIJkNj/rgpGXsmYuGIrlJZVKqeBUI4QQtLW1MT4+XvVrVIBaJoxKQtevDc6uRS28ieoJH8wGUL3zjeZy7kqCzqCnpHX6dCLDgaNDur2WzKjVzCgKjebXHfIaluyeOTXGgaNDDIeTdIe8PHBLD3dv77BU8q039vVrg/hd9ln5ecDjZGNLwLAbsKLxUcGpdpj9LFWAWiYqrW8t976Zu3rbSvZZuRw2Wv0ukGATkvNXYrNtLtr9Tl1RgVkJuxlFoaEX4S09uiXONp+DT/34DM1eJ+uavUSSudkW8NU2MawVd/W2cWAqacoFQ6FQ6KO8+JYJI3+9xbRz+GrfAJ/8wSm+2jcw65NndNwIIQABEglCe+5z2zgzFiOfl3iddvJ5yZmxGAGPvez18wPOfG+9omv5QoxaiIzqBD+jz+ru7R26x//jrDaXZp8Lm7DR7HPR7HVy4OhQlZ9q7ajV37NiZWL236EZDh48iBCCkydP6v7+oYce4oknnqg4xvxzfu/3fo9XX321ZvOzApVBLSNLzZSMshYjdVulbCbgdhDP5MnkCnicdgJuByDI5yWZfAG7zUYmXyCfl6zX2TRrds9YJQl/pbWphegdHw4nWdfsLTkW9Dq4PG2svLJyM61ykrg2sdqJ5rHHHuOuu+7i8ccf5+Mf//iSx/viF7+45DGsRmVQKwijrOXArKNBddnMqeEIJ4ajZLIFQl4nmRkpdCKd574dnXicNsLJLB6njft2dBL0lm+a7Qx5eO70GP9w6Ax/+70T/MOhMzx3esxQwm3kIL6pxbvkBn/dIa2sN59IMlcWQIuopoIKKzBbVTBDLBbjueee40tf+hKPP/44oKni/uAP/oAdO3Zw//33MzY2Nnv+0aNHef3rX88tt9zCm9/8ZoaHh8vGfMMb3sCRI0cA+OEPf8jtt9/O7t27eec730ks1hj/FlSAWkEYlclGTJTPAKaTWew2TQot0B7tNgECupt9vOvWjXzg9Vt5160b6W726QadaDzFU2cmSKbzNLntJNN5njozQTSuf02j0lf/TI+opfyjfuCWHqaTWaYTGQqywHQiM7tmpYeVNxLFtYuZMrZZvvnNb/KWt7yFbdu20drayrFjxzh48CCnTp3ipZde4gtf+ALPP/88oO3d+vCHP8wTTzzB0aNHed/73sef//mfG4595coVPvGJT/DjH/+YY8eOsWfPHj796U8vec61QJX4VhBGZbKuCuUzPUIeJ+FktkwK3dvu0/XX29kdKHN1+O4rYwQ9dlK5AtPJHE67IOix891XxvjgG7frXlev9PWNY5dw2qHvwpzzQm+7j1g4pzuGHkUhxIGjQ1ye1kqP779zk6FAYjScwmGDV4cjs0avW9p9xNLVX1OhWIiVTjSPPfYYH/3oRwH47d/+bR577DGy2Szvete7sNvtrF27lnvvvReAU6dO8fLLL3PfffcBkM/n6e7uNhy7r6+PV199lTvvvBOATCbD7bffvuQ51wIVoFYQZtVtRhtSK0mhF0red3YHdNe3Lk0lsNtt+JwObC4oSMgWCoxEkobz11v3cdjgJyfGyRU0k9ixSIr+8Tj3Xr/G1Gdz9/aOqhV7dhv0nZ/UzHg9mhlv3/lJbtvSauqaCsV8rHKimZiY4Kc//Skvv/wyQgjy+TxCCPbv368r25ZSsnPnTn72s59VNb6Ukvvuu4/HHntsSfO0AlXiW0GYVbdVsnSy2W3s6A7yxhs62dEdxGa36Uqhj1yc0i2H5SXk8xK7TSCEwG7TBBZOW7niD+ZaiDxzepyXL4V55vQ4n3v6PP1XYlyJpsjmJR6njWxeciWaYjKe0R2nFghAzjwiFjxvEKxUgymswSoF5xNPPMGDDz7IwMAA/f39DA4OsnnzZlpbW3n88cfJ5/MMDw9z6NAhALZv3874+PhsgMpms7zyyiuG4+/du5fnnnuOs2fPApBIJDh9+vSS5lwrVAa1wjCjbqs0hp4LApR79D1z+gr3bGsvKVs0eRy0eJ1MxDMlfoHZfIHdG5p1r2nUs+lyOMnmDj/RVJ5UJo/XZacj6OKETpPEWinjcgW4o7eVc1cShGfKinf0tpJtELu8RulLpjCPFQrOxx57jI997GMlx97xjndw4sQJrrvuOnbt2sW2bdt4/etfD4DL5eKJJ57gIx/5COFwmFwux0c/+lF27typO/6aNWt45JFHeNe73kU6nQbgE5/4BNu2bavp+1gMKkBdo1TbUr496ObV4SgdwTkZdyyVY9f6ZgqFAscHw8TSOfwuB7dubuH2rfqlOaOeTadGIwhZKhFPpnOMx7KzKrta36A7Qx4GJ+Ilx+LpfMXGj8tJvfqSKRqTp556quzYRz7ykYqvuemmm3j66afLjj/yyCO649577728+OKLi52iZagSn2IWPRXSzu4AV2LpMnn4A7f0EPK5uLEnxE3rm7mxJ0TI56rgmKDfs8njtHNuPK61e3faSGXynB1P0NHktkxlt6nFy+H+KSKJLEGP1vjxcP8Um1q8V3/xMmClGkyhWEmoAKWYpahCmo/b4WDX2iAvXw5z8OdDvHw5zJ1bWulp9SElaEYUAiTacwNuXh9iOpkllc0jkaSyeaaTWTa0+OgIenDYBclsAYddk72HfNbdoPunkty6sYWg10l0RnV168YW+qeMBR7Lid7fQy37kikUKwXLSnxCCA/wNOCeuc4TUsq/FEI8ArweCM+c+pCU8rhV81BUj54KqX8ijhBw49oQe7e0EUvleO78JO6LU2xq8/Oanrk1p0gya1iG+vWb1un2bLIh6Ai6OHclMdfgL5QhmS3t4nu1G7QZZ4jRcMpU48flxsq+ZArFSsLKNag0cK+UMiaEcALPCiG+N/O7/yqlrGwapVh29MQTXUE3Hp3eTD87f4X7dnSVvL6S1dHmNU26PZuePTdRth7U7nczHEnrNknUC0Sg34DRaM3K6s7JS8XKvmQKxUrCsgAlpZRAURvrnPmpUARSNALV9maC8u67V7vJ6wkzhiYT/P/tnX10VNW1wH+bSAgmgaIEXoAaEH0qoKQBQ1wIJtRGpS4+FLQ8Xq3LdrF41VroKl9Pl+XRqmh96vNjgaKvfjyLFBVKra2yNGDhGQnByKeKfBUeGBALhAAhJPv9cU+SIcwNGSYzmZns31qz5sy+5557ds7k7jlnn7v3m/Whmjx/0N+PVzPx6l6cqOWsuwzrMgGHsqkgHmYoFs/PMCLsgxKRJBEpA/YDy1X1Y3foQRFZLyJPiEiHSPbBCA8/f0idT6nx5olQ00r4+YNO1HpJEn95w2X8MC+LPhlpviGKynYfCmlTgUUcN4z4IKLbzFW1BsgWkW8BS0RkADAL+ApIBp4HZgBzGp8rIpOASQAXXXRRJLtpNIFv9IrBvdjzzbEzkgQ2dZMPtjwXij/IL4J6S83mQiWSEdGNOOXgNthWBBX7ID0T+hbAhX3Dbvarr75iypQplJSU0KFDB3r37s2YMWNYtmwZb7/99hn1f/KTn/CLX/yCfv36hXSdsrIy9u7dy8iRI8Puc0sQlV18qnoIWAHcqKr71KMK+B2Q63PO86o6WFUHZ2SEFvbGODvNjVTgN9sAWL39Gwb06MzY7/RiQI/OrN7+jW87fhHEk9rR7B1rkZ7NhYJFRDfO4OA2WPcKnDwKnXp47+te8eRhoKqMHTuW/Px8tm3bxubNm3nooYcoLy/3PeeFF14I2TiBZ6DeeeedoMdOnYp+rMqIGSgRyXAzJ0SkI3A98JmIZDqZAGOAjZHqgxGcUG+ufTLSmr3c5veskl99gWYbF7+UHaOze0Z9yc4iohtnsK0IOnaBlM4g7bz3jl08eRgUFRXRvn17Jk+eXC/Lzs5m2LBhHD16lHHjxnH55ZczceJE1D3rEZhKIy0tjfvuu4+BAweSl5dXb9gWL17MgAEDGDhwIMOHD+fkyZM88MADLFq0iOzsbBYtWsTs2bOZNGkShYWF3HHHHezcuZNhw4aRk5NDTk5OfQT1FStWMHz4cMaOHUu/fv2YPHkytbW1hEskl/gygZdFJAnPEP5BVd8WkQ9EJAMv9FkZMLmpRoyWpyUiFYSasNCv/tGqU83esXa23W3RXF4LVX+jDVCxz5s5BdIh3ZOHwcaNGxk0aFDQY5988gmbNm2iR48eDB06lNWrV3PttdeeVqeyspK8vDwefPBBpk+fzoIFC7j//vuZM2cO7777Lj179uTQoUMkJyczZ84c1q5dyzPPPAPA7NmzKS0tZdWqVXTs2JFjx46xfPlyUlJS2Lp1KxMmTKg3hGvWrGHz5s1kZWVx44038tZbbzFu3LiwdI/kLr71wHeCyEdE6ppG82jq5tpcv0qoW7Wbqh9qHMFgdaPtD4r1repGK5CeCVUV3sypjqoKSPsn/3PCJDc3l169vCX37Oxsdu7ceYaBSk5O5uabbwZg0KBBLF++HIChQ4dy5513ctttt3HLLbf4XmPUqFF07OhFWamuruaee+6hrKyMpKSk04LK5ubmcvHFFwMwYcIEVq1aFbaBskgSbRA/X05SO5q99Oe33Obn9wm1fii0hj8okvoYcUrfAjj+DzhxGLTWez/+D08eBv3796e0tDTosQ4dGjZBJyUlBfUTtW/fvj4tR2Cd+fPn85vf/Ibdu3eTnZ3NwYPBl6dTUxtiVD7xxBN0796dTz/9lLVr13LyZEPWgcapP4KlAgkVM1BtEL+bq0Cz/SqhbtWO5Nbu1vAH2VZ14wwu7As5d0Bymresl5zmfQ5zF9+IESOoqqpiwYIF9bKSkhJWrlwZVrvbtm1jyJAhzJkzh65du7J7927S09OpqKjwPefw4cNkZmbSrl07Xn31VWpqGlIArFmzhh07dlBbW8uiRYvOmMmdCxbNvA3i58t5c93/+aaU92snlBtypB4+bS1/kD1Ma5zBhX1bZFt5ICLCkiVLmDJlCnPnziUlJaV+m3k4TJs2ja1bt6KqfPe732XgwIFcdNFFzJ07l+zsbGbNmnXGOT/96U+59dZbWbx4MQUFBafNrq655hpmzpzJhg0b6jdMhItoUxE+Y4TBgwdrnSPOiByvFu+ispFf5cjxalJTzuOHeVkRu264/qPW6reR+GzZsoUrrriitbsR86xYsYLHHnss6DNZjQn2NxWRUlUd3LiuLfEZ9bSGX6Ul/EfmDzKMxMQMlFFPa/hVWsJ/ZP4gw2hd8vPzmzV7ChXzQUWReAiNE22/Skv5j8wfZBiJh82gooSFxgmOJeczDMMPM1BRwkLjBMf8R4Zh+GEGKkqUHz4RUkqItoL5jwzD8MN8UFHCQuP4Y/4jI1HYdXgXxfuK2X9sP93O70ZeZh5ZncN/1KG8vJypU6dSXFxMly5dSE5OZvr06ef0rNGTTz7JpEmTOP/888PuV6SxGVSUsKUsw0hsdh3exZIvl1B5qpLuqd2pPFXJki+XsOvwrrDaVVXGjBnD8OHD2b59O6Wlpbz++uvs2bPnnNp78sknOXbsWFh9ihZmoKKELWUZRmJTvK+YTh06kZ6cjoiQnpxOpw6dKN5XHFa7H3zwAcnJyael28jKyuJnP/sZNTU1TJs2jauvvpqrrrqK5557DvAenM3Pzz8jFcdTTz3F3r17KSgooKDAixG4cOFCrrzySgYMGMCMGTPqr+Enjya2xBdFbCnLMBKX/cf20z21+2mytPZplFf6JxZsDps2bSInJyfosRdffJHOnTtTUlJCVVUVQ4cOpbCwEAieiuPee+/l8ccfp6ioiK5du7J3715mzJhBaWkpXbp0obCwkKVLl5KbmxtUHm54pVAxA2W0OPHwvJdhtDTdzu/G0eqjpCen18uOVh+l2/ndWvQ6d999N6tWrSI5OZmsrCzWr1/PG2+8AXjBXLdu3UpycnKzUnGUlJSQn59PXdbyiRMn8uGHHyIiQeXRNlC2xGe0KPa8l9FWycvM40jVESpOVqCqVJys4EjVEfIy88Jqt3///qxbt67+87PPPsv777/PgQMHUFWefvppysrKKCsrY8eOHfUzqOak4vCLxRorMVrNQBktij3vZbRVsjpnMfaSsaSel0p5ZTmp56Uy9pKxYe/iGzFiBCdOnGDevHn1srpNDjfccAPz5s2juroagC+++ILKysom2wtMqTFkyBBWrlzJ119/TU1NDQsXLuS6667zlUcbW+IzWhRLhW60ZbI6Z7XItvJARISlS5cydepUHn30UTIyMkhNTeWRRx5h/Pjx7Ny5k5ycHFSVjIwMli5d2mR7kyZN4qabbiIzM5OioiIefvhhCgoKUFVGjhzJ6NGjAXzl0cTSbRgtiqW+MBIJS7fR8li6DaPVsOe9DMNoKcxAGS2KPe9lGEZLYT4oo8Wx572MREJVEZHW7kZCEKpLyWZQhmEYPqSkpHDw4MGY2XYdz6gqBw8eJCWl+fFHbQZlGIbhQ69evdizZw8HDhxo7a4kBCkpKfUPDzcHM1CGYRg+tG/fnj59+rR2N9ostsRnGIZhxCRmoAzDMIyYxAyUYRiGEZPERSQJETkANM761RX4uhW6E23aip7QdnQ1PRML0zN8slQ1o7EwLgxUMERkbbDQGIlGW9ET2o6upmdiYXpGDlviMwzDMGISM1CGYRhGTBLPBur51u5AlGgrekLb0dX0TCxMzwgRtz4owzAMI7GJ5xmUYRiGkcCYgTIMwzBikpg1UCLy3yKyX0Q2BsgWiUiZe+0UkbKAY7NE5EsR+VxEbmidXoeOj57ZIlLs9FwrIrlOLiLylNNzvYjktF7PQ8NHz4Ei8pGIbBCRP4lIp4Bj8Tqe3xaRIhHZIiKbROTnTn6BiCwXka3uvYuTx+WYNqHnePe5VkQGNzon7sa0CT1/KyKfuTFbIiLfCjgnkfT8tdOxTETeE5EeTh6d762qxuQLGA7kABt9jv8n8IAr9wM+BToAfYBtQFJr63CuegLvATe58khgRUD5L4AAecDHrd3/MPUsAa5z5buAXyfAeGYCOa6cDnzh9HkUmOnkM4FH4nlMm9DzCuAyYAUwOKB+XI5pE3oWAuc5+SMB45loenYKqHMvMN+Vo/K9jdkZlKp+CHwT7Jh42cNuAxY60WjgdVWtUtUdwJdAblQ6GiY+eipQN5voDOx15dHAK+pRDHxLRDKj09Pw8NHzMuBDV14O3OrK8Tye+1R1nStXAFuAnng6veyqvQyMceW4HFM/PVV1i6p+HuSUuBzTJvR8T1VPuWrFQF0OiUTT80hAtVS8exNE6XsbswbqLAwDylV1q/vcE9gdcHyPk8UrU4Dfishu4DFglpMnmp4bgVGuPB74tisnhJ4i0hv4DvAx0F1V94F3MwC6uWpxr2sjPf1IZD3vwptNQALqKSIPunvRROABVy0qesargZpAw+wJvGlmY+J5//y/AVNV9dvAVOBFJ080Pe8C7haRUrxlhZNOHvd6ikga8CYwpdGv0DOqBpHFja5tXU8RuQ84BbxWJwpyelzrqar3uXvRa8A9dVWDnN7iesadgRKR84BbgEUB4j00/PoGb7q9l/jlR8BbrryYhiWChNJTVT9T1UJVHYT3g2ObOxTXeopIe7x/8tdUtW4cy+uWQNz7fiePW1199PQj4fQUkR8BNwMT1TlmSEA9A/g9DcvwUdEz7gwUcD3wmaruCZAtA34gIh1EpA9wKbCmVXrXMuwFrnPlEUDdUuYy4A63gyYPOFy3bBSPiEg3994OuB+Y7w7F7Xg6/+iLwBZVfTzg0DK8Hx649z8GyONuTJvQ04+4HFM/PUXkRmAGMEpVjwWckmh6XhpQbRTwmStH53vb2rtH/F54v6j3AdV41vrHTv4SMDlI/fvwfoF/jtsBFw+vYHoC1wKleLuBPgYGuboCPOv03EDALqlYf/no+XO83UJfAHNxkU3ifDyvxVvqWA+UuddI4ELgfbwfG+8DF8TzmDah51g3vlVAOfBuPI9pE3p+ieeDqZPNT1A938TzFa8H/oS3cSJq31sLdWQYhmHEJPG4xGcYhmG0AcxAGYZhGDGJGSjDMAwjJjEDZRiGYcQkZqAMwzCMmMQMlJEwiEiNNES7LxOR3iKSLyJvu+OjRGRmlPv0koiMi2D72SIyMuDzbBH5ZTPOExH5QAIiyLdgn15v9PyMYZwTZqCMROK4qmYHvHYGHlTVZao6N5IdEJGkSLYfhGy851VCZSTwqTYdnuhcmQdMj0C7RhvDDJTRZhCRO0XkGVd+SUTmi8jfROQLEbk5oM4fReSvLp/PrwLO/1cRWeNmZ8/VGSMROSoic0TkY+CaZvZlmoiUuFw6/+FkvV0+ngUuJ897ItLRHbva1f1IvFxEG0UkGZgD3O76dLtrvp+IrBCR7SJyr08XJuKiWbjrfiYiL7h2XxOR60VktXj5q+rykc0WkZddv3aKyC0i8qh4+bz+6kLlAPwNuN6FJTOMc8YMlJFIdAxY3lvSjPq98UJKfR+YLyIpTp6LdwPPBsaLyGARuQK4HRiqqtlAjasDXhqCjao6RFVXne2iIlKIFwIn111jkIgMd4cvBZ5V1f7AIRpin/0OL4LKNe7aqOpJvOjSi9yMsS4+5eXADa79XwUYjkCG4kUrqeMS4L+Aq9z5/4IXXeCXwL8H1Ovr/l6jgf8BilT1SuC4k6OqtXiRFgae7W9hGE1hv3CMROK4Mx7N5Q/uZrpVRLbj3ZgBlqvqQQAReQvvRn0KGASUeGHL6EhDwNcavJAwzaXQvT5xn9PwDNPfgR2qWpcpuhToLV621nRV/V8n/z1ekFI//qyqVUCViOwHuuOFHwrkAvXy/tSxQ1U3AIjIJuB9VVUR2YBnyOv4i6pWO3kS8Fcnb1xvP9CD042gYYSEGSijLdM4zpc2IRfgZVWdxZmcUNWaEK4rwMOq+txpQi8PT1WAqAbPEAZLbdAUjdsI9n9+SkTaOQPd+JzagM+1jc6vAm+WJCLV2hArrXG9FLxZlWGcM7bEZ7RlxotIOxHpC1yMF9wT4HsicoHz/4wBVuMFeB0nDRHYLxCRrHO87rvAXeLl3kFEeta1GwxV/QdQ4aJGA/wg4HAFXi6tUPkcT+dI8c/Apgi2b7QBzEAZbZnPgZV42VAnq+oJJ18FvIoX0flNVV2rqpvxUoK8JyLr8VLUNzfF9XMisse9PlLV9/CW6T5yS2VvcHYj82PgeRH5CG9GddjJi/A2RQRukmgOfwbyQ6jfbESkO95ya8ynDTFiG4tmbrRJROQl4G1VfaOR/E681AH3BDuvtRCRNFU96sozgUxV/XkY7WUCr6jq91qqjwFtTwWOqOqLZ61sGE1gPijDiA++LyKz8P5ndwF3htOYqu5z29k7ReBZqEN4M1DDCAubQRmGYRgxifmgDMMwjJjEDJRhGIYRk5iBMgzDMGISM1CGYRhGTGIGyjAMw4hJ/h/lLUiVU1QoBQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for name, group in grouped:\n", " plt.plot(group[var1], group[var2], \n", " 'o', alpha=0.4, label=name)\n", " \n", "decorate(xlabel=var1, ylabel=var2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using those two features, we can divide the penguins into clusters with not much overlap.\n", "\n", "We're going to make lots of scatter plots, so let's wrap that code in a function.\n", "\n", "And we'll generalize it to take `by` as a parameter, so we can group by any column, not just `Species2`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def scatterplot(df, var1, var2, by):\n", " \"\"\"Make a scatter plot.\n", " \n", " df: DataFrame\n", " var1: string column name, x-axis\n", " var2: string column name, y-axis\n", " by: string column name, groupby\n", " \"\"\"\n", " grouped = df.groupby(by)\n", " for name, group in grouped:\n", " plt.plot(group[var1], group[var2], \n", " 'o', alpha=0.4, label=name)\n", " \n", " decorate(xlabel=var1, ylabel=var2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a scatter plot of flipper and culmen length for the three species." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(df, var1, var2, 'Species2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Make a scatter plot using any other pair of variables." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Solution\n", "\n", "scatterplot(df, var3, var4, 'Species2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can think of these scatter plots as 2-D views of a 4-D feature space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Clear the labels\n", "\n", "Now, let's pretend we don't know anything about the different species, and we'll see whether we can rediscover these clusters.\n", "\n", "To see what the problem looks like, I'll add a column of labels to the `DataFrame` and set it to 0 for all penguins." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "df['labels'] = 0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now if we group by label, there's only one big cluster." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(df, var1, var2, 'labels')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see what happens if we run k-means clustering on this data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Clustering\n", "\n", "First I'll use the implementation of k-means in scikit-learn; then we'll write our own.\n", "\n", "In the dataset, we have 344 penguins and 19 variables." