{ "cells": [ { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:15:23.538216Z", "start_time": "2018-04-02T08:15:22.004079Z" }, "collapsed": true }, "outputs": [], "source": [ "# a bunch of import statements for the functions we'll be using\n", "from sklearn.cluster import KMeans, AgglomerativeClustering\n", "from scipy.cluster.hierarchy import dendrogram, linkage\n", "from sklearn.feature_selection import SelectKBest\n", "import numpy as np\n", "import pandas as pd\n", "import csv\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import re, string, codecs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# CUNEIF 102A\n", "---\n", "\n", "\n", "### Professor Veldhuis\n", "\n", "This notebook teaches how to group texts together based on their similarities/differences and how to visualize the results. By the end of the notebook, we will be able to put in a new text and see where it falls in relation to all of the other texts.\n", "\n", "Module Developers: Sujude, Erik, Jonathan, Stephanie\n", "\n", "\n", "---\n", "\n", "### Topics Covered\n", "- Clustering Documents: Using K-means Clustering\n", "- Multidimensional Scaling (MDS): Visualizing the Data\n", "\n", "\n", "### Table of Contents\n", "\n", "1 - [Section 1: Clustering Documents](#section 1)
\n", "\n", "2 - [Section 2: Multidimensional Scaling](#section 2)
\n", "\n", "\n", "**Dependencies:**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Section 1: Clustering Documents\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Clustering Documents #\n", "\n", "Clustering is the grouping of a particular set of objects based on their characteristics, grouping them according to their similarities so that \"objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters).\" (Learn more: https://en.wikipedia.org/wiki/Cluster_analysis)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reading in the DTM ###\n", "First we'll read in the DTM (Document Term Matrix) from a CSV (comma-separated values) file. We're using a DTM that has been cleaned of all stopwords and normalized.\n", "\n", "The first line of the csv consists of a list of all the words, and the first column of the csv has all the text names, so we'll load those in first. Below I use the file path 'Data/stop11tfidf1gram.csv', but if you want to try out different DTMs (all of them can be found in the Data folder) you can replace the filepath with your chosen file name. All file paths should be of the form 'Data/[name of doc here].csv'." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:08.461557Z", "start_time": "2018-04-02T08:47:08.458550Z" }, "collapsed": true }, "outputs": [], "source": [ "filepath = 'Data/cleanonegram.csv' #this is where the dtm is stored" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we'll read in the csv file using the relevant pandas function. Below I do so and display the first 5 rows of the resulting DataFrame (a DataFrame is what the pandas library uses to represent a table)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:09.685311Z", "start_time": "2018-04-02T08:47:09.180469Z" }, "collapsed": false }, "outputs": [ { "ename": "FileNotFoundError", "evalue": "File b'Data/