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(344, 19)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But some of the variables are NaN, which indicates missing data.\n", "\n", "So I'll use `dropna` to drop any rows that have missing data for the two features we're going to use, flipper length and culmen length." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(342, 19)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "features = [var1, var2]\n", "data = df.dropna(subset=features).copy()\n", "data.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll extract just those two columns as a NumPy array." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "M = data[features].to_numpy()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can use `KMeans` to identify the clusters.\n", "\n", "`n_clusters` indicates how many cluster we want; this parameter is the $k$ the algorithm is named for." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sklearn.cluster._kmeans.KMeans" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.cluster import KMeans\n", "\n", "kmeans = KMeans(n_clusters=3).fit(M)\n", "type(kmeans)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is an object that contains \n", "\n", "* Labels that indicates which cluster each penguin is assigned to, and\n", "\n", "* The centers of the clusters.\n", "\n", "I'll store the labels as a columns in `data`. " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 1\n", "1 1\n", "2 0\n", "4 1\n", "5 1\n", " ..\n", "339 2\n", "340 0\n", "341 0\n", "342 2\n", "343 0\n", "Name: labels, Length: 342, dtype: int32" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data['labels'] = kmeans.labels_\n", "data['labels']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That way we can use `scatterplot` to show the clusters. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(data, var1, var2, 'labels')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `KMeans` object also contains the centers of the clusters as coordinate pairs in a NumPy array." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[196.7311828 , 45.95483871],\n", " [186.99166667, 38.4275 ],\n", " [216.88372093, 47.56744186]])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kmeans.cluster_centers_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot the centers, I'll transpose the array and assign the columns to `x` and `y`:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "xs, ys = np.transpose(kmeans.cluster_centers_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll plot the centers with x's and o's." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "options = dict(color='C3', ls='none', mfc='none')\n", "plt.plot(xs, ys, marker='o', ms=15, **options)\n", "plt.plot(xs, ys, marker='x', ms=10, **options);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As usual, let wrap that up in a function." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "def plot_centers(centers, color='C3'):\n", " \"\"\"Plot cluster centers.\n", " \n", " centers: array with x and y columns\n", " color: string color specification\n", " \"\"\"\n", " xs, ys = np.transpose(centers)\n", " options = dict(color=color, ls='none', mfc='none')\n", " plt.plot(xs, ys, marker='o', ms=15, **options)\n", " plt.plot(xs, ys, marker='x', ms=10, **options)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's pull it all together." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(data, var1, var2, 'labels')\n", "plot_centers(kmeans.cluster_centers_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This figure shows the data, color-coded by assigned label, and the centers of the clusters.\n", "\n", "It looks like k-means does a reasonable job of rediscovering the species, but with some confusion between Adelie (lower left) and Chinstrap (top center).\n", "\n", "As a reminder, here are the right answers:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(data, var1, var2, 'Species2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the color coding for the clusters is not consistent because the centers we get from k-means are in a random order." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Here's the code from this section all in one place. Modify it to use any two features and see what the results look like." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "features2 = [var1, var2]\n", "\n", "data2 = df.dropna(subset=features2).copy()\n", "\n", "M2 = data2[features2].to_numpy()\n", "\n", "kmeans2 = KMeans(n_clusters=3).fit(M2)\n", "\n", "data2['labels'] = kmeans2.labels_\n", "\n", "scatterplot(data2, var1, var2, 'labels')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementing k-means\n", "\n", "Now let's see how the algorithm works. At a high level, there are three steps:\n", "\n", "1. Choose $k$ random points in the dataset as initial centers.\n", "2. Assign each point in the dataset to the closest center.\n", "3. Compute new centers by calculating the \"center of mass\" in each cluster.\n", "\n", "Then you repeat steps 2 and 3 until the centers stop moving." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To select random points from the dataset, I'll use `np.random.choice` to select three indices." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([253, 185, 167])" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "index = np.random.choice(len(M), size=3)\n", "index" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then use the indices to select rows from the dataset." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[215. , 47.2],\n", " [220. , 49.1],\n", " [210. , 42. ]])" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "centers = M[index]\n", "centers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll wrap that in a function:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "def choose_random_start(M, k):\n", " \"\"\"Choose k random elements of M.\n", " \n", " M: NumPy array with rows of coordinates\n", " k: number of centers to choose\n", " \n", " returns: NumPy array\n", " \"\"\"\n", " index = np.random.choice(len(M), size=k)\n", " centers = M[index]\n", " return centers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's how we use it." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[209. , 47.5],\n", " [187. , 38.1],\n", " [193. , 37.8]])" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "centers = choose_random_start(M, 3)\n", "centers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's what the centers look like on the scatterplot." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data['labels'] = 0\n", "scatterplot(data, var1, var2, 'labels')\n", "plot_centers(centers)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The next step is to assign each point to the closest center. So we need to compute the distance between each point and each of the centers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compute distances\n", "\n", "To demonstrate the process, I'll pick just one of the centers." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(209.0, 47.5)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "center_x, center_y = centers[0]\n", "center_x, center_y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now it will be convenient to have the `x` and `y` coordinates in separate arrays. I can do that with `np.transpose`, which turns the columns into rows; then I can assign the rows to `x` and `y`." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(342,)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x, y = np.transpose(M)\n", "x.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Along the x-axis, the distance from each point to this center is `x-center_x`.\n", "\n", "Along the y-axis, the distance is `y-center_y`.\n", "\n", "The distance from each point to the center is the hypotenuse of the triangle, which I can compute with `np.hypot`:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(342,)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "distances = np.hypot(x-center_x, y-center_y)\n", "distances.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is an array that contains the distance from each point to the chosen center.\n", "\n", "To see if we got it right, I'll plot the center and the points, with the size of the points proportional to distance." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(center_x, center_y, 'rx', markersize=10)\n", "plt.scatter(x, y, s=distances)\n", "\n", "decorate(xlabel=var1, ylabel=var2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At least visually, it seems like the size of the points is proportional to their distance from the center.\n", "\n", "So let's put those steps into a function:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "def compute_distances(M, center):\n", " \"\"\"Compute distances to the given center.\n", " \n", " M: NumPy array of coordinates\n", " center: x, y coordinates of the center\n", " \n", " returns: NumPy array of float distances\n", " \"\"\"\n", " x, y = np.transpose(M)\n", " center_x, center_y = center\n", " distances = np.hypot(x-center_x, y-center_y)\n", " return distances" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the function to make a list of distance arrays, one for each center." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "distance_arrays = [compute_distances(M, center)\n", " for center in centers]\n", "len(distance_arrays)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Labeling the points\n", "\n", "The next step is to label each point with the index of the center it is closest to.\n", "\n", "`distance_arrays` is a list of arrays, but we can convert it to a 2-D array like this:" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(3, 342)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = np.array(distance_arrays)\n", "A.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`A` has one row for each center and one column for each point.\n", "\n", "Now we can use `np.argmin` to find the shortest distance in each column and return its index. " ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 1\n", "1 1\n", "2 2\n", "4 2\n", "5 1\n", " ..\n", "339 0\n", "340 0\n", "341 2\n", "342 0\n", "343 0\n", "Name: labels, Length: 342, dtype: int64" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data['labels'] = np.argmin(A, axis=0)\n", "data['labels']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is an array of indices in the range `0..2`, which we assign to a column in `data`.\n", "\n", "Let's put these steps in a function." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "def compute_labels(M, centers):\n", " \"\"\"Label each point with the index of the closest center.\n", " \n", " M: NumPy array of coordinates\n", " centers: array of coordinates for the centers\n", " \n", " returns: array of labels, 0..k-1\n", " \"\"\"\n", " distance_arrays = [compute_distances(M, center)\n", " for center in centers]\n", " A = np.array(distance_arrays)\n", " labels = np.argmin(A, axis=0)\n", " return labels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can call it like this:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "data['labels'] = compute_labels(M, centers)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here are the results." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(data, var1, var2, 'labels')\n", "plot_centers(centers)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we get lucky, we might start with one point near the center of each cluster.\n", "But even if we are unlucky, we can improve the results by recentering." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Find new centers\n", "\n", "The last step is to use the labels from the previous step to compute the center of each cluster.\n", "\n", "I'll start by using `groupby` to group the points by label." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 160\n", "1 92\n", "2 90\n" ] } ], "source": [ "grouped = data.groupby('labels')\n", "for name, group in grouped:\n", " print(name, len(group))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the `GroupBy` object to select the columns we're using and compute their means." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Flipper Length (mm)Culmen Length (mm)
labels
0213.71250047.981875
1185.21739139.428261
2194.21111141.297778
\n", "
" ], "text/plain": [ " Flipper Length (mm) Culmen Length (mm)\n", "labels \n", "0 213.712500 47.981875\n", "1 185.217391 39.428261\n", "2 194.211111 41.297778" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data.groupby('labels')[features].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a `DataFrame` that contains the central coordinates of each cluster.\n", "\n", "I'll put these steps in a function." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "def compute_new_centers(data, features):\n", " \"\"\"Compute the center of each cluster.\n", " \n", " data: DataFrame\n", " features: list of string column names\n", " \"\"\"\n", " means = data.groupby('labels')[features].mean()\n", " return means.to_numpy()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The return value is a NumPy array that contains the new centers." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[213.7125 , 47.981875 ],\n", " [185.2173913 , 39.42826087],\n", " [194.21111111, 41.29777778]])" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "new_centers = compute_new_centers(data, features)\n", "new_centers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what it looks like with the old centers in gray and the new centers in red." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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aWZBarRD/+RcjgBT7Oowe81EfFiKgLfY5C72mmE2AagcOjO+HigMCkFJKb15npihuPHUQDUxlTqDdd9cu+lSml/KAydtIPII/6ge0zCkYD+KP+nlD4xuyHjuTqGD/C71cvbp0QWKD+fznz8UFaikGkHxjVDxSCDl9Ic5Z6DXFbNag7gduAEqklF4ppUcFJwUteyE8ChEfyJR2Gx7Vji8yQ2NDuK3p/0HdVjdJmWTf+n24LC4GQ4O4LK45BRLPdAzxRw8d5Y6vPssfPXSUZzqGMsps+33hBctvja4HKa+3/GFUTl0IOX0hzlnoNcVsMqhTwG+kVEb9imlUtsD2906p+Ny1sOltBVl/qi6pzljKW1u6NivF3jMdQ9z/5CnKnFbqy5z4wwnuf/IU19R7cdsts75B1pU6F/zNcndLJd94povhUIxoPIndaqbSZePePfoKqYOdw6SSKV7p96fZLhWbO/lSXMsxminkqvRl5L3KdM6Ofj8Ptnfnxbqo0GuK2QSofuBpIcRPgejEQSUzV1DZUhSy8ra6Nr79m28zEhshloxhM9uosFVwz9X3ZD3G/he00klZiQ1g8rZndIwSu3bRmi4quOu6hsm1qIWIDYz0azp53s+50TFKbBZKHVYiiRSvDgYIxZKGzplPlqqThFHxSC5KX0bfK71znhsOcWZ4jPrykrxZFxWyJJxNgDoz/mMb/1Eoig+Btnd24segGq7fF6a+zJl2zOu0cP5SJOM3yIaKEkPfLGd+cx0ORPA6LIzFk8SSKRw2M16HJWNG5IvEMQuB02oGwGk1E40n8UXixl5sHim0Nc508pkpGA1oenMx+l7pZdwjwSjbG8uXjHWRUS4boKSUf7kYE1Eo5kt7fzuN3kY2V22ePBaIBWjvb896Q25dqVbWm8icAPzhxKySynSMNrKb+c31568M4rSaWeVxUOq0Eo2neLU/QDhDRlTmtOIbixOJJ7FbTUTjKZIpSfm0b9SFptCqrwnynSkYCWhnLgTTNru+Nhjg5T4fFpNgY136cv7Ee6UX0GB2xj0WTeBymHXH0KNYPp9sycZJohX4f4C1pDtJqL1RiqIgF/ud7rqugfufPAVomZM/rH0jfsvVNRkvdEDW39D1vrmmJPgjcRortNYdDquZSDzJaDiue4HaUOelxGZmIBDFF47jdVpZU+GhsbJ4Wn8UWvU1wXwyBaNrZ9kGtB8c7+PsxRClJTZKnVpp9uzFEA6riYbyklnvlcWE7t+c3SJmdUh+umOIl/sD3Oxxpo1RrNZFRsmmxPefwCeAE4ByLlfkngVaJs0lksiWCWfy/S/0cv6S9i3zAzeu4+xoWPdC94PjfUQTMutv6HrfXD12MwP+BOF4ctJGKSklQkrdC9SNzRX0jYbZXOtNKysVk0tDsTh6G80U8rl2drznEt4Sa1ppVpZYGQ3GuBSOT85t4r2yW4Tu39xzXRfZ1liWJpKp89o50efHH45nbV1UDJ9PtmQToC5IKX80n8GFEGeBAJAEElLKViFEBbAfzdvvLHCnlHJ0PuMrlgETlknOcm3jbzSg3d/+3qyDVFtdGwdOHwDmv98JYE1tmD3bT026UaypreTQWf0L3XNdF7mhuSrrb+h631zL3XZsFhN2iwl/JI7HYWVtuYfz/ojuBersaLjoXRoKrfqawGimcLBzmFQqxSsD2sXe67y8QjL7jEsgZohfhIQSu0X3vXr0aB+ReCItEDVXlTAWS9LeNaJlYuMimY7BIFfXeyetiy73fs/n8ynqhoXAnwshvgn8gnQV3/ezPMdeKeXFafc/BfxCSvlZIcSnxu9/MtsJK5YZObBMWlu6ln3r99He385gaJDqkmre0PgGQ67lmdworI6dBCM1sy50IIgmErSfmbqgtVSVEPQldMfX++Za6bJRUWJjXaUr7dtsmdOquydnwBdZEptsczHHhV4UjWYKHf1+uofHcNktWa0HGsm4tjWW8lzXCEKIybXDS+E4NzRX6L5XZhOzAlF71wgCidRWnzRbLDQ9UIXLxnvasv9bz/T5ZFr30ls/+9BNzUVjdfR7wEbAylSJTwLZBqiZvB24efzf3wGeRgWolUuOLJOy3e80wUzvvuHwsK4bRVie4tIFzbl8+oVuXYWTX3eOUD6+rhCNp/h15wg3ZHA51/vmOrHfaea32YOdw0tqnSDX5KLcZjRTuBSOYzYJHONluOnrgXoYWeN6+9Z6BgNRhkMxLo3FsFvNNK9y8fYMhsMTgWdmIJJScOP6Cjovjk2uQe5qqSCeg10Gmd7zsWhcd/3sB8f7+OgtGxZ+4suQTYC6Vkq5ZZ7jS+DnQggJfF1K+Q2gRkrZDyCl7BdC6C4UCCHuBe4FWLNmzTxPryh6cmSZZKTvk1629Ovzv+bG+hvT1rHcVjeh2KDuhe4Hx/smLxzIqQvKXLvZM31z1Tu2lNYJck0hpNClDiu+cHzWemCpQ18haWSNq2mVm3v3NGedESZSsKtldiA6es5HKJoejULRZE5EMpne8ydfHaB5lXvW+tnxnksLPmc2ZOXFJ4TYLKV8ZR7j3yilPD8ehJ4QQpzM9onjwewbAK2trcrFYrnSsldbcwItc4oGNMukTW/LegijfZ/0vPsqnZWcHD3J7pLdk4+bEFroBZZkCtqaK+i6ODa5ftTWXEFiDhlRtmWrYlnHKRS5kEJnknZnKk1tXO3FNa6QnL4e2Filf/E3usZlpOxZU+qg52Jo6tuOhFAkyboKJ4fPjo4HEgv+sTjnhsfYs74qq3HnYtAXwWpmVsk6lkjprp8Z3mg4T7IJULuB9wkhzqCtQU2YxV5WZi6lPD9+OySEOADsBAaFEHXj2VMdMDT/6SuWPDmwTMpkFptpH5SeLH1TxSYOnj9IIBbISmhRM+6F19Y8paDzh+O4HPr/pYyWrYysEyy3wJULKXQmafcPjvfxjq31s97D3S2V7B8Ns7kuO4VkPtVw68qdPDrubKJteYhzbmSMa+q97FxbzkAgSiCiBZErq92cHQ2zZ4HntJjQLVnXeR1cCsd1188Wg2wC1G/NZ2AhhAswSSkD4/9+E/BXwI+A9wGfHb/94XzGVywjFmiZZHQfVHVJNT2BHobGhgjEAnhsHqpLqtlVt2vSWPZyQgujF6hclK2Wqo2QUXJx8c8k7X6uczjj9gAjWWumLBcw5Iunx9nRMDvXaYHIH47jLbFyZY2bjsEAt2yuZd208VJS5mSTbVqJelrJekOth1hKZr1+lmsyBighhFtKGZRSdl/uMRl+XYPWpmPiPA9JKR8XQjwPPCKE+ABwDvjt+U9foTC+D6rR3ciPOn+E1+bFa/Pij/rpDfRy37X3sathV1bnNFqGy0XZaqnZ1GRDpoxw4SVOfWn3yFg843v4nra1C3ofe0fGFtwjDLS/lTWVLtZVpQeijsFgTsQzeu/5XCXrO7bPzjiLQWb+QyHEcbQM5wUpZQhACNEM7AXuBP4V+C+9J0spu4BrdY4PA8Y2qCgUc2B0H1RPsIft1dsZCmsZlNfuZX3ZenqCPYbOa3RdYaEXl6ViU5NtGfJy60QLuQhuayzlqY4LxJMp4kmJ1Sywmk2UzyHhN/oaZ2az3zh4hk01ngV/gcj0t7KtsVR3Y6+RzDJTFm63CBxWi27JupBbGzL2g5JSvgFt79OHgJeFED4hxDDwH0At8D4ppW5wUigWk4l9UNn2fRoaG6LR20hrbSt71+yltbaVRm8jQ2P5Ww7NRV8do/2jCoGRnlUT60RCCEqdVoQQk+tEC+W6NeXEEiniyRRISTyZIpZIsbnOk5P3UK83UyKVot+fHugmekqduRDkwfZuPvezDh5s756zh1emv5W3b63nrtaGyU25LofFcHaWqaeUgIL2fcrEnGtQUsqfAD9ZpLkoFPPGyD6oXFgjGSUXZatC2dQYEWYYcWTItE6UCwnz2dEwe9ZXTQoKPOO9s5x284KzENDPZqvcdoaDsbRjwUgCs4k0F/LXhsy8ct7HvXv0FYWX+1tZSDaTKQsPRhNFqRzNRiShUCw6RvY1GSVX1khGWWippBDyc6PCDGOODPrrRDMlzFJKwseOEznxEslQCLPLhWPLNTi3bWV8jXsWg74Ia6pcuoKCXFj91JQ6OHcxNClL9zqsOC0mTELM8sULR+N0XQhRXmKjrMRGNJ6i60KIHx7v4yMZNrvmq6w2V6m5GJWjKkApig6j+5qMkgtrpJWCUWGGEUeGuSyAzlwI8mzHILafP0bLc4/jkknKbr4Jk9tFbGSU0YceRjgclN99N2V3vBNhTd9QO58LsR6ZAnRLpZNnTl8kkUqBhD4BFpOJ9+9aSyRFWvD7ix+/QpnTmvaelDmtHOvxZTWHXDKfPlaFVI6qAKUoOozua5oPRq2RioFCXCyMCjOMODJksgC6bk05//XsKXY98DmsqQSn3vkBzq7ZxF0710y+TplKEXruOYa/9nUCTz5Jwxe/gMk1tak2V+XQTAH6Jy8PYLOYEEnSRBh9vohOViSRMxI97f7i+w8YzcILrRzNKkAJIcxosvHp/aDO5WtSipVNLvo7LUcKcbHIlIlUe+309PTQ19dHNBrFbrdTX1/PhjoP8USSVwcD+MJxSp1WNtV42LjaO2vsTBZAz3YMsuuBz2EfC3D+t99P6urtlIXjaa9TmEy4b7wRhODC/f9E74c/QuNXvzKZSeWqHJopQHdeCLGp1ovTNnUJDccSPHt6mEpP+j6orY1lHOoaQZSIyaDtH4tz/SJtdp2JkQyy0MrRbBoW/jHw58Ag6WaxqmGhIi8UQsSQS/JVsy/ExWJmJhIYizHS00EscI7vHUogSmsJJwVOs0S2H0YKE8PxVVSWr6WpyoU/nOC1CyHedu1q3fH1LpbP//O3sKYSnP/t97Pua5/l7H2fIbXx2lmvM9R+iPN/8nFW3/85hr/6NS59/wDld90559hGyRSgbRbTrKwoGIsz4I9MKhin9/Ea9EcZCcXwhePYLCbWVbl4xyJtdl0IhW5wmFFmPo0PAxuklFdJKbeM/6jgpMgbbXVt+KN+ArEAUkoCsQD+qJ+2urZCT+2yGJFZG6UQMvOJTMTlsNA/EiDwytNUxoa4btfriF55C86m61hz9U6cTdcRvfIWUqu3sFYMUz9ylMBYBG+JlZ3ryjk7Gs7qfFJKWp57nK5b7yR49XbO3vcZ1v3L32F58Wja6wy1H6Lvox+l/vOfx71rF5V/8CFGH3oIKXNbNssk+d7VXIl/TCtlSikJx5P0jUZYU+GcJeE+OxrmQzc1s+fKVVxdX8qeK1ctWruKhZKL7RELIZsA1QMs/mqeYsVidF9TMZFpn8nBzuEFj12oi0XTKjf/a0cDdSPHKbNJ3vSGm+mKuSkvsaW9zvISG78JOKjdsA23OcXmyCtcv7acNZUuBrPM8sLHjuOSSc6u2YQ/HMe/8Vpe+f1PsvEbn+UG3xkgPTi52q4HYGj9FnyXAnzr6z+67D4jo69db+/R793YxLoqF1JKfOE4UkpKbGZ2NqWX7Sb2QTWtcvOetrV8/NYNC3asWEwyvf6Cq/iEEB8b/2cX8LQQ4jHSGxb+U57npljB5FvEkC8Zez7LcIV0OT927BjJZJI3vvGNPProo6TWXk/9mvT3y+2w4IiMMPDSi9Rd+zpGO1/C33cKUdWcdZYXOfESZTffxF0710y9zmu34/67/0vqLz7DhY53M/rwd9OC05kLQf712bNsabyKsZde4pCrnlfO+7jtqlrOjoYXXGrNVCr80E3p62fDgQh2S/oltdg2Us+HQjpJzLUGNbEAcG78xzb+A4WQnygUOSKfMvaaUgfnhkNTRp/jG1Vz0bMHCnOxkFJy5MgR3vSmN9Hc3My73vUu/uPh/ZxNphgSpZOvs1r6qB99Ecv6G0i6qilrvoYLJw9jKmmYU8Y8/SLfNjRKqdul8zrXcqHj3Vz8ylep+sP/PRmcAH54vI+uCyE22px4ZRwTgpf7fJwaDPDGTbVZKx6Nrh3OnONEeRdWZh+vfJAxQEkp/xJACPHbUsrvTf+dEEIZvCqWLPmUsc9qlZDDnj2Fore3l3g8TlNTEwBNTU1cu/tWDj/9U2JV2/CW1xAbGSBy8Rg7b34zWzZdoWU/kXKQSV7fYMq4AXSmw4IcCNPmiG/rjuYAACAASURBVDJTDhNqP8Tow9+l6g//N6MPf5eSnddPBqljPT7KnFZKEhF83jIcVjPxpCQQiWWteCxEF1/F5clGZv5p4HtZHFMolgT5lLGfHQ3nrWdPoejr62P9+vVprg0+WwWOK3ZR0/kc/mgjNaEerFfswmerSMssfpLqQo6N6o47kflMd1h4yd3A5l9+G5lKIUzaEvnMNaeSndfPWIOSSFI0nn6J0++4EYBIIkkylaK9a3jS6aG5qoRgNKE7l1xJ+IvRjWEpM9ca1JuB24B6IcSXpv3KC+h/ygrFEiCfMva5LHaWKhP7nKYz6IuwrqmJ0eQlTJ0vUtFyLeVNTbNep91uJxZL96ebYCLzme6wEGjeSOiXZsba23Ht2jUrOJ25EOQgtSR+52Nc98cfpuRvPsvWxjp6n3iaoLDwlLka80CAYESTc0cTKUodWsPC9q6RjHuP8rl2WGg3hqXMXBnUeeAIcDvwwrTjAeCj+ZyUooAMd051t/XUaS3ZF9BMsBjJpxdfofeN5AO73c7oaHoWVFPqYKS/F/+5k1S0XIvv3EmkaxU1dQ1pj4tGo7hcmdbfdBwWTIKj217Puq99HQmc/5OPpwWniQu9u3UHr1g/ycbPfJIN932K9c//hGc234QEEqkkUgo8Ds2lGzHVjC9To/J8fm6FdmNYysy1BvUi8KIQ4iEp5WwjLcXyY7gTjj4AznLwroZoQLu//b1FE6Ryob7LpxdfoRzH80l9fT3PP/88UsrJMt96R4ifv/IM5Zv3UF7XgHStYvSVZ9jRdPvk86SUdHZ2smXLFt1xMzksiNvehvivTi7c/0+svv9zk2tNMy/0qa3XcfL3P0Htg99Alpbju/m3qI9JvE4rPcMhykus2KwmfOMijl0tFcT1PGvJ7+c26ItgMcEr/f6syo2KKbJZgzoqxEzPYXxo2dXfjDcgVCwHOp/SgpOjVLs/cdv5VG4C1AKzs3ybyOaC5bhQ3tDQgNVq5cyZMzQ3N3PmzBkOPvEYb3rL7ZyOuLTXWdfAjqbbOfjEY9SWOmlqaqKrqwur1UpDQ4PuuO/YWq/rsPD269bSsOcL9H74Iwx/9WsgJa4bbkgvw6VSeF4+Rs3jj9Bvc3Nw330c7vETjCRwOyxUuSyEE2be2JTegK/CrX/Jm+tzW+j6kdkE7V0jlJbYsio3KqbIJkD9FEgCD43ffzdapuwDvg28LS8zUyw+gX4tc5qO3aMdXyg5yM7mUt9N3GaTWeU70BVy30g+EELQ2trKM888A8Cjjz7Ku971LpqamrhhxmNrS53sf+R7lF+1h6HXjlHRuJ6zF0MZ+x7N3Es0/eLf+NWvcOn7Bxj6h38kFQnTun4rEauDkkQEz4kjpOwOevfcxr+7N3OqM4DDasZtNxONpzg1NEZ9aXJW64u5MiK9zy0X60dp5cUsyo2KKbIJUDdKKW+cdv+EEOJZKeWNQojfzdfEFAXAU6cFjonMCbT77tqFj52D7GxobAirycqRkSMEYgE8Ng9N3ibOB87TH+rPOuAshlv6cmPbtm2cPHmSJ598kjvuuGNScj4L9yoCtdsInDhEwmSlJ1xG7zNdczbnm1P1VnYtNZ/aya5wH/UnX+HEqQHi5TUMf/DjDNZfwaVIgtET57GYwDbej8lmkSSSgnhKTDogTM+InukYYv8LvfT7wtSVOrnrugb2bNAXyORi/SiRgl0tFXReHMuq3KiYIpsA5RZCXC+lPAQghNgJTHwyqoi6nGjZq2U1oGVO0QCER2FTDpLkubIzndJft8UyKyMyCzOHBg5Rai/Fa/MSSUY4NHAIp9lJa11r1gFHuaUbx2w2c+edd/LII4/wP//zP0gpaW5uTpOeSyn5r6ePEO97FbPFRqRhB6ak6bLN+Wail7V8L1rJXb99N9tgKuNyWrn16lp+cKyXGq+DUExr8W4xm6jxOhgdm710/kzHEPc/eYoyp5X6Mif+cIL7nzwFoBukjKr7MjU3DEUStGVZblRMkc079PvAt4QQbrSs1A/8vhDCBfx9PienWGQqW7SS20SwcNdqwSlThmNkTSlTdmYyzyr9dR/6Fw54PXjL1qZlRGOxscmnymlmJsF4ELc1/dvsXAFnqbulFwqbzcbdd9/N8ePHeeKJJxiLRDU384QJpyWF9A0wOpYk7l1HrHIdQphwmDDcnG+urEXPd7DKbedSOAaIyb8KfziBhFnO4if7fdhMgpGxGOcvhXHYzDjMJva/0KsboIyo+/Q2Hk9YLj3bNQIsH+HMYnHZACWlfB7YIoQoBYSU8tK0Xz+St5ktR5aChLuyJbs5GV1TypSdmR2zSn/tvhBe/xie6quBqYyoY6SDnbU7Oes/O1ni21m7k5cuvGQo4BSq5ftywGw2c91111HeeCXfffpFHDEfHluSuDQTWX0dpy4Kyj12SsSUD7UUWq+kB9u7sxIaZMpaXj3vp280PGs9qG1dGQ8e7sEkBCYBKQnxZIobmitmBbmTA37cdit2ixmn1UwiKRmJxgjF9ItBRtR9ehuPuy6EeOHc6LITziwW2fSDsgN3AOsAy0RKL6X8q7zObLmxBCTchjC6ppQpOzv+kBawpjEkE9Qk0gv0ExmS3WKntbZ18nggFmBL1Rb8Uf/k46YHnEyy9J01OznQeYDB0CA1rhr2tRSPEnAp8GzXCBXVdXidayaP+cNxXMGLmlR8mnR80BfGbDLNymYyCQ0yZS2+SJzGipJZQad9wEed187IWIJoIondYsZqAos5vVmD22EhkYJUSmId/53VLAjHEmmlyukYUWXqbTyeyB4/cssGFZDmQTYlvh+iKfZeYJqbucIg+ZZwLzbzUfzpZWeeOhg9C/7zEPGBo5Rqc4Sg3cP0sBWMBzMGon3r9wHM2tcE6Kr1dtbs5PDgYTZVbmJH7Q6C8SCHBw9T76nXDVL5cj5fymTKchrLSxgOxei6GGIslqDEZsGE5Pr1lVkLDTJlLWVOK25H+iXL7bBoRrF1pZRYp353csDP2YtjaY8NRhLUlToYCcUYiyVw2MxEYkmiyRRbVuXCzLd4WrsvF7LpB9UgpbxLSvkPUsr7J37yPrPlRqB/VqaA3QPBgcLMZ6FMrClNZz6Kv4oW6P41hLXgRNhH28Ve/DbnrIaFb2l+i6E+UdPVekIIPDYPXruXA50HSKaSdIx08HTP03SMdJBMJSfl6tOZkKSHEiFqXDWEEiEOnD5At6/b2OtcZmRqnljptlFaYmVNZQlNVS7WVJYAghK7Oe2xE32S9MjUg2hDnZdzwyHazwzz81cGaD8zzLnhEDaLmZk7NatcVhIpOat31hs2VrN7fSV2qxnfWBy71czu9ZW0Nun31DLSgHJrY9msJob+sThbG8uyf2MVaWSTQf1aCLFFSnki77NZzuRTwl0IcqX4G+mENTdoATziB2cpa6s3slPAgeFXdUtwMwNSpn1NgWiAqpIqOkY6Jtes1nnX0e3rxh/z47Q48dg8RJNRXrv0GmPxsVnTU5J0fTJlOXaLYG2Fiy31Uxflp18b4pX+ANVe5+Sxy9kI6cnPe0fGdJ3ir65z0++PIYTAbjURjaeIp+D1G1bNkpkD7D/Sy1u2eNLmnanpoxGZeaaNx0uhtXuxkk2A2g3cI4Q4g1biE4BUbd8Nkk8JdyEwqvjLRKAfKprSntcdGebw0CE2XfnmrEpwmYJIx0gHXf4uSu2lk4Ho8MBhoskoJkw4LNoF0mFxEE1E6Q/1s//k/rRSnpKk65NpbebRo31E4ok0W5/VXjsv9fl1N80acWk4OxrmymoXrw4G6LoYpLTEyqYaD6vLnDjtUYZDMS6NxbBbzTSvcnHPjU26YxkRLMwlM9eb+1wbjxXGySZAvTnvs1gJ5OqCXkxkUvwtUH7e7juF11G54H1NY4kxTONqMjFt377T4iQlU0QSERxmB5FkhFAsRDgZnizlTWRhNpNtxUvSMwURvSzHbIKnOoaIJSWJZIpBswmbWdBUWcJvzvvSNscChlwaOvr99Pui1JeW0FylZUr9vih2i5l792QfGIw4fWQSbFhMmef+nraVm1nnmmxk5t1CiN3AFVLKfxdCrGJqo67CCNlKuJcyOZCfD0WGsdRuo2PgSFppLhQL6Z4y074mp8XJ1lVbOeM/gz/mx2PzcH3t9bx44UXWl69naGxo8rjdYqe8pHxWUIzEI4YVgssJo1Y/l0IxhgIxPHYLTpuFSCzJ+UCURBLedu1q2porCUYSPNs1guPcKKlkKi3bqvXYM4onLoXjmE0iTSUXiScZDcfpHRnjUNfwZABcV+7MSeYyVykzFw7lqk/U3FxWJCGE+HPgk2hNCgGswH/kc1KKJcx0taIwabfOcu24HhOZpc2tZVw2N+barRwOnCaajKaV5szCrDtEW10b/qh/lqjimqprsFlstNa2snfNXlprW7FZbGyp2oJZmNlQsYGbG29mQ8UGwokwG8s3po3rtrpJyqSuMANYduKJMxeCPNjezed+1sGD7d2TF8+JC7FJCLxOK2VOKwc79T2iz46EqfPaCMYS9I6MEYwlsFtgLJaYNcazp4d5dTAw2bMpmkjx6mCAk+f9umOXOqwkx8UHEyKEpJSEwjH+7qcn6Rjw4xuL0zHg5+9+epJnOoYW/J5kEmwkU+gqCjMJP/QwIsBYqWRT4tsHbAOOAkgpzwshPHM/ZQohhBnN+bxPSvlWIcS3gdehSdcB7pFSHjc0a0Xxkgv5+bGvQKATSC/NZSJT+wxAd0Ounix91+pd2C3pTfkmSnlrS9fOyoz2n9y/rMQTmTKlYCTOxjpv2mPnsvoZi8YZCScod9qwuASJlKRndIyyEjlrjNFwjAphwxeOE4kncVjNOCwmfJG4bmaxcbUXl83MQCCKPxLH47CyttzDU68NEYkn8TpsWMyCRFLij8T41q/PZPTYM4JeSbCm1MG54ZA2l3F/vVqPncbK7OXqqk/U5ckmQMWklHKi5ca4xZERPgy8itaJd4JPSCn/y+A4iqVADtSKSZnk+trrZ5Xm4qnMbcn0gggwZ9+n6Y+fUAJCdu4Sy008keli2Ts6ZqiRn8thYcAfQVoBoe0AMpsEFlP6F41gJIHTaqbvUhiXzTK5J2k4GMVjt+gGyxubK+gbDbO5zptWbgtGE5Q5rWmbb912C50X9EvCuWBduVNXUbhnfVXWY+Szi+9yIZsA9YgQ4utAmRDig8D7gW9mM7gQogF4C/C3wMfmPUvF0iEHasXqkmpCidAsx4hyS7nh6WQKXHqPM9LEcLn5+WW6WJY6rFwKxyfvX85HrqGshEA4QTieJBxLYTEL6sscpCSzVHxVbhtOq5lIIkU0nsRhM1NWYmUwEGVH0+xgeXY0rKvAe/LVARIpyfT8N5GS2CzZbPOcH2dHw+xcW85AIEogomVQV1a7OTsaZk+WYyzH7su5JhuRxOeEELegmcRuAP5MSvlEluN/AfhTYGZJ8G+FEH8G/AL4lJRylkOFEOJe4F6ANWvWzPy1oljJgVqxUF552QYzWH5+fpkulhtXe9ndUpm1LHtDnZeSiTLctNJXic08a0/SN5+Jc250jHKXfdIWaSyWIBRN6K7vDPgiuuW2Xc2VPPnKICBwWk2E4ylCkQRv3Jw/M9ZBX4Q1VS7WTZtLSkpD2c9y7L6ca4SUxm04JvpBXeYxbwVuk1L+oRDiZuDj42tQdcAAYAO+AXReztevtbVVHjlyxPA8FUuXpaCQWwpzzJbpa1DTL5ZGGvMZHefB9m56LoYmsxDPuIrvvD/C1atL04KlPxzH5bBMBsvpa1MA//izjjR7peYqF3fvaOTsaHiWQs6ock7v8Qc7hwnNCOgTczQiM1cqPg0hxAtSytZZx+cZoHqklI2XeczfA+9B6xnlQFuD+r6U8nenPeZmxgPXXGOpAKVQ5J9cXSyzHSdTMLuxuYJnu0ayPn5Xq7anavo515U7DY+RizkaDegKjVwHqHNSyqzrbjMzKCllv9Dsgz8PRKSUn5rr+SpAKRTLk0zBbKFZy4Pt3bqP/c15X8bsTC/zyTROpmxOBaf5kSlAZVyDEkK8M9OvAGeG32XDf45v9hXAceAPFjCWQpEzllPJLpfkoiRm1NVB7/ijR/uyVr1lEn30+8K0NVfOOp5p7WgupZ0RRwrF/JhLJDGX7Oq/jZxESvk08PT4v19v5LkKxWKQyXB2Lrf0lYBRJwmjjzeCEdVbpsfWlToNKeeU0q6wZAxQUsrfW8yJKBSFRLmW63Owc9iQHVE+N58aUb1leuxd1zUYar+ulHaFJX8bBRSKJcTQ2NBk194J3FY3Q2MLt8tZypw87zdkRzToiyzYAigTmWyHMpUI9R67Z0N11mMYPaci92SzUVehWPYU28bbYpEf+yJxzELgHDdodVrNRONJfBF9V49clcSMOKhnIldrRJnGKZbPaDmjMiiFgsyGs211bYs+l2IyES1zWkmmJJF4Eol2m0xJyqcFoOnsbqnkUjg+q5NtpoaAeuTz9c81tp5ZbiHmqJgiqwxKCLELWDf98VLKB/I0J4Vi0TFqdZRPislEdEOdl1giyauDAXxj8ckmgVfWeTNmEEYaAuqRz9efaewfHO8jmpBZizuK6TNazlw2QAkhHgRa0CThyfHDElABaqVjpDFhjsinFDyT1dFiy8+LyUR0XbmTh9q7SaRS2M0mIrEkJ/r87FhbPqdabyEX6Xy+/kxjP9d1kRuaq7IOOMX0GS1nssmgWoHNcj47ehXLF6ONCXNAIaTg3b5uvv2bbzMSGyGWjHHad5qTwye55+p78nbOYpI2v3BuFJvFhEhCPCmxmgVWs4nHXh6grSn7C7oR8vn6M40NIqP/32LPUTFFNmtQvwGy75WgWBkYbUyYA6ZLwYUQeGwevHYv7f3tORm/29fN/pP7+eej/8z+k/vp9nXzWNdjnA2cRSDw2rwIBGcDZ3ms67GcnFOPXKzj5IpjPT5qvQ6urPFy1epSrqzxUut10HUhlDe13nxef7brR5nG3tZYOh6oppgr4BTTZ7ScySaDqgJeEUIcBiZdx6WUt+dtVoriZz6NCRdILnswzSzbNbobOTx4eFZ2dmzoGOX2chwW7ULlsDhAwomLJ3LymvTIxTpO7pDIGT0jpQCbxcy5caPX6fujGquMtoubjdHXb2RzcKaxAUP7nYrrM1q+ZBOg/iLfk1AsQXLQmNAouZKC65UKv/PKd6hx1dAf6icQC+Cxeah2VnMpeokye1na8yX5r3YXi43O1sYynu4YIpaUJJIpLGYTNrPg6jo3h7tHpxr2heOcGxljzxXZN+zLFUYFC5neW6MBp1g+o+VMNv2gfiWEWAtcIaV8UghRApjzPzVFUdOyF578Kxg5DdEg2N1QsR7e+Gd5O2WuejDpuUYEYgH6Q/00lzXjsXmIJqO8duk1HCYHQ2NDxFNxkqkkZpMZq8nKnvps29ItbVrXlPOzlwdIpkCgtVOXUuJ12ti5zjnV96nEypU1xhr2ZcKoXVKuBAsq4BQf2aj4PojWOLACTc1XD3wNWJqd2ZY6BVDO6TJ6TgtOyQRYHNrtyGnteJ7mkyspuF6pMCmTxFPxtFJeNBHFaXESjAdJoK1PJGQCkrB11dbcvKgi5+xomJvWr5rVs6ljKMAtm2tZVzX/hn2ZMJoRKcHC8iWbEt99wE7gEICU8pQQYmn2tV7qFEA5l5FjD4C7DkqmtWEfG9WOr9+74OEzSbuNdL3NhF6p0CIsWE1WIokIDrODSDJCSqaQQnLD6hsYCg+llf56gj0LfYlLgkydYzuGgnkLCkYzIuWXt3zJJkBFpZQxrX0TCCEssAhF+JWOXqY0XTkHU7edTy1+gPKfh9KG9GPOUvD3LnjofMvJ2+ra0qTjNrMNszCzddVWoqko/pgfj81Do6eR06OnKbGWQHjq+SXWkhXj0ZcpO9nWWMqlsGZ3lOugYDQjUoKF5Us2AepXQojPAE4hxC3AHwI/zu+0VjiZMqVoAGquSn9snpVzGfGuhrAvPYMK+8CzOvNzMjEjGLebI/l3FhdoX7PGf6pLqjGbzGwo25C2vtXobuTwwGFK7aWTa1OHBw6zo2aH4VMuxX5TGV3Bp3WxnRkUFupRN5+MSK0fLU+yCVCfAj4AnAA+BPwE+GY+J7XiyZQpXTq36Mq5jGx7Lzz1N9q/naVacIqMwg33GRtHJxgPDR6kZt1emFaCm6+cXEpJ+NhxIideIhkKYXa5eKl0iMaWBjZXbZ58XCAWIBKP4LK40ta3Hut6DHzaYwQiw1kuz1LtN3W57GRmUMhFPyiVESkmyEbFlwL+dfxHsRhk2mPkLIfw6NT9aEC7v2mu3pJ5YmKd6dgDWlnPs1oLTkbXn3SCcbWjkuDgCTyeKR2OUTm5jMe59Oj3GX34YWQkgmvPHkxuF7GRUer+/cfUOxyM3LaT0TduB4sZt9VNKBbiro13pY2TlEmur72eM/4zk6W/62uvJ56KG8qIlnK/KSPZidH+Ubk4p2L5ko2K763AXwNrxx8vACml9OZ5biuXTHuMqjdPrUUF+rXMadPbCqPiAy0YLVQQoROM20qv4MDQIYgFZsnJswkKqVCI3g9/BBmLUfPJP6WkrQ1hmjJN+dU7m7Ece5W1B57H+9yr9HzqLnzmmG4ArC6pJpQI0VrbOjXlWIBUPGUoI8rlJuNi5uR5P+dGxyixWSh1WImM948KxZKXf7JCMYNsrI6+ALwPqJRSeqWUHhWc8kzLXi0zivhAprTb8OiUpHzn78Pr/1/ttlDBKVdMBONprMXCvlU7J8ttLouLfev3AXDg9AFCiRA1rhpCiRAHTh+g29c9+VwZj9P74Y+QHB2l8g8+hGvXrrTgBNBWv4vfrDPzy9dXMHZxAPdffo3e4W7d1hqZ2nAAhmyXJpSD0wnGg5iFeZa90lJmev8oMX5rFiJj/yiFYi6yCVA9wG+UWewiUtmiScdtbi3DsLkLIyVfDDIF4zWzg0U2XnyXHv0+MhZj1Z98jPN/8nFC7Yd0T7vq5CBv/NYJnr29GUs8RdOzXbqPm9h7NTNYJmXSUAdevUDX4+vhQviCbsA10puomDDaP0qhmItsRBJ/CvxECPEr0r34/ilvs1JowWg5BqSZTATjaWXL7sbrOHDxhVnls2AsyJUVV6Y9fXqZTErJ6MMPU/PJP8W1axf1n/885z7yYTr/5B2caXFNlgRP/Pxhdn3tOZ66dwd9zXZOWEu44fuv0b7vOd3ynN7eK6O2S3qbjFeVrMJhdcxal/rvU08TuHD9goQGhWJDnZcSm5mBQBRfOI7XaWVNhYfGyoV79ClWHtkEqL8FgoADsOV3Oop5c/qpccHCeW1NZ9t7c7Jhdl5kcru4nAvGeJLefvFFXUFBX7CPnkAPQ2PTNs2WVNPg1iTP4WPHkZEIJW1a9nVxUy3P/+Eetv7jI4hP3MXgphC/+uGX2fKln/PjezYyfIUHr9nB2Sus7AyPMfz8c7Dp3Vm9xPnYLs0MdP989J91s7D2M6+x3bM7J60sFrst+e6WSvaPhtlc602TiCuXb8V8yCZAVUgp35T3mSjmz+mnNMm3o1zbPBv2TUnAFztIZdrD1XQznHk6q+OZZOYiJTg6eBSvzYvX5sUf9dMb6OWG2hsAiJx4CdeePZNrTu397SS2b6L3T6tY8w+P4H7zDsp/epj//J0G/BsqKJ2wNbI5ObepEufp7DcZ58J2KVMWlkp4MvYmMhJwciH5NoqSiCtySTYB6kkhxJuklD/P+2wU8+PYA1pwmtg0O3E7l+1QLjz9jLhdHHsA6q7N6ni1o5KevkMMldWl2QtJk2R79fZJ2yGv3cv6svWTtkPJUAiTe6qUNKGcC13jYeTNO6je/ysG73wdZ1pGcMbHuBC+QCKVwGKycIUthTeezX+HKRZqu5QpC9tSsVPXScFiwlDAyVVbcqNZWD4l4oudESoKSzYiifuAx4UQYSGEXwgREEL48z0xhQH857XNstNxlkLgvP7jJ7KcWFDLWmJB7f5wZ/bnzDTG4MvaHq3p2D3aHDMdj0fg7EE4+RicPUijtHM02I0/6sdj9eCP+jk6dBQhBY3eRlprW9m7Zi+tta00ehsnhQlml4tUMDQ5/ESG4nqpi4qfPs/QXa+j4vHDXNtjJprUllMnNt9awjHsnhnvYZ7JJMC4ffM1us3wJEwGHJMQeJ1WypxWDnYO644/6IssuKngRBYWiiSoLXUQGg+KhRBtFNNcFItDNht1PZd7jKLAzGU7lC9Pv86nNNXdwAlNeeco1eYRuaS/h2uirDfzuN0DZ58Zn08ZJCL0XDjFdm8NQ3bvVKZUvp6B0EBGYUK3r5uXSoeo+/cf86t3NtNWv4u2ujZ+9cMv0/DlX3DuE3cxuGkVlhYPb/nSE8Te14zv6jXYzXai8QhXdHTS9abcmIsa2cCbKQvTK5M9erRv0duS5yoLywXFNBfF4pAxQAkhts/1RCnl0dxPRzGJkRJcJtuhq/blz9Nv6BUtW4qFIBWHwAD4eqG0Ud/tYtt7tbWmmccrmrVxgAknoSGSNFo9rJm2OVZKSTgentyDNL0ktrFso7ZptqWCeocDy/FXORAe5PZLzez4yjN0fuJOzrSUUG1x0fb2P+IZYeadX/oZv/xgOaeaY1x5OozV5WZ0/arsX38GcmVppFcmMxpwcuHynateS7mgmOaiWBzmyqDun+N3Enh9jueimMBoW41MtkMjnfnz9PP1aEHJ4QWbC5LxqfvbP63vdlG+Zvbx4w9B001w8TUtE7N7qa7aSDAZYXrqHowHuaL8Ctrq2mYJE6bvjxq5bSdrDjyPfMcOQl98kOYvfYVNbdenTb19xzaO/nGcm7/0JOF7NnLtz/s484ZNmE0W9p/cvyAz13xaGhkNOLkQLBRTr6VimoticcgYoKSUBdIoLyHy1TxwPiU4PduhXxzMn6dfJAAmMyDH5eFSux8JZN7DpXfcU6etX63bPXmozX+OA6GzulZHeiWxDSgTgQAAIABJREFUH3X+CIvJQsdIB6ENft7xqxBr/uNXvHTfG9gyIzgBNLob+ZfKH3H+fRu56UfdBF1mvrd+mLW+LhxWx4Iyn7ksjRbqZj6fgLNQwUIx9VoqprkoFodsvPjeq3dcSvlANicQQpiBI0CflPKtQogm4LtoHXqPAu+RUsayn3KRkM/mgZnMYo221ZiHp5+e+7djyzU4t21loicYoGVNlkaI+iEeBqtTK++ZLcYCd8te7X2beI3RAGuTKfZd837aw+ezknCbhXmyJYbLWcrjv38Ne79+hKYfHCW4/llcN9yQZnfU4+/mTYPVrHnieUJuMwf/oI0y6Seeii8488kkHTcLc95Kf/mkmGTjxTQXxeKQja52euMbB1qr96NAVgEK+DDwKjDh3/d/gc9LKb8rhPgaWiuPr2Y5VvGQz+aBmQKL0bYaOhf/yUxpRjYj43EufXe/rvv36EMPIxwOyu++m7I73omwWqG+FboPgrdea/meiGhjV15pLHDrOEmw6W2srWxhPgUxgSDhsPD9D27gra+6GPqHfyQVCePevQeT200qGGT9k/+NKHEy8uYbCbxxG1stZn557pfEkunfk+Zj5ppJOm4z2VaEm3m+Kaa5KPJPNiq+P55+XwhRCjyYzeBCiAbgLWhuFB8T2lfw1wP/a/wh3wH+gqUYoHKV5egxV2AxQoaL/0xXh5S1kt5/exYpLbru3zKVIvTccwx/7esEnnyShi9+AdO1d2pjhi9qggyLHSpawF0BFqexwL1AWye9lhgb62+gty7OO/7kX7SM8DcnSIVCWCorOP/Rd3GhpRyPfcrz2Ga2zeoTbbTFB2TewPujzh/pukYsNzdzhSKXGNuZqDEGXJHlY7+A5uU3Ue+oBC5JKRPj93uB+nnMofDkKsvRY67AMp+xZj5vuBMOfhHCF5HRCL2P9JKMwKqPax52MxEmE+4bbwQhuHD/P9H74Y/Q+NWvIHZ/WJtjcECbY8teTfTg0tnvNFfgXuBaXnVJNS9ffJluv7Z3ymv3YjfZuarqKoQQlGzfRsn2bZOPv2ZcaYcQk1lOha0ChNZKI1vrokzkwrtPoVBktwb1Y6a+W5qAzcAjWTzvrcCQlPIFIcTNE4d1Hqrrki6EuBe4F2DNmjWXO93ik6ssJxP5NIt98ZFJhd+ll2PIpGTVbjfn/7+/ob68EddMYcHppwg9+s+c/24Hq++8kuEXBrn0/QOU33WnvujBSOAe7oRnvwShC5CIguVVGDhB97Xvoj18PitBgU3YOHj+IC6LC6/NSygW4uD5g2xbtU338XpZzj1X30NfoI8DnQcYDA1S46phX0vuut3Ox7tPoVjpiMt10RBCvG7a3QTQLaW8rGmZEOLvgfeMP8eBtgZ1ALgVqJVSJoQQNwB/IaW8da6xWltb5ZEjRy53ysVn4pv/9AxirqCSL9WfUR68A6wOpMXJmS8fo+bNzbjW2gidHqbvMT/1n//8VJA6/RShb32Svp8Eqf8tB64GK8FeydBxL00/fSJdODHxGtMCjh1cq+DG/6P/Wp/+ezhzUFuzsjogHqE7PMiBsnK8V/xW2sU8k6DgE7/6BEOhIWIyRiQRwWFxYBM2ql3V/OPr/jGrt2T6/qVszjkfFqriUyiWK0KIF6SUrTOPz7VRdz1QI6X81Yzje4QQdinlnL44UspPA58ef87NwMellL8jhPge8C40Jd/7gB8afTFFg5EsJ5+qv/kgIXwugIynKGkuhUQY11oX9Z//S/o++tHJIBXa/w/0/SRA/Vu8uNZp+51cNT5S/ijhY8fTSmdTY0stV574metLUM8RMFnB3zepBmy3g9c/lLWgYDA0SJ2rDmGaCpYyJekPZb8euBgt2Rfq3adQrDTmKvF9AfiMzvHw+O/mW8v6JPBdIcTfAMeAf5vnOEuLfKr+jNLYCmcOEumO4bqyHJGMaBZFTbtxtV1P/ec/T99HP0r53e9m9HtnqX+zRwtOAGYrwu7BvfoSkd+cmB2gOp+CymZwTDse8WV+nfExGO0BkYRUCqI+hhJmapxlaQ+bS1BQ46rBH/NTOq2s6I/5Z+1Hms7MbObU6CmqnFUcGTkyaVDb5G0iFAtlHEOhUOSXuQLUOinlSzMPSimPCCHWGTmJlPJp4Onxf3cBO408f1mQK9VfLsqEW+4E/wDJ6AlMprjmqVe5Xjs+3InLdILytnoufuWrVF1nxlUbh+AFSMbAbAOTBZPdQiqkc/Gez+uM+cBaomVSqTjV8Sg9TjdDA0fS3MwbPA26T9/Xso9/efFfALQ2HDE//pif92x6j+7j9eyIXht5jZfly9S4avDavESSEQ4NHGJHzQ7dMRQKRf6Zy818Lv8QZ64nsuyZEA9Mx6jqb0J91/VL6D+u3R78ojEXctAC2o3/B/PqDaSsldDyem2NCODoA4Re6mD0YCdVb93O6MspQqcuauU3k1W7DV0gZanE5NLpkmr4dUotOMXDEB6BeJhGaeUosVlu5o3uRt0RdjXs4r5r78Ntc9Mf6sdtc3Pftfexq2G2IhH0W8fbLDb8Mf/4jOZel1UoFIvDXBnU80KID0op/3X6QSHEB4AX8jutZYhR1Z9epjRNfYejXNscO9KpHX/9p43Np7IFx1vvZfTTn0a2vl/b93T4m4S6x+j7+i+o/+PbcW1eS4l3iL7v91D/RoFr1RhY7ciSKoJdQSx3V/Naezv/f3vnHh3XVeXpb6tUqpJLKtmyrIdl2ZZfiQMmfsdxSAJJMAywEowdOzTDY+heNNMDBGZ1T0PTq+mB1Wuafs300OkODM800G1j40WAAHHeSQfFdhLFSfyWFVuyZckPSaVnlap05o9zJZWke2WVVSWrpP2tVeveOnXuqbPrSrXrnLPPb0ejUQKBAJWVlSxY8i7k1X8dv50mOcjCOoaGXGEpPk5EWzkTOUM4EGbF7BWDeZ/c2Lxgs6dDGombHJHf56ckWELAFxgctW0s30i8P+7RiqIomWYsB/UFYJ+IfJQhh7Qem/Z9a6Y7Nu1IZW+TV0DF2ZcgNNfKCoFzNHD+2iIc89esRoJBumtqCG3eTNfLtZz73ouDzgkgVB2m8r4Kzv3iEpXbFhNcMp/XjuWTSLxMzYkTLFu+nEAgQGtrKwcPHsTv97N+5SbW5DbiG88erpwcuw7lnwW+IkjEOCkJmumnPFTO4vBiehO9NHc3k9ead012jqR0VikNkYbBxIeFeYXEE3FmB2ezPklBvSPWQXFucVreU1GU1BlLLLYZ2Cwi7wbe7hT/yhjz1KT0bDoy3qg/r4CKnlaYNXd4XUen9VoQEeZ85CNcevhbGOD8916k8g/vHnROAOQGCK2soHLpnTR+81GO3r2CigO1FN+9ms9+7nPDwsyNMZw+fZrnn3qcY7F2dizv56oupT8xNMUXjUCOn/aCEFEMka5mehO9BH1BAr4A7bH2azN0BFUFVTxa9+iw1PFXeq9QFChKy0ZdDSdXlPRw1Yy6xpinjTHfdB7qnCaDjib37LOzim20XV8PYOyxt81G5V0js7d9GMnL4+Lf/wPzv/ZnhBbNslF3pt8eQ/Mgv4Tg4iKO3vVO5r9wkKJQDss++4VRe6BEhKWz4Y7ZF+iO9rH7ZB6J3o6rZ+vN8UMgBIEwBEKI+GgiQU+ih2BOkJ5ED01dTYhx2+dtHWNDQwM1NTU8++yz1NTU0NDQgNcev4bOBtaWrSUcCNPRZxMibq7czJKiJaOy26bqWAYCMLriXTbdfLyLfaf2cab9TErtKIpybVJHSqbxUmNYcgdELthNsD1tNqJuIPruGhG/nwX/+H9ofPALXP7Jo/B79xLKbUUGpudu+zymv5/D3/kWFQdqCZcU8tj6dxLozqPapb36A79h70kf29bM5blTEWov5bKudI4dFcLodbVAoU3TEZwzGMVnpI3yHD+x3Hx6473k5+ZT5C/CyHCHk0gkePXVVzl06BB9fX0sW7Zs9HTj+vWsWbMGn883eF1LdwtVhVUsDA8plBhjaO5qZueNO6/5s4TJ2U+lKDMFdVBTEa+AirUfh9azNjFh92W7PnXThya8jyonFKLqX/6Ztp/to+Wh79Lf0UbBjaXkhOfQn3eczoOHiXd3U/yRB1j26U8TaGxkz549bN+ymero0UGHUx9YyZ5XLrF9XQnVJfkYYP/RNtYuKEUuHrVJDkeuqwWLwBeA1jODYezhuXOI5IaYM6vMpmRPROmJ9xD2D4m7xmIxdu/eTSKRYMuWLVRXV7tPNz7/PMeOHWPHjh3k5dkJx3Tp4rlN5Y2VD0pRlNS46hSfch0YCKjIK7Bf/nkF9jnYtOkVN8M7dthj/TOph5m7IH4/c+5ZR/XnNzD/v9xJXlUlOb5+8mgk9w8/Rs2O+1n2R3+E+P1UV1ezfctm9vxyP/UX2iA8n/oLbez55X62r8yluqAPgCUlQfoShsaWNui+MrSuJjn2mD8HIk12mtLvKKD781kRjbLCVzgYURfwBVgxewUrilcAduS0e/duuru7uf3221myZIn7dOPSpdxxxx10d3cPOjOwuniRaISOWAfGGDpiHUSiETZVbBr35+U1lecTH519ncPqqiisolwb038ENVX071LFLaDiwHcyq0ZR9zQyq5hZby9i1kBYTG87J85dYtnyG4Y5geroUbavKmDPmz2s7/Bx6GwP21cVUB3uG8zWK4FClhbncO5yB1XFs93X1SLnrAZfMDw4xbcp1s6+WAc3FN8wLGBhwIG8+uqrJBIJ7rnnHvbu3cv27dvJKc4ZNZrpv9LP3r172bZtG8899xy1tbWsW7fOMyVGKlNwXlN5vX29RKJ2P5WKwirKxJjeDupa9O+mikNz60cmc1CBZ/vRyCkCff3w5KFhfamumM/6Dh/PnYpwx7Iw1RVh20ZSOH0gkE+sZCUUX3JfV8NwpriamlgzLf1dlOYG2DRrCVvjHdQ4AQvJDsQYw6FDh9iyZQtLlixh+/bt7PrpLqIro1wpuEIsEeNU+ymOnTxG4GiAnffvpLq6GmMM+/fvZ+3atYjIhHXxvKbyumJdE3Z+iqJYpreDSlX/bqoIuiblayIehYtHoekwFFVA61sQOW8j7IJFtp+zx/jyS8XhFlbAlXpbd6D93HwCvVFac8LDPxN/kPqmVg6d7eGOZWEOne1kcWGC6vLyYaO/6GOPEZpdDEtXua6rnZm7iH39bYRDxZTho5ME+2JtbJ1V4Rqw0NjYSF9fH9XVNkSjurqa4Jog3Qe68d/kJzg3SOJygsSRBMGNQXKKc9h1bBfNXc10dnVy6NghNqycuHyR216qATkmFYVVlPQwvR1UqiOO6yXoOtKJtBx3V4yI9UDbaVuWXwQ97dZhLbnLu91UHG7xUnjt34a3f+klKkvv5mBTPwZBnM+kvqWLPUc77bReRZjFhQn2vN7J9kW3Dkb3GWOoq6tj1apVMLfKdaNyzREf4ROPUSh+8OdT2BeDeJSaJTe5pnw/d+4cy5YtGzbdeJzjhFaGKDhaQLwyTv65fDpXdnImfgZOQTgQprygnIayBp564ylK55dO2IG47aVq7Gjk1opbdR+UoqSJ6R0kkaounNf+o84LmekfDDmRWKd1IrFOOPVbyMm1gQMi9pg/G5oPw8JbrfPojdjjwlut83Ij2eEmByYMhHyP5EodLNps24067YfKWJDXgT9HqL8cBaC+08+eo3G2f/A9VJfPttN95bPZ/sH3sOfxF6mvrwfg9OnT+P1+FixwRF7nLoWNfwB3/bk9zl1KS2gOBSs+YNehelvBH6RgxQdoCc1x7eKArFIyBkPf7D7ilXH8b/mJV8bpm91He7R9mOZeMBAkjzxqmmpSv08jcNtLtbZsLbUXa3UflKKkiek9gkpV/y6TadzBfbrNbdSWkwtdl6AgKfLLYEdSxdXDRz+m33tEONYI0muNa85iKF6S1L5Bui6yftFqnj/ZDsaw99XLbF9bQvXNtwG3DVatBraH57Nnzx62bdvG888/z4YNG0YnNUyidFYpnXkhCss+MVjWGevA19fLrmO7Ro1Cuvq7OHXhFG++8uZg+TtK3sHrJ17Hd85H36I+fOd8xIIxigqLKPAXDLab6EuQX5BPS3eLZ3/Gi9deqqfPPs2yOcs4fuX40NTfrFLdB6Uo18D0HkF5hWt7Tdctfbd1YMlKCj2ttnyiuI2UXnkEWo6MHrXNXQbR9tGKEfNWpDYi9BpB5vjc+yK5o+sXVUKOjzXzEvhy4Imjl9m2PEH1xve5vmV1dTXbtm3jiSeewO/3s3r16jE/FreQ74ZIAxe7L44ahbzY+CJH4kfoaOqgdFbpYPnCvoWU15XTeWMnlysv03ljJ+V15azxrxkM+TbG0NXUhSkyaQn5HthLlUxnXyfdfd2cuHKCaCJKOC9MNBHlxJUTnGw9OeH3VJSZxvQeQUFqWW9TEXRNFa/1rbazo0dt824YcpLJihE3fcjue4LxjQi9RpC+oHtf4j1wvhYunbROK68ASpbD5gfxXaljx4pOdp/w81xbCaYNlhQbz82xoVCI+++/f5iCgxtuId/z8ucR9AdHhXDvq9vHjeU3cvHIRbpbuiksL6S3pZfaA7W89973cib3jB1xVZWyaMUinnnsGatGXglcBuMz9IZ6U9rv5MWmik3sO7UPGB5OHvKHMBiCuTZbTTA3SDQeTZuOoKLMJKa/g0qVVBxaKnhNt+XPGdw3NOhEJAfu/JJdE+q8YB3lQPTdnIXjd6BeDrf2J+5rbRfesM7JxCE3YI+XnF/+G/+APOAjdyWora1l//799PX1sXTpUgKBANFolLq6Ovx+Pxs2bGD16tWjnZNHROHIqLdvvvLNYVNzMKTGsKF8A4nlCS69eQkMXDlwhVlrZ7Hp7ZvYxHDHUxYqY9dPd0EAmt5oomR5Ce9b/r60TLV57aV65M1HaOxqpDfeO6iC0U//MBUMRVHGh3gJak4l1q9fbw4duraUElOGA9+xo5LkkVJvux2lDKxFjXRGk92XN/ZZcdhZSQEK3a0QLIT7vz+sCWMMjW++xLkjNcS6IuSFwlTetIkFb7vFfc0pOaJwpHzTCFt3HdtFV7xrmBRRR6yDo5ePsnLuSgpyCzj77FkS0QQFbyugpLKEqoIq9tXto7mrmbJQGVuXbmXzgs2cPn2aJ554glAoxAMPPHDVEd1E2XVsF40dja7h5xPV+VOU6YqIvGyMGaV6rSOoyWKsgI1MjdrG6kvyPqvcAOSXAMauT10+Zde9/PkQKoWO86OakCunqWr6NVXz50Cg0trT9GuomOduSwoh/F7TZ1uXbuVA8wEAFty2gDMvnKH1SCuFuYU8dOohwoEwFaEKIrEID9U+xOXGy1w+dnnc043pYFPFJvZ17fNUwVAUZfyog5os0rW+5bXxNlUFDBEnj5RzFLGjuYvHrOxQ3ixI9Nnn81aMvj7VPWMp7EkbS4qosrBycI/RojsWUXylmBdqXmBJYgmU2HWmkkQJJZdKOOg7yH3vvs99ujFDpENGSVEUizqoyWSiIyWvjbfV77LBE+PdkFv3tHVCsU6rIO7Pt88R6I9bxyS59tgfh6LFo9tIdRP0GCH8Xhtb3b7U3cp/1P4jKhOV5HTmIHGhP6+f/pX9nPOdY926da7dyeRmWlWSUJT0ML3DzKcbXhtvX30ktQ25LUdsQEQ8ajcAx6P2eawDbvgA5DqbZnOD9vmsotFtFFZA3bPw3N/B/q/aY92z3iHvHiH8Z8pumPDG1rKCMtry20hUJYhXx0lUJWjLb6OsoMy1viYVVJTsQB1UNuGldBE5n5oCRk8riM+OnHCUKsRnz4vmw7pPwG0P2mPRfHen0xuBuicg1m3fK9Ztn/dG3N/TY09aTc/5YWoPhXmFhAPhlNQeti7dSiQWob23HdNvaO9tJxKza1ZuJCuRX+t7KoqSeXSKL5vwmiYbmNYbrwJGcPZQ6vjcoFWoIGH3PI0Mee9phfKbbeRf8vrWkZ/bOvGos1fLb58f+Tnc8d/d39dlirPlzGP4c/wcunJoMOqtOlxNV6xr3B/L5gWbAbtPqqmribJQGR9b+bHB8pG0dLeQm5M7TO1hcXhxSu+pKErmUQeVTXhFAq75eGobeMveBnmhJNXysJU4mrN4KOR9IJCj/Gb39a22s+DLhbx8kAIwCUjEXSP+BnEJ5PCJj2cbnqWPPhL9CVp6WjjbfpbbF9ye0kezecFmT4c0Ep/4OHDhAEWBIgrzCokmohy4cIANZRNXOVcUJX2og8omxooETGUD74CjK1813KElSzoN7I87W+MerUe/dUh+q5iA5EKs10b/ueGRQqQtHORS7yVCeSGCOUF6+3tpj7XT1ts24Y9rPAjeOoHXE1VEVxR1UNmHVyRgOiSdYHSU4OmnYOndw6cPA4UQLIbuizYFiD8Ifb3Q32ednhuv7XZNIdLQE2PxnMV0xjvpjfeSn5vPvOA8jrcedxWLTQcJk+CW8luoj9QTiUUozCvklvJb6OvvS0v7E2UgiCMcCFMWKqOzr5N9p/axddlWdVLKjEId1ExlvCnlQ/Nsmo/C9wzVi3ZA5Wro74dzh+zzvAJYdBtUe0zNnTtkIwb9+fa5Px8wmOgpDMPVTLr7urnSe2Uwyi7dX9Cls0pp7GwcVtYV72JBwYIJt50OvNLJqyK6MtPQKD5lCLcowYqbofPiaIX3NR+3DqfiZqhcb4/5s8dWfh+pqmVgIbmciZyhJ95DMCdIT7yHtyJvMTc4N2NRdlUFVbzS/AqRaIRCfyGRaIRXml+hqqAqLe1PlJbuFlctwnSkCVGUbEIdlDKEW3qO3ADMXw1Nr8Hh3fZY/S675mUMCEOPsXQdq9YPRQ4mpRCZHV5ISX4JuZJLb6KXXMklkBugKDB871U6v6AbOhtYWzoi2WDpWho6G9LS/kTxSuWRjjQhipJNZGyKT0SCwHNAwHmfPcaYr4rID4A7gYH8A580xtRmqh9KCrhFCV4+bWWQKm6Gxe+0ZfXPwNkgzF0CwTVD1/e2e0sdrdoBkQvQdXFYCpHE3LncGSqlPlI/GPJdFiujN9E77PKrfUGnElTQ0t1CVbiKhUXDkw02dzWP+6PKJF5ahHdX3X2de6Yok0sm16CiwF3GmE4R8QMviMivndf+xBizJ4PvrVwLbsETRRWQmz86iq/+ebjx/cOvH0vqaO5SuO3zo1TbSy8eGrUeNDd/Lhe6LtAR6xj1Be3miICUggoGRijJaulTaYSien6KYsmYgzI2j8fAPIXfeUz93B4znZHBE09+HUIuKhWQ2uZgt7aBqp5mHq17lHBemHBemEg0QiQWYfuy7cRMbNgXNLg7orycvJSCCrJhhKJ6foqS4TUoEfGJSC3QAuw3xrzkvPRXInJYRP63iAQy2Qdlgnilja9a76qtN2aQhAte60ExE2PnjTv53NrPsfPGnSwqWuQpUfT6pddTCioYGKGEckM0dzUTyg1pCLeiTEEyGmZujEkAq0VkNrBPRN4OfBm4AOQB3wb+FPjayGtF5NPApwEWLlw48mVlsvBSr1j7cWg9a4VqI+ftvqk1HurpA7goSaSyHtTS3UJZaLgA7IBjSnXKLh0jFN1MqyiZZVKi+IwxbcAzwPuMMU3GEgW+D2z0uObbxpj1xpj18+bNm4xuziwu19l9T09+3R4v17nX8xB5BWywRMXN8I4d9lj/jHc7A6lCYp3WmcU64ZVHKDUy7og1r+i2VSWriEQjdMQ6MMbQEevIeJJAVURXlMyTySi+eUCfMaZNRPKBe4BviEiFMaZJbF7wDwFvZKoPigdeeaW88keNd1MveEfxeSQ43NTdwz7iwNXXgzwz7S6zquWTGVSgm2kVJfNkcoqvAvihiPiwI7XdxphfishTjvMSoBb4TAb7oLiRajZcN1JNWOhRf1FHE1uX7RiXc7ladNtkOgav6capEqquKNOBTEbxHQbWuJTflan3VMbJWM5lvKnjx8iQ68oY9VNZD/KqO9nrQVM9VF1RpgOqJDET8YrMw+e6TuS6ruSRIdczii/V+ilwPdaDNlVsmvR1L0WZaaiDmol4OYscxp863it4wmuKMNX6KXA9MuRqqLqiZB5VM5+JeKXbqP2J+6bcsdQhUnEwqdYfJ9drPUg30ypKZlEHNVNxcxapriuliYmuH+l6kKJMT3SKTxkig+tEXqRj/UjXgxRleqIOShkig+tEXqRj/UjXgxRleqJTfJPJeEO4rycZWifyIl3rR7oepCjTDx1BTRYeUj+e0kAzBE3OpyiKF+qgJotk9YarhXDPIHT9SFEUL9RBTRYdTUN5lAYIFNrkfTMYXT9SFMULXYOaLK5TCHc2oOtHiqK4oSOoyeI6hHAriqJkM+qgJovrEMKtKIqSzegU32QyySHciqIo2Yw6KCX9ZMN+L0VRpjw6xaekF93vpShKmlAHpaQX3e+lKEqaUAelpBfd76UoSppQB6WkF69svbrfS1GUFFEHpaQX3e+lKEqaUAelpBfd76UoSprQMHMl/eh+L0VR0oCOoBRFUZQpiTooRVEUZUqiDkpRFEWZkqiDUhRFUaYk6qAURVGUKYk6KEVRFGVKIsaY692HqyIiF4EzI4pLgEvXoTuTzUyxE2aOrWrn9ELtnDiLjDHzRhZmhYNyQ0QOGWPWX+9+ZJqZYifMHFvVzumF2pk5dIpPURRFmZKog1IURVGmJNnsoL59vTswScwUO2Hm2Kp2Ti/UzgyRtWtQiqIoyvQmm0dQiqIoyjRGHZSiKIoyJZmyDkpEviciLSLyRlLZLhGpdR5viUht0mtfFpFTInJcRN57fXqdOh52rhaRGsfOQyKy0SkXEfm/jp2HRWTt9et5anjYebOI/E5EXheRX4hIOOm1bL2fVSLytIgcFZE3ReRBp7xYRPaLyEnnOMcpz8p7Ooad9zvP+0Vk/Yhrsu6ejmHn34rIMeee7ROR2UnXTCc7v+7YWCsij4vIfKd8cv5ujTFT8gHcAawF3vB4/e+Bv3DoEbw+AAAHcUlEQVTObwJeAwJANVAH+K63DddqJ/A48J+c8/cDzySd/xoQYBPw0vXu/wTtPAjc6Zx/Cvj6NLifFcBa57wQOOHY8zfAl5zyLwHfyOZ7OoadK4EbgGeA9Un1s/KejmHnFiDXKf9G0v2cbnaGk+p8HnjYOZ+Uv9spO4IyxjwHXHF7TUQE2AH8m1N0H/DvxpioMaYeOAVsnJSOThAPOw0wMJooAs475/cBjxhLDTBbRComp6cTw8POG4DnnPP9wDbnPJvvZ5Mx5hXnvAM4ClRibfqhU+2HwIec86y8p152GmOOGmOOu1ySlfd0DDsfN8bEnWo1wALnfLrZGUmqFsJ+N8Ek/d1OWQd1FW4Hmo0xJ53nlUBD0uuNTlm28gXgb0WkAfg74MtO+XSz8w3gXuf8fqDKOZ8WdorIYmAN8BJQZoxpAvtlAJQ61bLe1hF2ejGd7fwUdjQB09BOEfkr57voo8BfONUmxc5sdVAfYWj0BHaYOZJsjp//r8AXjTFVwBeB7zrl083OTwH/TURexk4rxJzyrLdTRAqAvcAXRvwKHVXVpSxrbJ3pdorIV4A48OOBIpfLs9pOY8xXnO+iHwOfHajqcnna7cw6ByUiucCHgV1JxY0M/foGO9w+T/byCeBnzvlPGZoimFZ2GmOOGWO2GGPWYX9w1DkvZbWdIuLH/pP/2BgzcB+bB6ZAnGOLU561tnrY6cW0s1NEPgF8EPiocRZmmIZ2JvEThqbhJ8XOrHNQwD3AMWNMY1LZo8ADIhIQkWpgOXDguvQuPZwH7nTO7wIGpjIfBT7uRNBsAtoHpo2yEREpdY45wJ8DDzsvZe39dNZHvwscNcb8Q9JLj2J/eOAcf55UnnX3dAw7vcjKe+plp4i8D/hT4F5jTHfSJdPNzuVJ1e4Fjjnnk/N3e72jR7we2F/UTUAf1lv/vlP+A+AzLvW/gv0FfhwnAi4bHm52Au8EXsZGA70ErHPqCvCQY+frJEVJTfWHh50PYqOFTgB/jaNskuX3853YqY7DQK3zeD8wF3gS+2PjSaA4m+/pGHZude5vFGgGfpvN93QMO09h12AGyh6epnbuxa4VHwZ+gQ2cmLS/W5U6UhRFUaYk2TjFpyiKoswA1EEpiqIoUxJ1UIqiKMqURB2UoiiKMiVRB6UoiqJMSdRBKdMGEUnIkNp9rYgsFpF3icgvndfvFZEvTXKffiAi2zPY/moReX/S878UkT8ex3UiIk9JkoJ8Gvv07yP2zyjKNaEOSplO9BhjVic93kp+0RjzqDHmrzPZARHxZbJ9F1Zj96ukyvuB18zY8kTXyr8A/yMD7SozDHVQyoxBRD4pIv/knP9ARB4WkedF5ISIfDCpzs9F5DdOPp+vJl3/n0XkgDM6+9aAMxKRThH5moi8BNw6zr78iYgcdHLp/E+nbLGTj+f/OTl5HheRfOe1DU7d34nNRfSGiOQBXwN2On3a6TR/k4g8IyKnReTzHl34KI6ahfO+x0TkO067PxaRe0TkP8TmrxrIR/aXIvJDp19viciHReRvxObz+o0jlQPwPHCPI0umKNeMOihlOpGfNL23bxz1F2MlpT4APCwiQad8I/YLfDVwv4isF5GVwE7gNmPMaiDh1AGbhuANY8wtxpgXrvamIrIFK4Gz0XmPdSJyh/PycuAhY8zbgDaGtM++j1VQudV5b4wxMay69C5nxDigT3kj8F6n/a8mOY5kbsOqlQywDPhH4B3O9b+HVRf4Y+DPkuotdT6v+4AfAU8bY1YBPU45xph+rNLCzVf7LBRlLPQXjjKd6HGcx3jZ7XyZnhSR09gvZoD9xpjLACLyM+wXdRxYBxy0smXkMyT4msBKwoyXLc7jVed5AdYxnQXqjTEDmaJfBhaLzdZaaIx50Sn/CVak1ItfGWOiQFREWoAyrPxQMsXG5v0ZoN4Y8zqAiLwJPGmMMSLyOtaRD/BrY0yfU+4DfuOUj6zXAsxnuBNUlJRQB6XMZEbqfJkxygX4oTHmy4ym1xiTSOF9BfhfxphvDSu0eXiiSUUJrCN0S20wFiPbcPs/j4tIjuOgR17Tn/S8f8T1UbCjJBHpM0NaaSPrBbGjKkW5ZnSKT5nJ3C8iOSKyFFiCFfcEeI+IFDvrPx8C/gMr8LpdhhTYi0Vk0TW+72+BT4nNvYOIVA6064YxphXocFSjAR5IerkDm0srVY5jbc4UK4A3M9i+MgNQB6XMZI4Dz2KzoX7GGNPrlL8A/CtW0XmvMeaQMeYINiXI4yJyGJuifrwprr8lIo3O43fGmMex03S/c6bK9nB1J/P7wLdF5HfYEVW7U/40NigiOUhiPPwKeFcK9ceNiJRhp1unfNoQZWqjaubKjEREfgD80hizZ0T5J7GpAz7rdt31QkQKjDGdzvmXgApjzIMTaK8CeMQY85509TGp7S8CEWPMd69aWVHGQNegFCU7+ICIfBn7P3sG+OREGjPGNDnh7OEM7IVqw45AFWVC6AhKURRFmZLoGpSiKIoyJVEHpSiKokxJ1EEpiqIoUxJ1UIqiKMqURB2UoiiKMiX5/7o/ZTGqNcdaAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(data, var1, var2, 'labels')\n", "plot_centers(centers, color='gray')\n", "plot_centers(new_centers, color='C3')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The k-means algorithm\n", "\n", "Now here's the whole algorithm in one function." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "def k_means(data, features, k):\n", " \"\"\"Cluster by k means.\n", " \n", " data: DataFrame\n", " features: list of string column names\n", " k: number of clusters\n", " \n", " returns: array of centers\n", " \"\"\"\n", " M = data[features].to_numpy()\n", " centers = choose_random_start(M, k)\n", "\n", " for i in range(15):\n", " data['labels'] = compute_labels(M, centers)\n", " centers = compute_new_centers(data, features)\n", "\n", " return centers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's what the results look like after 15 iterations." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "centers = k_means(data, features, 3)\n", "scatterplot(data, var1, var2, 'labels')\n", "plot_centers(centers, color='C3')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results are (as far as I can see) identical to what we got from the scikit-learn implementation." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "kmeans = KMeans(n_clusters=3).fit(M)\n", "data['labels'] = kmeans.labels_\n", "\n", "scatterplot(data, var1, var2, 'labels')\n", "plot_centers(kmeans.cluster_centers_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Animation\n", "\n", "Here's an animation that shows the algorithm in action." ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "image/png": 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pA6tDe11UmxyxgRAgYeQTIPX/+1MtPU+XcjAJLBQXiESWIfc191FZaGfN0vzRc05vcNZEEvEEqP8TQlwvpfx9ymejmDMk5cM/ScRayrMYLLiD7tHgCeAOuinOLo5/8L5maHkOyq6Aqm3aB3rLc9rftTw3M7Va87NQWA1L1l44l2orotkIIKlswpgipiOnTkdAm+17pntvVzwBqgloHNkPFSRqOSmlI6UzU2Q0xdnFM//wTxKxsjlf0IfT7wS04OkOunH6nVxbcW38g8cSFbz6My1ozURsMJ16UDKytjkYQFJNonLqdOwPSsc90y2SiKcGdQ+wGciWUjqklLkqOCkayhpw+p24Ai6klLgCLpx+Jw1lDbM+l57hHnLM4/+D5phzCMswO+t2YjfZ6fZ0YzfZpxRIHOg4wOef/zwfeuJDfP75z3Og40BsqyPn2ZlbICVaD0q1RHwBk6icOh22Rum4Z7rbjcSTQZ0C3pBS+fQrLlCZV8nOup00dTXR7emmOLuYayuuTUv9aapsrjKvMq45Heg4wHde+w4Oi4MyexnOgJPvvPYdsFWzRU+VFl3Wm4larXYH7P8WeHoh5Nc2BNsXw9a79K9vfhYiYTh3ZLztUqa5k89BJ4lEM4VkLX0lsmQX654nupw82NSWEuuidLcbiSdAdQHPCSH+D/BHTyqZuSLeD/9U01DWwANvPEB/oJ9AOIDFaKHQUsjtq2+Pe4zG5kYcFgd5IwEnemwM97HFa9QuGisqWPehC7WomYgNEunX1P0mDLaC2Q62fE3y3vMmBIcTu2cqmaNOEonKr5Ox9JXokp3ePd/q89DSN8zSguyUWRelc29XPAGqZeTLMvKlUGQeAk0FF/1KUAzX7emmzF427pzD4qDL0wWbYogKCpYlJjaYmFkM90JWHgQ9EAqAKUt7HSsj8g0CRjBnaa/NWRD0aYExU0j1RuAESGWmkGhA05tLonWvbbVF/HDvGfo8AfzBMFazkX63n/UVBXPGuihRLhqgpJT/PBsTUSimS1NXExWOClYuWjl6zhVwJSR5L7GX4Aw4RzMnAGfASYm9hDaTiSZHLj0mL8XZuTSYTFRCYmIDvczi+BNgyoacxZCVrwWbc2/EzoiyCrRNwkEvmG3a9TIM2YXxzWE2yBAniVRnCokEtJZe97jNrie7XbzZOYTJILisbHw5P7pMqBfQYCTBliBGtiUM+0PYbUbdMfRItyovUeJxkqgH/haoZLyThNobpcgIkiF531m7U6s5oWVOzoATZ8DJ9cuuj+1GEQrFX2vRyywiEfAPapkYXMiIhvv16zjFK8Fi1wQaviFtT1ZhNeSnf5l1lAxxkphOppCohDvegPbo4U5az3vIy7aQl2XGF4rQet6DzWygvCB70jKhyYBucLWaBFVFdi4vv7An6bkTPbzZ5eLq3KxxY2SqdVGixLPE9z/A54EjgHIuVySdmVomJUPyvqV8C6DVoro8XZTYS7htxW20u9v1NySf/g2V/b3x11piZhZntYwoaqNEGDDo13Gqr4ahds20dmzdK5NcGjKkB1WimUIqJdyH2wdxZJvJMmuZTpbZiMw2M+AOMOgNjs4tukxoNQnd4PrimfOsq8jnaJcTpy+Iw2amzGHlSKcTpzcYt3VRpjuujyWeANUrpXxsOoMLIVoBF9r/upCUsl4IUQjsRvP2awV2SSkzaBFdMZskwy+voayBxtONwAz2OwFLc5dSX1I/GiiX5i7l5Z6X9bOz1n2Qf3n8tRa9zCK7EEwWTb3nGwKbQ2uE6OzUr+P0N2e+S0OGOEkkminsa+4jEolw9Jz2Ye/IMlOaa01SxiUQE7QvQkK21aS7TPjIK534gqFxgahmUTbDgTBNZ/q1TMymZWInut2sXuoYtS66WO1sOqq8jG5YCPyjEOJHwDOMV/H9Ks577JBSnh/z+kvAM1LKrwohvjTy+ovxTlgxv0iGZVIyJO8Ju1GEw5o0vHXfBcn3oku1vUl66GUW9sWQvQiKasZnG1kF+nusXF1zY5NtMuY4Q6l6opnCiS4nbX3D2K0m8rLM+IMRjnW58AbCutcnknGtq8jjxTP9CMAeHkJ6+jH5/axc5MDkK+PPNi1DjLG4MhqYFIiazvQjkEit+qR54qHpgQrtFm5riP/feqylyVh1L7362Z9fVZMxVkcfAS4DzFxY4pNAvAFqIu8Frh7580+B51ABasGSLMukRCXvE5cV+7x9iblRZC2Blhe0YBIVOLS8ANUxXM71MovofqeJ2UbzsxlRx0kbSZCqJ5opDHqDGA0C28gynM1sxBcMMzCyBDeRRGpc71pdAvt/R1Hzq5gDAbzZBTjLKymtyuXRRx/FbDZTX1/PunXrMBqNo4FnYiCSUrC1rpDm88MMjWR5W2oLCerH0ISIFXCH/UHd+tmjhzu5+7rlM7/xRYgnQF0hpVwzzfEl8HshhAR+IKX8IVAipewCkFJ2CSF0CwVCiE8CnwRYtmzZNG+vyHSSZZmUSB1LL1s6cPYAW5duHTePHHMOnoBHPzsb+sWFAccu30xVpY2VWeidy4A6TtpIg1Q9z2ZmyBvEGwxjMxnwhSKEpSTPZta9Pp4alwwGOb9nD0M/+CHbg0EGVq1nOL+cUhmg9MWnsby+n/xbP0j/unXse/FFjh8/zq5duwhFYEvt5ED0yltDePzjo5HHH6aiyD7j548VcJ8+do6axTmT6meH2wdnfM94iMuLTwixUkp5dBrjb5VSnh0JQk8JIY7H+8aRYPZDgPr6euViMU9JRv0o0TqW3rJiUVYRxweOsy37QgY0pRuFDEHVdug7daF+VLVdOx+LeJetMqSOkzaSIFWPJe2OtTR12RIHdouRcy4/Tl+QXJuZyoJcKhbpf/hfrMYV8Xhov+vTdHd00Lp9G1d+5CNcWVc3eq2MRPC8+CJ93/8BlqefYfvdn+GZ/fvZs2cPxTVb6ej3XvjFR4LHF6aqMIuDrQMjgcSEczjIW33DbK9bFPf3JRbdQz7MRmhquVCDq12UTSAU0a2fJadj58WJx4tvG3BYCHFCCPG6EOKIEOL1eAaXUp4dOfYAjcBGoFsIUQYwcuyZ3tQV84Fo/Shevzw9Eu37pOfdt6JwBX3evvi9BXPLtL1IVdvgshu1o9mWPB+9olrY+HG45u+0YzQ49TXDwR/BM1/WjvPRhy8JPaui0m4hBHlZZoQQo0tTLb1uHmxq4+u/O8GDTW209LrZVluEwWhgZZmDa1eUsLLMgcFoiOk5N5VHnQwG6fj0Z3B1dtKxuYH6j32MXzU20tLSMvp+YTCQs3UrRX/x/xg+d46Ouz7NtVdfTSgUwjLQxsG2AS1Q2Ew4vUEOtg0ggY2V2qZc10hw3FhZQOuAdzrf5XGYDHCguZ9AMEJelplAMMKB5n7KHDYGvUF8wTASiS8YZtAbZF1F3sUHTQLxZFDvmM7AQgg7YJBSukb+fD3wL8BjwIeBr44cfz2d8RXzh5laJiVaxyrOLqbd1U7PcA+ugItcSy7F2cVsKdsyGigvKrRIVE6djGWrOWojlDBJkKrHkna/2NyHPyR1xQ2J1Kxi1bgAnvz6f5FzbpATK1az+fH/o+Qdf8LNN9/Mww8/zM0330x1dTUAnqaXaP/M3TRt2czmzrMUvnqY7du3s+fRx9mw/Fq63QEtSGWbubQkhxPdLq5bWUrVmDlFpEzKJttozUuOvIi+Xl6aSyAi6fMEGBwOYDUbqVls571rl874nvEQM0AJIXKklG4pZcwWqdFrYvx1CVqbjuh9fiGlfFII8UdgjxDiY8BbwAemP32FIvE6VkVOBY81P4bD4tA25fqddLg6+NQVnxrdD3VREl2GS4bDQgbZCCWNWMueM17i1Jd29w8HY4obbmuonJEyraN/mP3NfVz79G9offcuzgUGOPBnn8Pw6c+w7Jv3jQtSxd09vHXXXby4dSs77rqTxWfP0vO1/6T6AzcTDAVZYhymuvrCL10RKTnR7U7KJls9tV44Ag01hZw5Pzy6xNlQU0goAjetX5qRMvNfCyEOo2U4L0spPQBCiBpgB7AL+C/gYb03SynPAFfonO8DEtugolBMQaJ1rHZ3O+uL19Pj1TIoh9VBXX4d7e72xG6ciJw6GQ4LGWIjdFHirbX1NcO+b4L3vCbZ7z0GXa/Dtk/PWKq+riKPZ0/0EgxHCIYlZqPAbDRQkGXWbasxHRfyiaq3H+5rYau3E1MoSE9JMTk+O+HqKznh+GuMd9/N0nvv5eabb+bZb93Ppr17eWn7dnbcdSfV1dXIykoiPi++w6+RW1yOs6+H7MILAcrtC7GuIk93Y28im2xjqfWsJoHNbKKh5sKSptMbxG4zpdUsNmYNSkp5Ldrepz8H3hRCDAkh+oCfA6XAh6WUusFJoZhNEq1j9Qz3UOGooL60nh3LdlBfWk+Fo4Ke4RSWQ2t3aMtUviGQEe2YqAtEEmozKSeRWttre7TNxxjAVqAd+5u18zPkymUFBEIRguEISEkwHCEQirCyLBe3b7yQZTpZiF5vplAkgvHkMZyX1xOJhDGYtGB4eslyDP/07zTf+WmO3PcAVz7/As9v3ED1e949utwnDAZytm3H98YRKhflMezzTapvvXftUm6pLx/dlGu3mRJ2uojVU0pAWvs+xWLKGpSU8gngiVmai0IxbRKpY6WlG3Aylq3SZSOUyKbZ5me1ADy2Z5Vjif4yZOchbQ/ZWHd2JJw9NOMptw542V63iHMuP66RJavSXCtZVuOMsxDQl5kvyrEScnuIFGVjMJkJDvtw+0IYDfBjVyGXXrGDht/t4Y3Vl9O15iqcB/9IVVXVaJAy5OQQ8XiwLYqwvmoxfTHcIWaSzcSSx7v9obT2fYpFPCIJhWLWmak/31QkyxopYWbqsJAO+Xmiwoyeo9DfopnaxuPQPnEDidQ5Nw26h3wsW2TXFRQkw+qnJM/GW+c9o7J0h81MlslAwGoj5HZjdSxioO0Y3pI1+AIhIq8c4oqXn+KNNZdTe7qZQ5cNk7e2YZxwIuJ2YywspLm5mfe9731UVFTM/Bsxgank8Yk4TMxW4IpHZq5QzCrRfU2ekIcSewmekIfG0420DcXU6yREMqTtaWe2GlyPFWYIg3bMKtDO6+EdABHtWSW0ozBqDu0TqajXelwFvYDUjr5B7fwM5fTRD+KxjP0gvq2hkr+6YflFhRHRmo3HF6I0z4ZnpGZjM8De0+c51jVEZ/8wx7qGONLppHbbBhYdfYUBacdoNHFVaYTIq69wy+Pf5cWtW3npTz7O07vuZtfj32foSMuocOJMczPufXvpLyzEbDZTXl6e0PPGS6It3GM9f0tvLG1cclEBSpFxJLqvaTpU5lVyy2W3cOf6O7nlslvmRnBKdC9VMnB16fsCus/pX2/LB8JasJEjQYewFtQmsmYXFNVpS4LeQe1YVAflDTN+zkQ/iGMRq2bzxJvnsJgMmI0GEJoAw2IycHpxNXn5OdyRP8h1b9tC928f4X2/vp8DW7bSsv5dhLIXc7Z6FY+//y9532Pfobi7h5tvvpnn77+fkNHI/vO9bNiwYZw3XzKJyuPjrWPFev59zX0pmd9E4lriE0IY0WTjY/tBvZWqSSkWNsny55t3pENmnqj6sGQVhANae3rfoBawSlZpvawmUlSr+RE2P6sFvJxSrb6VhOecjmu3HrFqNs29HlaUOsiyXPgI9QZC7G/uZ3nD9Zz993vpfe+t1DU+yoFrruOVqm2YzYXYpMQXinC0+BIqP/4Fcu++myX3fJ3NnWc5WVOD2WJh7dq1Cc0xURJR5aW7wWE8DQvvBP4R6Ga8WaxqWKhICWkRMSSTGTpxxyQdMvOphBl6z1lYC689NOLSXgveIeg9Dqtv1h9fry53+BdJec5kyKNj1WwsJgNyQpLjDgQ55/Tx1sZrueLlAyz9359w8LbPEbT7KXe+xcCwiSFTIRazkapFdq666h0sXltGx79/hYFIGNfGd/GBD3wAo9FIppDuBofxLPF9GlgupVwlpVwz8qWCkyJlNJQ14PQ747cdyiRSuQyXDpl5VJhhydEChCVHew36z/lWE1Rugaw88Du1Y+WWETl5nGSQnD7WUuGWmiKcw5q5rJQSbzBM54CPZYVZ5OZk0Xrn3yPz8lj17KNUGBki9YQAACAASURBVPLYeuUVLHGfoub8PlaEm9lo6qD15//F63//D/QFg1j+9m/54J/+KRaLZdafcSqStVQ6XYS8SLFVCPEscJ2UU7lgppb6+np56NDMpaeKuUMqVXwp5eCPtA/rsUtiviHtg33jx2c29lhF3dhsJh1WR7Ges2Wv5k0oxvzuKyNacLvm7+IbezrPmaqslfj6JFlMBjoGhrlhVQmLo+3XQyEK9/6Ogt8/RpE5gn3bNjwRibunB+ORIwirleyb3k/VRz+KIcMC01hmQ8UnhHhZSlk/6XysACWE+OzIH1cBy4HHGd+w8BtJneEUqAClSDYpC4DPfFnLKGbyAT0V0Q/isTWbdNgcxXrO409A9faZB+hEnrOvGfZ/Czy9miOFyQr2xbSv+BjP9eWl7IN14gd3n8uHzWwatxzm9AaxW43cZB3A98YRIh4PBrsd25o1ZK1dmzIxxFwjVoCaqgYVLQC8NfJlGfmCpOxUUCjSQzLazMcktwwGWsF5dvxG1fwkZX+z3FFXSon31cP4jrxO2OPBaLdjXbOGvmABZ4+24fe4sEaGWeowUF6yCFFRr2U7EN9m4liZTyLPeWQP9J3WMq7sAgj68J47Qcu5n+K59I6LdryNkmimMLHGFZVkw+RNwNmLq8hevy6+51GMEjNASSn/GUAI8QEp5f+O/TshhDJ4VcxZktFmPiZRkYCtQKu/eIe0gFVzzQxnPbvIYJDBR37FwEMPIX0+7Nu3I7Kz6Tp+nOD3vk/YIAiuKCK8qpwBcy5/7LBgbvdRv/4y1l25EWPr8xffTDwp8zmmOVBsvSuxINx+SFMLjnGk6AlmURk6SkccHW8hsRbusUiWclBxgXhk5n8N/G8c5xSKOUFKZez9zbBss/bh7BsRCRRfNiISSMB3L41EPB46Pv0ZZCBAyRe/QHZDA8FQiD179hAuKmTbXXdR8vwD9DU+j+g5T/nOMt5RWsCZyBL2nn6L432SXbs+dPGCv07mQ99p7fzVf53YpCeslPlCEcxS0nSmb9TpoWZRNm6/fik9kRbuU5GJbgxzmanabfwJcCOwVAjxrTF/5QDSJphQKGZKSmXsri4orB6fAURrUHOAaLO98MAAiz/3WexbthAOh9mzZw/Dw8O8/e1vp6amBtqscNPV9O7eS8f/+aj43GZqjQJh6uTpvmH27NnDrbfeOrVkWifzQUrtfCz0lgSX1sOp30MkAJEwGIzkBiLsYx3+UIQ8mxlfKELTmX421RTqDpvK/T7JyM4WKlPJzM8ChwAf8PKYr8eAG1I/NUU6aBtqY/fx3dz/yv3sPr47afZCmURKZewZJJGeDoOP/AoZCLD4c5/l7Of+Ck/TS7z66quEw2He/va388gjj9DS0oKnPcjZ7/yWxR98GzIYYvCFI7R0DfDICcHb3/52QqEQhw8fvvgNJ2oEhM65KLEk/PnLtM3BkZD2y0AkhDES5Lh5pTaUuNCML9bQU1kjzZR0uzHMZaaqQb0GvCaE+IWUMjiLc1KkiZSKB5JEMtR3US++pq6m+LrnJkK6HMeTgJSSgYceouSLX8C+ZQtL772Xzrvv5vQ1O9j+sY9RU1Mz2s9o8769LPtIA/a6AnjPJjoe/AO/CeRz87uvp7qmBiklTz31FOvXr4+tVFtaD237AAEmG4R8muVR5Tb962M6TDwNdddowhS/E6wOWk02tmUN8ajZwJA3iCPLzJbaQoJh/aG31RbFFDjMlO4hHyYDHO1yxrXcqLhAPDWoV4SY2JuSIbTs6l9HGhAq5gEpFQ8w8+AyFwJoWhzHk4T31cNIn4/sBi2TtDdswvw3f82Kv/8Hit/9bqipobi7h8379/Pitu3Ytt1Etf8YPQ4nbneA919aQ/UVWwGoqakhGAzS0dER25X7il3a98h7HnwDmjy8sFY7r0csJw3nWTCYtU3CfhdYcynMXosxZKNh+fgGfIU5+h95UwkcZlo/Mhqg6Uw/edmWuJYbFReIJ0D9HxAGfjHy+oNomfIQ8ACQ+b8aKuIileKBZASXqQJo9BhP8Et5oJtlKXiy8B15XVPrGS6s/HcvXoz3ox8h6+7PUnDrBxl46Jcs+9a3sJUU8/DDD1NfX8+hlgHee/UOCnwjmVJfM6L5WWqt/XS++AgV2TECdFGt1j033v1OsXwBQwE48YSWhVkdEPJRc/5Z3sjdjtMbjDsj0hM4JKN+NG55MY7lRsUF4glQW6WUW8e8PiKE2C+l3CqE+LNUTUwx+6RSPJCM7KxnuAezwcyh/kO4Ai5yLblUO6o56zpLl6cr7oCT6kxxrhL2eDDk2Med8/v9yNWrKbj1g5z/7vdYdMdfYG/YRDVQX1/PCy+8wFVXXUX+4deIeDzjpONWbz6BQK/2OpZ0PFYw1xNDxFo+9Q2CwQQmCwgBJgvGSIjlnOF1naZ/e0/0sPvlDrqGvJTlZXHLleVsX67/bzwZ6r5QBLbUFtJ8fjiu5UbFBeIJUDlCiE1SypcAhBAbgehPRi2iziNS2chvquxMb+kPJmdERmHkpXMvkWfNw2Fx4Av7eOncS2QZs6gvq4874Ci3dH2MdjuB/oFx56xWK96DBxl46JcsuuMvGHjol2Rv3ERPSTGHDh3iqquu4tChQyzt6WXRmtXjpON+QzZ24zSk41M1SdRbPn39f7U/Bz0QDoLRDDmlGL2Dk4bee6KHe54+RX6WmaX5WTi9Ie55+hSAbpBKVN0Xq7mhxxeioTq+5UbFBeL5Dn0c+G8hRA5aVuoEPi6EsANfSeXkFLNLouKBRGpKsbIzozBOWm574I0HQECFo2JcRjQcuNCVVY4xM3EH3eSYx/82O1XAmfNu6SnCtuZyBn7xEDISGV3mK+ntxfnfP2HJ979HTkMD2Rs38dZdd/Hi1q3cfLtWg6qsGqZ/z7MYN6yicEQ6Lk1ZNLttrCn3gil/aun4RKZqt1E7spdsrEWbfTH4og0RtfMBv5vzMm+00V50ae541xAWg6B/OMDZQS82ixGb0cDulzt0A1Qibt4tvW5+uPcMfZ4A/mCYkz1Gjp4d4sZVpew/o80v2QKM+c5FA5SU8o/AGiFEHpp339hfS/akbGbzkLlggFqZVxnXnBKt48TKziwGy6Tltv5AP0hYuWjl6DmAE/0n2Fi6kVZn6+gS38bSjbze+3pCASdtLd8znKx1axE2G8NNTdi3bMHT9BLBf/8Kx955I7nFxeQAPSXFvLh1K5v37aW4zgtXLKfYFSKQY+FXJ89wc6GR6kI447FiNkjKswLaOktwWDOYjcfMNZYYovtNGGqfnFlVboNDPwaDQNs5E4FQmNaKT0xamjt+zkmO1YzVZCTLbCQUlvT7A3gC+otBiaj7fn24kzO9HgqyLeRnW/AHI5zp9fDyWwPKYWKaxNMPygrcBFQBpqhkVEr5Lymd2TxjTijQEiDROk6s7Oyx5scmZT+BcGCS22P0GqvJSn3pBU9JV8DFmkVrcPqdo9eNDTixfinYWLKRxuZGuj3dlNhL2Fk7N38OyUQIQcGtt3L++z9AAmc/91csvfdenCYje/fuBeCRRx7h5rvupPiKHDq//RuW/GUxfY+9RMmf1HPzZbk8/NpybuIUe912NhS4ESEvOLvAYLywf2nskp1ekIolhvAOaHueJmZWrfu1cYd7R5f4hsxFZJvHB50cm4lQBCIRqXXCBcxGgTcQiimFT8S+6NX2IfKzzNjM2uZkm9lIfpaZV9uH+Mx1y1VAmgbxLPH9Gk2x9zJj3MwViTHfCvPTqePoZWfF2cW0u9rpGe4ZzYpC4RDZ5uxx17mD7piBaGfdToBJwQ/Q/aVgY8lGDnYfZEXRCjaUbsAddHOw+yBLc5fq/izmQuabLPJvej+up5+m955vsOSer2Nv2MS6cJjjx4/z9NNPc9NNN1FdXQ1nzCz51Lvo/eXzGB3Z5F+1hgKj4CZPD0+31WCXLtYO74WwHRBQeXX8HXJjiSGi7TfGYs2F8yehdDWYrxw9PdzdR0H/6+MudftClOXZ6PcEGA6EsFmM+AJh/OEIaxaPF4dMDzmpiaH2WnlrT5d4GhaWSylvkVJ+TUp5T/Qr5TObZ/QM9+jWSXqGe9I0o5kRreOMZTp1nIqcCl7pfgWn30muORen30m/rx+zwTzJ6eGdNe9kZ91O7CY73Z5u7Cb7lBno2F8KhBDkWnJxWB00NjcSjoQ50X+C59qf40T/CcKR8KhcfSzRzNcT8lBiL8ET8tB4unFeOmwACLOZ8m/eh7GggL7vfR/3/v0YhGDXrl1kZ2fzwgsvcPrUKdwtPvoa92N0ZFN+13vBaKD5bD8vdOdgtwg+sKwf46K6Cy7ulgnZgzVXk5brEatJYvFKzXi3dR8cf1w7DrRq8vIJMWCR3UwwIic12rv2smK21RVhNRsZGg5iNRvZVldEfbV+A76ozDxay/KM1LJaet2Trl1bkT+piaFzOMjaivzEfgiKUeLJoA4IIdZIKY+kfDbzmPlWmE9WHafd3c764vX0eLUMymF1UJdfhz/k51jfMd0luIkBKdbyqcvvYlH2Ik70nxjNzqocVbQNteEMOMkyZZFrycUf9nNy8CTDweFJ85tvmW88GOx2Kr73XQZ/1UjP1/6TiM9LzrbtXGfPpru1laHvf59+oxH/2hoCV67gjdMumnu8mEWYDUtMrK1YhDG77sKAp56C7tch97oL5y5m/6QnPx94S98pvuxybbOuEGC2QdCHPeKm8NLN2CfIzAF2H+rgnWtyx9WUYnWITURm/r61S+l2+un3BBjyBrGYDFQtsvO+tUvj+8YrJhFPR92jQB3QgrbEJwA5m23f50PDwrEfohOXp+bqB10ylr7uf+V+Suwl42oAfcN97Du7j2uWXRPX92r38d14Qp5xwd8VcPHHrj/iC/vIs+ZhNVrxh/0M+Yfo9/azJGcJeWNqHEO+IQSCt1W8bdzzPNb82KT5SSnp9nRz5/o7E3rWuchoP6ixzfZWr+H8oiLOnj5C4NwJLGE3S4uLKL/yBsRrD2muDn2nLvTDyi6Cs6/CZe+c3CEX4u+Ee/BHcPYwdL+h7X2y5UPJashfCs5zWtuOcACMFk3ZF2PvVSLOEF//3QlK82wYxvz8I1JybsjHTeuX6nbaVa7liTOdhoVR/iQF81lwpNT/LU3EUvzNVH5+rP8YRVlFM97XNBwaxjDS8VWM2befZcoiIiP4Qj5sRhu+sA9PwIM37B1dyotmYRaDZV5lvokihCC70kF2KACu85BrhkoHy4qWsWzZMuCdE95gglO/0wJFOATGLi1gFF0CXa9pmY5jCawbCU6x9jvpBameo+DshLxyWFSntedwdoLZqgWjOB0pYrXE0COWzNxkIKbDxG0Nc/f/dKYRj8y8TQixDbhESvkTIcRiLmzUVSRAvBLuuUwy5Od93j5WFa3i0LlD45bmPAGP7j1jLZ9mmbJYu3gtLc4WnAEnuZZcNpVu4rXe16grqKNnuGf0vNVkpSC7YFJQ9AV9CSsE5xVTbZrVCwC+AXB3a5ZDlmwIesHdqTmNr74JqrZpY7Q8Bx02rT3GuSMXsq3cstjiCe8ACOP49hxBHwz3a8t/bfsvBMDC5NhNxZKZW00iKf2jVJ+oqbmoSEII8Y/AF9GaFAKYgZ+nclKKuUssYYKeAAEuZJZjhQ8rC1dycvAk/rB/tEZ08NxBjEK/t1Cs9hmXL7oci8lCfWk9O5btoL60HovJwppFazAKI8sLl3N1xdUsL1yON+TlsoLLxo2bY84hLMO6wgxg/okn+pq1ZbRnvqwdo3ZD0U2zwqAdswq087HGyF0KfjcMtmlHo1XbBzVpjOeh502tm64tXzv2vKllSnrY8oGwFvSk1I6Ewe+Bp/4Ouo9qQaz7qPb6dIw5JkBUZh6tZdltJm6pLycc0QLWWHJsJroT6B+ViABjoRLPEt9OYB3wCoCU8qwQInfqt1xACGFEcz7vlFK+SwjxAPA2NOk6wO1SyjgaxyjmAsmQn3/31e+O/usQcVhqxlo+BXSFHHqy9C1LtmA1WceNG13K08t8dx/fPb/EE7EyJb8LSlaNv9aaG7sBY8AD3j7IzgfDYogEYaAdDAWTx/AOaAHLO6gFG3MWmLK083pefCWrwGIf6VY8BDYHFFRpIoyQT3ttNGt7oXxOeOm7UDfzLsZ6S4IleTbe6vNwzuXHOeKvV5prpaIofrl6srr4zmfiCVABKaWMttwYsThKhE8Dx9A68Ub5vJTy4QTHUcwBkqFWDMswm0o3TVqaC0ZityWLtXw6Vd1v7PXRpUmIT5U47/z8YtkLDb6lv2k2lgJvNHiJC1/CABM76/pdWjAaateCjjlLC1Ke81qg0QuW1Vdr15euGS+2CLg0ZZ9xpE5kNGvS9N6Tyfv+TKCqIItHXu4YCTAmnMNB3uobZnvdorjHSGUX3/lCPAFqjxDiB0C+EOITwEeBH8UzuBCiHK2K+m/AZ6c9S8WcIRny8+LsYjwhzyTHiAJTwRTv0ifeul+iIpb5tm0gpr1QVoEWBKKvL9aAMb9Cy15CHs281WjWzsmIlvWMHSN3MViytOwn6NOCVFaB5jyxrGFysOxv1jeLPfEkyBAwJgOWIW1/VIpoHfCysbKAcy4/Lp+WQV1anEPrgJftcY6RiM/fQiUekcTXhRDXoZnELgf+QUr5VJzj3wd8AZi4JPhvQoh/AJ4BviSlnORQIYT4JPBJYEQtpJgLJEOtmC6vvERELPPOzy+WvVDxSm15Ld4GjMUrtYxoTHdbHEs0wUR04210jAPfhsFWTYYe7agb9GjLhHqOEa4u/f1RVVfBySfQOvNmQcir1b4uvTGZ36FxdA/5WLbITtWYpbio/DxeUtnFd75w0X1Qum8a6Qd1kWveBdwopbxDCHE18FcjNagy4BxgAX4INF/M128+7INSJMZcUMjNhTnGzdga1MS9Somo4RIZ5+CPtI22ri4t67I5tEDp7ISyK8YHS9+QFuDGBstobQrg6X+B/tOa358lBwrr4Mrbtaxrwh6rRJVzetfva+7DMyH7cXqD2G2mhGTmSsWnEWsf1HQDVLuUMkYf59FrvgLchuZlbEOrQf1KSvlnY665mpHANdVYKkApFLNAVJgQT3fbZIwTK5hVX63J0OM9P3bDb/SehbW617ZX3cT/nLaQn2Uel7XE6pA7tqPu2Ou31hSy/0x/3OMopibZAeotKWXc624TMygpZZfQtubfC/iklF+a6v0qQCkU85RYwUzvfPOzWoakl1lt/Pj4cQ/+SPfaprMBDhffFHfm82BTW8xMKZpJLfTsJxkk7CQhhHh/rL8CsmYwl/8Z2ewrgMPA/5vBWApF0phXS3bJRE/yPVVmlcj1sVq+650//At9IYee5D2G6EMOvUHOssn7l2LVjqZS2iXiSKGYHlOJJGLIdAD4bSI3kVI+Bzw38udrEnmvQjEbzLd+XUkjUSeJRK9PhFhCDj3Je4xrRV5ZQso5pbRLLzEDlJTyI7M5EYUinSxE1/K4aH42MTuiqdq1zzRAxeoTpSd5j3Ht0nU38dxpbT9dPMo5pbRLL/H0g1Io5j3zrV9X0uh+MzE7IleXvkQ8Vu+nRIjVJyrWEqHOtRWXXK5rXRRrqS6W1ZFa2psd4tmoq1DMezJu422idZ9U4RsEdAxao5t3J5LIMtxUxHr+WDUrPRK5dgpi1ZqURDz1qAxKoSC24WxDWcPsTyZaxwm4tTpOwK297mue/blkFYAcMWhlxKBVhiG7UP/62h1a8PINXXCP8A5c2K8UDyl8/qkMWlt63TzY1MbXf3eCB5vapjRtVUavs0NcGZQQYgtQNfZ6KeXPUjQnhWLWyah+Xams4yRK8UoIBSY3CVy8InaWo2dHlMi8U/j8sQxaHz3ciT8kdfs76WVFyuh1drhogBJCPAjUoknCwyOnJaAC1AInHbLsVN4zGQ0Yk0IsX7xYDuKppLAWDv1E87YzWjQbobOvwrLNU6v1ZhJIUvj8sWTjL545z+aaRXEHHGX0OjvEs8RXD2yVUt4hpbxz5OuuVE9MkdlEZdmz2Q8pXfd84I0HONB1gKP9RznQdYAH3nggtX2fonWcsUynjpMMOprAZNXauAuDdjRZ4eijifWJSoQUPn9UNj4W7bVIqL9TrHGU/Dy5xBOg3gDS8D9Dkckk2phwLtyzbaiN3cd3c/8r97P7+G7ahtp4/MzjtLpaEQgcFgcCQaurlcfPPJ6Ue+qSjDpOsmg/pAWM4hVam4viFdrr8ydTp9abzvPrNVvUYVttEYPeIE5vkIiUOL1BBr1B1lXkJRRwYo2zrbZo2o+tmEw8NahFwFEhxEFg1HVcSvmelM1KkfGkox9SMu85cdmuIqeCg90HJ23UfbXnVQqsBdhGWjfYTDaQcOT8kaQ8ky7JqOMkk4k9IwWa+3h/y5jmgSP7owqqZn6/RJ8/gc3BUdn4vuY+zo2o76J7mhLZ7xRrHFV/Si7xBKh/SvUkFHOPdMiyk3VPPdeInx79KSX2Ero8XbgCLnItuRRnFTPoHyTfmj/u/ZLE/SsTJkkS6RmztB5OPwVhP4RDYDRpLdzLroC3XtQaBWblgXdIcyavTXK7kXi8QhMUVcSSjScacJTVUeqJpx/U80KISuASKeXTQohswHix9ynmNw1lDdz/yv20uFrwBr1kmbOozq3mzvV3pvSeyejBpOca4Qq46PJ0UZNfQ64lF3/Yz8nBk9gMNnqGewhGgoQjYYwGI2aDme1L421LN8dZ1gDHf6O5SQi0ICUlWPOgcsuFvk9ZeVCyQmtvwQyXIhO1S0qSqEIFnMwjHhXfJ9AaBxaiqfmWAt8H5mhntrlNphiadro6aXW2EpZhLAYL4UiYVmcrna7OlM0nWVJwvaXCsAwTjATHLeX5Q36yTFm4g25CaPWJkAxBGNYuXpuch8p0+puh9prJPZt6jsFlN0JhzYVrZSQ5SsNEZebJ2hysyDjiWeL7FLAReAlASnlKCDFH+1rPbTLJ0LSxuZHF2YvJG/OhMOQborG5kS3lW2Y8fqxAnEjX21joLRWahAmzwYwv5MNmtOEL+4jICFJINi/ZTI+3Z9zSX7u7faaPODdwdUFh9fjAICNagEpVUEg0I0rEo08xp4gnQPmllAGtfRMIIUwwG4vwCxu9D+hMMjTt9nRTZi8bd85hcdDlmflv0KkOxA1lDTzwxgP0B/oJhANYjBaMwsjaxWvxR/w4A05yLblU5FZweuA02eZs8F54f7Y5e+F49MXKTirqL9gdJTsoJJoRZZqoRJE04glQzwsh/gbIEkJcB9wB/Ca101rYxPqAdgfcXFp46bhrU62ci0WJvQRnwDkug3IGnJOWzuJhYjDu8/alPhALtF+zRr6Ks4sxGowsz18+rr5VkVPBwXMHybPmjdamDp47yIaSDYnfM1P89RIhVnYytovtxKAw0+ecTkaUKaISRVKJZx/Ul4Be4Ajw58ATwN+lclILnVj7fYYCQ7iD472+0mVourN2J86AkyHfEDIiGfIN4Qw42Vm7M6Fx9DbfHug6QCAUGHddMp3Fm7qaqHBUsK18G9dUXsO28m2sXLySxVmLsZvsdHu6sZvs7KzbSb7tgoJPTNJbJ0Am+eslwlQO4kW1Wifba/5OO0aD00yfMxHXcsW8Jh4VXwT4r5EvxSwQa7+Pw+zA6XeOvp6uii0ZROtMjc2NdHm6KLGXcNuK2xKuP+ktWxZlFXGs/xjbsreNXpfMQBzr++sJeLjlslvGnQ/LMJtKN9HibBld+ttUuolgJJiYYCWT/PUSJZHsJNH+Ucm4p2LeEo+K713Al4HKkesFIKWUjhTPbcESa7/PpYWXjtai0m5oihakZiqI0AsWlxVcxv7O/bgCrkmBOBkqxkT2UxVnF+MJeagvrR895wq4iAQjidXJMslfL5V0vwmDrWC2j/SP8mn9o4LD6Z6ZYg4STw3qPuD9wBEp49k1p5gpU+33SYaKLZPQCxZWk5UtS7aMLrdFAzGQFPGEnkii0FLI7atv171W72dhMVgSq5PFKvxj1Kx55lJdaioS7R+lUExBPDWoduANFZxmj+h+n4n1kPkUmACklNTIGnqP9dLxWgd9x/s433WeId+Q7j6jpHrxTRBJxCovxfpZhGU4sQ68ev5yfWc07zq9ek2c3nIZR6L9oxSKKYgng/oC8IQQ4nnGe/F9I2WzUsy7TGksoVCI1/fsofO55xE+H/XFhZwty6ZzUQ6RUxKrxcrepXtZVLdoxirGWHL9HEsOw6Hh0c25OZacmNmP3s8iYdslPSl0XhmYsibXpY7s0bKOeJ0UMonilWCxaw4TviGwOrR9VPnz89+yIrXEE6D+DXADNsCS2ukopsuBjgM0NjfS7emmxF7CztqdSdkwOx1i1Yla+5o5+dPv4fjVAYyhMBWbN7BkxQqGBrooevw5lpsEgzc2cKy2jGCLZKB3gJxtOaNBoNPdSburnZ7hMZtms4spzymPOQ+9JcEudxeD/kGyzFk4LA58YR8n+0/iDXp1x9FjWrZLEwv/z3wZ7DqO4C17oXp7cgQVsy1tj0rES9eMl4inw4ldMeeJJ0AVSimvT/lMFNPmQMcBvvPad3BYHJTZy3AGnHznte8AzHqQihUUNjouJ/Q3XyFrIMSbmzfgu/4SgoUhNpZs1FzEb/4opcd6KNz9LLXP7qXl4zcz3BKmfV87y962jBxzDiIieKX7FRwWBw6LpmjscHWwuXSz7lxibWx+8eyLFNoKJ9kaDQWG4n7OpNguxaxLod/KwtWVWMBJ1NMuGahNs4okEk+AeloIcb2U8vcpn41iWjQ2N+KwOEY3zUaPU9kOJUMNF6/bhQiF8Xzxn8gdkhzbeCWGd1zBwIudFG4spNHdyIqiFeRacvGsc4AAx/cfZdW9j/P0HZsQ7Sb6D/dTVFuENEjWF68ftR1yWB3U5dfFtB2KJSeXUjIcHKbX20soEsJkMGE32VliX6I7TixmvAwba0Pq0nr9wGUw94chagAAIABJREFUJhZwkiVtTzQLS6VEfC5udlZMm3hEEp8CnhRCeIUQTiGESwjhTPXEFPHT7enGYRmv+ndYHDFrM8noTBtrjJP9JyeJByqeP0nY7+ONdeu48qkXKOntoXxrOf0H+xnqGsIf8nPo3CFOPv0ryv7jl7yxch1eo4slbxwnUhXB0G7gle5XEFJQ4aigvrSeHct2UF9aT4WjIqYwIVonGos76GZR1iL8Ya2cGt186w/7Kcqa5WZzsTakXrFLv2FfhMS62Lq6Zt5UMJM2GGfSXBSzQjwbdXMvdo0ivUxlO5QqT7+mribCMsyJ/hPj6kHOoHO8eEBK8p94iX3Xr8ZDCe1fvIVlX9sDX9jF8MZCgi8GeV28TvWAm+t+fJQDW7ewt36AS2qW8o4nznF0yxIWy2KusFxBr+iNKUzQe85YdaLynHK8YS951jysRiv+sJ8hf/zLexcjoew0Vraht0x2+Bexl/70SIbLdyZtMM6kuShmhZgZlBBi/VRfsznJhYhe+/FYxLId2lK6RTfLOTVwKjGJtA6nBk7xWs9rNA820+Xuonmwmdd6XsOAAaffiSvgQkqJPHIC/AFKVrwdwyID3SsW89bnd1H+td3kdLRgWWth1T7JdT94nRe3bqFlh53+rH76V5djD5u40VtHUXkRDp+DPEveuLFdAdeoX57ecwK6EvFcay4bSzdiNVpxBVxYjVY2lm4kLMPT+2GNIRnZKaBvIxQNOGOZKuAko3V8MrKwZJFJc1HMClNlUPdM8XcSuCbJc1GMkKibdyzboXZ3u26m1OnunHFn2rPus/QM95BrzSXLlEVQBukZ7iHHnMMddXeMigdWnukj76q3scS+FJvIImAKcKbWg/z8Ljbc8yhFOy5h6f43OLB5Ky1X2DEWGbjEfwn+iB/3+kvIPtWJsbIWr9/LJQWX6DppTJUR3nLZLboS8Q53x7hzw6FhsoxZ7D6+e0Z1uZQ6zidqopoMwUIm9VrKpLkoZoWYAUpKqXShFyFVzQOn8yGnZzt0/yv3p8zTzx10YzQYQYIUEiQYDUY8Qc848UBv03eRlgB9Viu2YRs7Lxsxk10PvV3Z8N3vcfTy1chrVpF3eoDyS8vpK+jTZN/WMCavH5/fR8gaGtcTaiyPNT+GyWAat9xY5ajCE/Dozr0ip4LHmh8bpwY8PXCa6rxqbGbbjFwqYgkzuj3dM//3Mp2AM1PBQib1WsqkuShmhYuKJIQQH9L7ivcGQgijEOJVIcRvR15XCyFeEkKcEkLsFkLMyb1VSVvK0SGaiYxlOm7esUQClxZeOmOnCrtZU72ZjCZ8YR8mo4kl9iVkm7PHLU++7j7JUH8XS5cu5fTp00QNSTxNL3H+5//DibWXU9t8mpJQL0u3LKV9XzuyT/LhlR/G5oswaPDj7/ZzzeprYs7PKIwcPHcQf9g/riWGURh1r293t7O+eD0OqwNXUFMDFtoKCUaCM3apiPU9Nwpj6pb+UkkmOYtn0lwUs0I8MvOxjW9saK3eXwF+Fuc9Pg0cA6Iys/8A7pVS/lII8X3gY8D34hwrY0jlUk7CLgUxSKWn35pFa/hj9x8pyS4ZJzSozqketzzZVzNI3rcfx/SZP8dsNtPS0kJJTy9v3XUXL27dyo677kSeOcLyv/5nXrvzOpZuuZSel3oorSsh8uY5Sv/yTro7O6i/rP7ikyK+lhg9wz1UOCpYlrds9Nwf3voDgfDkFh+J9tpKmndfJpFJzuKZNBdFyrloBiWlvHPM1yeAdcTpKCGEKAfeCfxo5LVAq109PHLJT4H3TWfi6SZZWY4eDWUNumKAhrKGhMaZytMvERGGHu+seSdVuVVIJM6AE4mkKreKfFv+OL88sWY5WC0cfeqX1NfXc/jnPx8XnKqrq6m59j3UfOu7bPzuC9xiXcUtH7iF5++/n5DRyP7zvWzYsIFoR2c9oi0xrEYrzoATq9HKptJNMUUPelmOxWjBYhz/z3o6vxQkzbtPoVDElUFNZBi4JM5r70Pz8oumAkXAoJQyNPK6A1g6jTmknWRlOXokxaVgzFgT39c21DbOzfv00GmO9x3n9tW3x32PyrxKbl99+6SaymPNj43/IBaCwRs3kb/7GS69+yosj/6a12+8kas/+hGqq6tH59OU30rwjqu44q47yP7Xv2Nz51lO1tRgtlhYu3aycexYirOLefP8m7Q523D6nTisDqwGK6sWrdK9Xi/LKbQUgkC3xUeiJMW7T6FQxNUP6jdoqj3QMq6VwJ443vcuoEdK+bIQ4uroaZ1LdV3ShRCfBD4JsGzZMr1L0sq0vNgSIJVmsY+feZxWVyt51jwcFgf+sJ9WVyuPn3mcO9bdMen6WD5/8X4Qt7/tUlY1HaPvvvtYdu83eL29nRdeeAEpJcYiIz89+lP6ff0ESgOc/dBlbP2P/yRizuHUjnrMl/Tx8KmHpxQUWISFfWf3YTfZcVgceAIe9p3dx7rF63Sv1/sF4PbVt9Pp6pz0nMn6GaT634tCMR8RF+uiIYR425iXIaBNStkR6/ox7/sKcNvIe2xoNahG4AagVEoZEkJsBv5JSnnDVGPV19fLQ4cOXeyWs06iqqxUqf4S5S+e+gusRis2s230nC/owx/2873rxpcDD3Qc4Bsvf4OQDI22pTAJE5+98rO6NkptQ2088OYDWsCJ9lqyFfLh6lsw/P09SL+fgk9+glM2G398+WXOu88zkDOA2WyioqWfVftOEDIKfnvLZaxp2EiuNXf0wzyWkOPzz3+eHk8PARnAF/Jh+//tnX90XNV94D/f+aXRr5EtWZKNLSxsxyAoxDHYJkASoCHtxmwSF4i7y6bQ5KSHPds2yTnpJjR7mm66Pds07WZ3SbaEbrbAkm7cJtGJS04SEmJIAtjCgMEQ/xS2IxtZMpat0a/5qbt/vDfjkfTeeJ41M5oZfT8+c/R033333e978v3Ovd/v/X4DYUISoqOxg6+87ysFPZNc1/5cBVLMNCeV8v4VpdIQkZeMMXMMza4zKBFZB3QaY56dVf4eEakzxuSNL2KMeRB40L7mVuCzxph7ReSfgbuBbwP3Ad/3Kkyl4GWW43VvUykx9r/ZZU48ceAJa0ZU10xQgiRNkrH4GE8ceMI9EG0mv1LmY0Aa6un6u//F+e/18vbf/C0tsSk+fMstPH3yea4cm2bVm2dIBH28sqWDXVt8TPvf4uaw5VdzMYeCoYkhVjSuQHwXJuhm2jA4UXi22pLuX7Kp5RQqilIK8i3x/XfgTx3Kp+xzl7r54HPAt0XkvwCvAN+8xHaqinIMgIVy3bLreHHoRUSEsD9MLB0jmoiyqXPTnLrHosdoDDYS9AUBCEqQxmAjx6PHHdvePbibrpYurg5dnS0bS4xZcl61naXbP8qSj97D1Cv7iL2+n4mRZzneOM6Pr2/kzVUBfL4E44lxWsMzE9zl86jLF+rJjdmzmSPnjrCsfhl7R/Zm91JdEbnCdS+VoiilJ5+C6jbGvDa70BizV0S6vdzEGPMM8Ix9/Caw2cv1tUC+DZxeKMYy0dY1WzkzdYaR2Aij8VFC/hDdkW62rtk6p30MTKWmGE+Nk0wnCfqD+PFnFdalyCkiNGx8Fw0b38Xzy57myLkjhANBAr4AqekUqekUsWSMvacvKIuO+g5WNTvnfdq2dls2vUgkFCGaiBJNRPlYz8dcn+Hs2ezhkcO8Yd6gs7EzmyNqz+k9jkpbUZTykE9BhfOcqy92R2qdYnhxFcP7DmwPvGvmeuABcwbuOn8dp8ZP0RBqICQhYqkY8VScW1feWjQ5w4EwsekYqZSV+qLOX8dEesLyyMvN+7TCOe+TW6gntyVIp9lsKBDi7MRZOhs7XZc7FUUpL/kU1Isi8kljzN/nForIJ4CXStut2sOrF5fTTMmr910+nOwhOw7umDNwtze0M5oYxefzEU/HCfqDtDa0ztjkOh85s5gLn7RJU++v51z8HCeiJ4jURVi/ZL1r3idwDvXkhtMsL+gPsiy8LBtAtjlkBZRNTadcWlEUpdTkU1CfBnpF5F4uKKQbsDbpbit1x2oNL3ub3BwqXhl6haXhpTMywWJg/9v7i9JHp4E74AuwOrKazsbOGbaZ5HRy3nIC+MTHVHqK+kA9QV+Q5HSSc1Pn8OFjeeNyuiPdxNIxhiaHCJ0rTlSsjoYOBqID2cSHzaFmUukUS8JLuGH5BUeiscQYrYHWPC0pilJK8gWLHQJuEpHbgN+wi39gjPlZWXpWgxTqxeXmUHE+fp4l4SUz6hZzOcppeS7kDxEKhOYM3EsDS4tyz8xsKZaKMTY9RtAXxOfzkTZphiaGiKVjhP1h6vx1nlKy58MpWOxIbISWupaibNRVd3JFKQ6FhDraZYx5yP6ocioDbmGUloSXEE1EiaViYCCWsrzvrl12bVHu6xRiqTXcSmuoteCwS16D6ApCwBegIdhAc6iZhmADGEikE0ylpwj7wkylpxicGETMxePsFcLA+AAbO2cGi71p5U2saVkzrwC6UNogwoqy2LiUUEdKiXFzNNiyfIur910xcIywcM39AAUv2eVzp8/8zJ1ZNAYb8YmPlroWAhIgZVKMxkcJS5j6gDWzqg/U0xJssdJ6FIHhyWG6mru4PHLBjmaMYWhiiO1XbZ9X25W0nUBRqh1VUBWIm6PBtnXbsuF4zsXO0RRq4o7L7yj5wOe2NOm0lOXmZn545DCDE4Nz7GrNoWbCvjCnxk9lI0/4jZ/6UP2MSOlTqSkiwcicPlwKxYqL50V+r9sJFEUpYIlPKT9uEbEB+ob66Gnr4c61d9LT1kPfUF/Rlo+8LE+51fWL3zEf0mhidEaU80y+peHJYUaTo4T9YSLBCGF/GHywtG7pjJTs65esZ33r+qLIWYxo8V7l16CwiuKdmp9BVavBulA3cCje8pGX5Sm3urFkzDFbbyQYcbSrnZ44TdgfpinUlN2o68PHeHKcK1uvnNFGPgXi5T0XI1q8V/k1KKyieKemFdSlxL+rFIW2EMtH+ZbndhzcUVBfJhITjoP/7sHdjstqCCxvWM6p8VNZj72u5i4mU5PZGeTFFMilbGCeb1w8r/JXw5ciRak0alpBeTVYV0pAV7cBt72hnYGxAYYnL+zf6WjoYFWTcwigTFuFKlyn/UF1/jqGJoa4rPmyGc8k5Au52nHcBn8nu9ryhuUMTgzSEm6hTdpImRSDE4OsaVlTsMNCvg3MW9dsLckXDqdnlQnHpEFhFaU41LSC8jrjWCgPrNlKpP9cv+OAO5WcYmBiYMb+nZNjJ3n3cucQQF4VrtP+oDdH32TL8i3zXspyW1abTExycvwkyekkAV+A5HSStEnnVbqz2f/2flpCLXM2MO85vYfEdKIkXzicnlUmHFOlzMIVpdqpaQXl1VtrITywnJTIL079glXNq+YMuAfOHeC9q96b/dYeqYuwbsk61xBAXhVuZn9QZoYWqYvQFm4jlo7NqHepS1lOM4vmumZ+s+s32ff2PkbjliPFjV030hhqLPgZuqUPybRXii8cTs9q3dJ17Duzj76hvgWfhStKLVDTCsprXLhSp+V2+mbtpET8Pj8jsRHaGtqy1xoMyekkXZGuGXHwMvt3nMincN1sXE77g0ZiIzPauNhSnhc6GjqYCE1wV+td2bKxxBixZGyO3Wt1y2rHfrulD2kJtTg6ZhTjC4fbs9r1612sW7qOQyOHZizD6j4oRfFOTbuZu7lruw0UxXA/dsPNLfnIuSNzBtHVzautQXpWxIjuSLcnF+aMwp1d3y/+gl2kOxs78Yu/JM8EnJ/5QHSAM5Nn5vTv+ZPPO/Z7Q/sGuiPdGGPNmowxdEe62bJiS8lcvt2e7WRyksMjh4mn49nl2cMjhzly7si876koi42ankGBN2+tYrgfu+G23HZq/NScWduapWsYS45lB9xMxIg7Lr+DvqE+oLAZodsMMuQLubpI/+rMrzgWPcZUygrgekXkCu67+j4GxgdK4pXm9Mzb69sJB8Nz+tfb30tPW8+c8oHxgbzpQwp9Xl5we7aNwUYMZsbybDwVL1ocQUVZTNS8gvJKqTyw3JbbIsHIHGcDv/h54LoHGBgfmLPEtbJ5ZcEK1E3h7uzf6bj0dfDtgxyPHidNmpA/RJp0NnPufEMAgbtH4exn/tDLD7kuzW1avsmx3O29leoLh9uzffyNxzk5cZJYKpaNgjHNdNGiYCjKYkIVVJlws2+tb12ftUUVqnS8JiecXd+tLyfGTtDe0D4jdfpobJTe/l7HXEtevNW8eBS69S9znZON8PmTz9Pb38vQxBCdjZ1sW7uNm1bdVFKXb6e217eupyHYMMP9vKupyzUbsKIo7qiCKhP5HDbKvW/mxhU3zthnFfKHaA21YozBL35OjJ7IbpptC7c5OhV4dWH34lHoGotw7TbHJc6lwaV8/dWvEwlFWNG4gmgimk0BX2gSw2Jx44ob6Z3o9RQFQ1EUZ1RBlYli2bfcZi2e994IM7LYItAQaODo+aM01zVT768naZIcPX+UNS1r5lzu1YXdiwt/vmfltMT5tX1fIxKKZGd+mZ9uM79SUko7pqIsNlRBlZH5zpTcZi2bOzd72nuze3A3TaEmJlOTJKeThANWLDwRIW3SJKeT+H3+vJtmve4Zy+fCn882NRun8qGJIVY0rphRFglFGJwYzPssS7WZViNJKEpxqGk381ojd9aSGxG8t7/XsTyTg2k2R84dcXSFnkhOcHvX7YT9YaKJKGF/mNu7bqe5rnlOGx0NHbzw1gs88uojfHXvV3nk1Ud44a0XXF243Vz4u5q65p3gr7Oxk2giOqMsmojOUaAZNKmgolQHqqCqCLdMu0MTQ47lw5PDju2MJkbxic9yhRbLFdonPkSEzqZO7lp/F79/7e9z1/q76GzqdFQ60ViU5049RzwVpzHQSDwV57lTzxGNRR3u6L4nbWB8wJNydWLb2m1EE1FGY6OYacNobJRowrJZOeGm6L3cU1GU0qNLfFXEpXi3OREJRrKp43NdoVc3r3aMr3fVkqvmRHX46cBPaQo2EZ+OM5ocJegL0hRs4qcDP+WTGz7peF+npa+d/TsJ+oLsHdmb9Xq7InIFE4mJgp9Lxs7U29/L4MQgnY2dfKznY672p+HJYQK+wIxoD92Rbk/3VBSl9KiCqiK8ere5bUjN5wo92+X9qiVXOdq3To2fIihBGgIN+MTHtJkmlU5xevy0a/+d7D5+8fPswLMkSZKeTjM8NcyvR3/Ne1a9x9OzuWnVTQU7RPjFT9/pPlrqWmgONRNPx+k73cemzk0Xv1hRlLKhCqqK8Ordli+kU6Gu0PvO7HP01jPGkCZNna8OsAb9eCpOXaDO8Z5uKUSmklO8HXubxlAjYV+Y2HSM0cQo52Pni/HILoogZbmPZ872Q/8uGBuE5hWw9jZoW7vQvVKUsqIKqsrw4t2Wrw0nRQfM8RJ8/q3nuXnlzTOWD5uCTbSEWhiJj+BL+gj5QyTSCRLTCa5bep3jPd1yNp0eP23FGEyNE0vFqA/U0x5u59C5Q47BYotB2qTZsnwLx6LHiCaiNIea2bJ8C8npZFHanzdn++Hlx6F+KUQug/iY9fvG31MlpSwqVEEtUgpNKd9W38bBcwe5peGWbL3x5DjXtF/DdHqa/Wf3M54cpynYxPUd17P5ss2O93PL2XQ0eXROqozJ5CQjsZGsl12xU1Z0NHRwcvzkjLKJ1ISnHFQlpX+XpZwyET0yP/t3qYJSFhXqxadkcfIS7Gnt4ezU2Tnu4dvWbiMSjtDT1sM7299JT1sPkXDENWKCW86msD/MiegJplJThH1hplJTHI8epy3cVjIvu66mLl4eeploPEpzsJloPMrLQy/T1dRVlPbnzdggzHbtr2uGPPY9RalFVEEpWZxSSIQCIa5eejUHzh7gyf4nOXD2AJs7N7OyeWU2AkX2Yxwatblu2XVZz8HcFCKrmlexrH4ZAQkQS8cISIC6QB0tdS0zrs/nNu+VgfEBNnZsJFIXYSxpJRvc2LHRNfFj2WleYS3r5RIfg6blC9MfRVkgSrbEJyJh4OdAnX2f7xhjvigijwLvAzL5B+43xuwrVT+UwnHyEhwYHQCBnrYeNi3fxHhynL6hPkJnQnS1dHF16Ors9WOJMddQR1vXbOXM1BlGYiMzUoj48NHe0M6x6LGsR2FnonNOFt+L5XHyEhlieHLYU+LHsrP2NsvmBNbMKT4GU+eg518vbL8UpcyU0gYVB243xoyLSBD4pYj80D73J8aY75Tw3sol4JibqcE5N9OLgy9y2+W3zbg+X6ij1S2rHXM27R7cPcce1FbfxumJ04wlxua4zTspIpjr3JHPZlXqzMnzpm2t5RCR8eJrWm4pJ7U/KYuMkikoY4wBMutFQfuTZxFIqQQKzc0EeB7knRwzTo2dYmf/TiKhCJGQlRsrmohy97q7SZjERb0Me4/2uiZgdJvN5YssXzG0rVWFpCx6SmqDEhG/iOwDhoGfGGP22Kf+UkReE5GviojzxhmlInBLbX7tsmsdY+t5TSvhZg9KmATbr9rOH238I7ZftZ3VLatdQxTtf3u/p1BPbmGXNMCrolQWJXUzN8akgQ0isgToFZHfAB4ETgMh4BHgc8CXZl8rIn8A/AHA5ZdfPvu0UiZco1es28apsVNzkgTmG+Sdlue82IPcIqhDcWZzXillRHRFUcrkxWeMOQ88A/y2MWbQWMSBfwAcN84YYx4xxtxgjLmhvb29HN1cVJwYPcGOgzt46OWH2HFwh2skb7fZBkDfUB89bT3cufZOetp66Bvqc23HLYK4X/yOMzQn5VLq2ZwXNCK6opSeUnrxtQNJY8x5EakH3g98WURWGGMGRUSAjwCvl6oPijNes+EWuqkX3O0+bgkOY8mYY4BaJ3tQvtlc5h7lShLoNWGjoijeKeUS3wrgMRHxY83U/skY86SI/MxWXgLsAx4oYR8UB4oxuHpNWOhWfyIxUXAG2otlqy2nYvAqv6Io3imlF99rwLscym8v1T2Vwsg3uBZqV/Hqqp2vvtc4gk51y20PqnhXdUWpATSSxCLEzZbjF3/BdhW3DLludh+v9b2wEPagUsqjKIqFKqhFiNvgChScadarq3YpXbsXIkOuuqorSunRaOaLEDdbzs7+na4p5d3a8TIgF8O124mFsgeVSh5FUSxUQS1SnAbXhbKrzNd+pPYgRalNdIlPybIQdpVi2I/UHqQotYkqKCXLQthVimE/UnuQotQmusRXRqohNE657SrFsh+pPUhRag+dQZUJDY3jjJvLu9qPFEVRBVUmFsIVuhpQ+5GiKG6ogioTw5PDnlJCLBbUfqQoihtqgyoT6grtjtqPFEVxQmdQZUKXshRFUbyhCqpM6FKWoiiKN3SJr4zoUpaiKErhqIJSik417PdSFKXy0SU+pajofi9FUYqFKiilqOh+L0VRioUqKKWo6H4vRVGKhSoopaho6CJFUYqFKiilqOh+L0VRioUqKKWo6H4vRVGKhbqZK0VH93spilIMdAalKIqiVCSqoBRFUZSKRBWUoiiKUpGoglIURVEqElVQiqIoSkWiCkpRFEWpSMQYs9B9uCgicgaYHW10GfD2AnSn3CwWOWHxyKpy1hYq5/xZbYxpn11YFQrKCRHZa4y5YaH7UWoWi5yweGRVOWsLlbN06BKfoiiKUpGoglIURVEqkmpWUI8sdAfKxGKRExaPrCpnbaFyloiqtUEpiqIotU01z6AURVGUGkYVlKIoilKRVKyCEpH/IyLDIvJ6TtkOEdlnf46LyL6ccw+KyFEROSQiv7UwvfaOi5wbRGS3LedeEdlsl4uI/E9bztdEZOPC9dwbLnK+U0ReEJH9IvIvIhLJOVet77NLRHaJyAEReUNEPmWXt4rIT0TkiP1zqV1ele80j5z32L9Pi8gNs66puneaR86viMhB+531isiSnGtqSc6/sGXcJyJPichldnl5/m6NMRX5Ad4LbARedzn/t8Cf2cdXA68CdcAVQD/gX2gZLlVO4CngX9nHHwSeyTn+ISDAjcCehe7/POV8EXifffxx4C9q4H2uADbax83AYVuevwY+b5d/HvhyNb/TPHL2AFcCzwA35NSvyneaR84PAAG7/Ms577PW5Izk1Plj4GH7uCx/txU7gzLG/BwYcTonIgJ8FPh/dtGHgW8bY+LGmGPAUWBzWTo6T1zkNEBmNtECvGUffxh43FjsBpaIyIry9HR+uMh5JfBz+/gnwF32cTW/z0FjzMv28RhwAFiJJdNjdrXHgI/Yx1X5Tt3kNMYcMMYccrikKt9pHjmfMsak7Gq7gVX2ca3JGc2p1og1NkGZ/m4rVkFdhPcAQ8aYI/bvK4GBnPMn7bJq5dPAV0RkAPgb4EG7vNbkfB34kH18D9BlH9eEnCLSDbwL2AN0GmMGwRoMgA67WtXLOktON2pZzo9jzSagBuUUkb+0x6J7gT+zq5VFzmpVUP+GC7MnsKaZs6lm//l/D3zGGNMFfAb4pl1ea3J+HPgPIvIS1rJCwi6vejlFpAn4LvDpWd9C51R1KKsaWRe7nCLyBSAFfCtT5HB5VctpjPmCPRZ9C/jDTFWHy4suZ9UpKBEJAL8D7MgpPsmFb99gTbffonq5D/ieffzPXFgiqCk5jTEHjTEfMMZcj/WFo98+VdVyikgQ6z/5t4wxmfc4lFkCsX8O2+VVK6uLnG7UnJwich9wJ3CvsQ0z1KCcOfwjF5bhyyJn1Sko4P3AQWPMyZyyncDvikidiFwBvAPoW5DeFYe3gPfZx7cDmaXMncDv2R40NwKjmWWjakREOuyfPuA/AQ/bp6r2fdr20W8CB4wx/y3n1E6sLx7YP7+fU1517zSPnG5U5Tt1k1NEfhv4HPAhY8xkziW1Juc7cqp9CDhoH5fn73ahvUfcPljfqAeBJJa2/oRd/ijwgEP9L2B9Az+E7QFXDR8nOYFbgJewvIH2ANfbdQX4ui3nfnK8pCpXw3UnAAAEk0lEQVT94yLnp7C8hQ4Df4Ud2aTK3+ctWEsdrwH77M8HgTbgaawvG08DrdX8TvPIuc1+v3FgCPhxNb/TPHIexbLBZMoerlE5v4tlK34N+Bcsx4my/d1qqCNFURSlIqnGJT5FURRlEaAKSlEURalIVEEpiqIoFYkqKEVRFKUiUQWlKIqiVCSqoJSaQUTSciHa/T4R6RaRW0XkSfv8h0Tk82Xu06MicncJ298gIh/M+f3PReSzBVwnIvIzyYkgX8Q+fXvW/hlFuSRUQSm1xJQxZkPO53juSWPMTmPMX5WyAyLiL2X7DmzA2q/ilQ8Cr5r84Ykulb8D/mMJ2lUWGaqglEWDiNwvIl+zjx8VkYdF5BciclhE7syp830R+ZGdz+eLOdf/OxHps2dn38goIxEZF5Evicge4N0F9uVPRORFO5fOf7bLuu18PH9v5+R5SkTq7XOb7LoviJWL6HURCQFfArbbfdpuN3+1iDwjIm+KyB+7dOFe7GgW9n0Pisj/ttv9loi8X0SeEyt/VSYf2Z+LyGN2v46LyO+IyF+Llc/rR3aoHIBfAO+3w5IpyiWjCkqpJepzlvd6C6jfjRVSaivwsIiE7fLNWAP4BuAeEblBRHqA7cDNxpgNQNquA1YagteNMVuMMb+82E1F5ANYIXA22/e4XkTea59+B/B1Y8w1wHkuxD77B6wIKu+2740xJoEVXXqHPWPMxKe8Cvgtu/0v5iiOXG7GilaSYR3wP4Dr7Ov/LVZ0gc8Cf5pTb639vD4MPAHsMsZcC0zZ5RhjprEiLbzzYs9CUfKh33CUWmLKVh6F8k/2YHpERN7EGpgBfmKMOQsgIt/DGqhTwPXAi1bYMuq5EPA1jRUSplA+YH9esX9vwlJMvwaOGWMymaJfArrFytbabIx53i7/R6wgpW78wBgTB+IiMgx0YoUfyqXVWHl/MhwzxuwHEJE3gKeNMUZE9mMp8gw/NMYk7XI/8CO7fHa9YeAyZipBRfGEKihlMTM7zpfJUy7AY8aYB5lLzBiT9nBfAf6rMeYbMwqtPDzxnKI0liJ0Sm2Qj9ltOP0/T4mIz1bQs6+Zzvl9etb1cbBmSSKSNBdipc2uF8aaVSnKJaNLfMpi5h4R8YnIWmANVnBPgDtEpNW2/3wEeA4rwOvdciECe6uIrL7E+/4Y+LhYuXcQkZWZdp0wxpwDxuyo0QC/m3N6DCuXllcOYclcKtYDb5SwfWURoApKWcwcAp7Fyob6gDEmZpf/Evi/WBGdv2uM2WuM+RVWSpCnROQ1rBT1haa4/oaInLQ/LxhjnsJapnvBXir7DhdXMp8AHhGRF7BmVKN2+S4sp4hcJ4lC+AFwq4f6BSMinVjLrRWfNkSpbDSaubIoEZFHgSeNMd+ZVX4/VuqAP3S6bqEQkSZjzLh9/HlghTHmU/NobwXwuDHmjmL1MaftzwBRY8w3L1pZUfKgNihFqQ62isiDWP9nTwD3z6cxY8yg7c4eKcFeqPNYM1BFmRc6g1IURVEqErVBKYqiKBWJKihFURSlIlEFpSiKolQkqqAURVGUikQVlKIoilKR/H8J4bArAw9UugAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from time import sleep\n", "from IPython.display import clear_output\n", "interval = 1\n", "\n", "centers = choose_random_start(M, k=3)\n", "plt.figure()\n", "\n", "for i in range(10):\n", " # label and scatter plot\n", " data['labels'] = compute_labels(M, centers)\n", " scatterplot(data, var1, var2, 'labels')\n", " plot_centers(centers, color='gray')\n", " \n", " # compute new centers and plot them\n", " new_centers = compute_new_centers(data, features) \n", " plot_centers(new_centers)\n", " centers = new_centers\n", " \n", " # show the plot, wait, and clear\n", " plt.show()\n", " sleep(interval) \n", " clear_output(wait=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Run the previous cell a few times. Do you always get the same clusters?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Number of clusters\n", "\n", "All of this is based on the assumption that you know how many clusters you are looking for, which is true for some applications, but not always.\n", "\n", "Let's see what goes wrong if you ask for too many clusters, or too few.\n", "\n", "**Exercise:** Run the following code with different values of `n_clusters` and see what the results look like." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "kmeans = KMeans(n_clusters=3).fit(M)\n", "data['labels'] = kmeans.labels_\n", "\n", "scatterplot(data, var1, var2, 'labels')\n", "plot_centers(kmeans.cluster_centers_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standarization\n", "\n", "One of the problems with the results we have seen so far is that the lines between the clusters are mostly vertical.\n", "\n", "That's because the range of values is wider for flipper length than culmen length, about 60 mm compared to 28 mm." ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([59. , 27.5])" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.max(axis=0) - M.min(axis=0)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([14.04114057, 5.45159602])" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.std(axis=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When we compute the distance from each point to each center, the distances in the $x$ direction tend to dominate.\n", "\n", "This is a common problem with algorithms that are based on distance in multidimensional space.\n", "\n", "It is such a common problem that there is a common solution: [feature scaling](https://en.wikipedia.org/wiki/Feature_scaling).\n", "\n", "The goal of feature scaling is to transform the features so the distances along each axis are comparable.\n", "\n", "One version of feature scaling is \"standardization\", which consists of\n", "\n", "1. Subtracting the mean from each feature, and\n", "2. Dividing through by the standard deviation.\n", "\n", "Here's how we can do it with the features in `M`:" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([200.91520468, 43.92192982])" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "means = M.mean(axis=0)\n", "means" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([14.04114057, 5.45159602])" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stds = M.std(axis=0)\n", "stds" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "M_std = (M - means) / stds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see what happens if we run the algorithm again with standardized features.\n", "\n", "Notice that I have to transform the centers back before plotting them." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "kmeans = KMeans(n_clusters=3).fit(M_std)\n", "data['labels'] = kmeans.labels_\n", "\n", "scatterplot(data, var1, var2, 'labels')\n", "\n", "centers = kmeans.cluster_centers_ * stds + means\n", "plot_centers(centers)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That looks a lot better! Again, here are the actual species for comparison." ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "scatterplot(data, var1, var2, 'Species2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "scikit-learn provides `StandardScaler`, which does the same thing." ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "from sklearn.preprocessing import StandardScaler\n", "\n", "scaler = StandardScaler().fit(M)\n", "M_std = scaler.transform(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And `scaler` provides `inverse_transform`, which we can use to transform the centers back." ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "kmeans = KMeans(n_clusters=3).fit(M_std)\n", "data['labels'] = kmeans.labels_\n", "\n", "scatterplot(data, var1, var2, 'labels')\n", "\n", "centers = scaler.inverse_transform(kmeans.cluster_centers_)\n", "plot_centers(centers)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "The k-means algorithm does unsupervised clustering, which means that we don't tell it where the clusters are; we just provide the data and ask it to find a given number of clusters.\n", "\n", "In this notebook, we asked it to find clusters in a group of penguins based on two features, flipper length and culmen length. The clusters it finds reflect the species in the dataset, especially if we standardize the data.\n", "\n", "In this example we used only two features, because that makes it easy to visualize the results. But k-means extends easily to any number of dimensions (see the exercise below)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, what is this good for?\n", "\n", "Well, [Wikipedia provides this list of applications](https://en.wikipedia.org/wiki/Cluster_analysis#Applications). Applying clustering analysis to these applications, I see a few general ideas:\n", "\n", "* From an engineering point of view, clustering can be used to automate some kinds of analysis people do, which might be faster, more accurate, or less expensive. And it can work with large datasets and high numbers of dimensions that people can't handle.\n", "\n", "* From a scientific point of view, clustering provides a way to test whether the patterns we see are in the data or in our minds.\n", "\n", "This second point is related to old philosophical questions about the [nature of categories](https://plato.stanford.edu/entries/natural-kinds/). Putting things into categories seems to be a natural part of how humans think, but we have to wonder whether the categories we find truly \"carve nature at its joints\", as [Plato put it](https://mitpress.mit.edu/books/carving-nature-its-joints).\n", "\n", "If a clustering algorithm finds the same \"joints\" we do, we might have more confidence they are not entirely in our minds." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Exercise:** Use the scikit-learn implementation of k-means to find clusters using all four features (flipper length, culmen length and depth, body mass). How do the results compare to what we got with just two features?" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(342, 19)" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Solution\n", "\n", "features4 = [var1, var2, var3, var4]\n", "data4 = df.dropna(subset=features4).copy()\n", "data4.shape" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "M4 = data[features4].to_numpy()" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "scaler = StandardScaler().fit(M4)\n", "M4_std = scaler.transform(M4)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "kmeans4 = KMeans(n_clusters=3).fit(M4_std)" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "# Solution\n", "\n", "data4['labels'] = kmeans4.labels_" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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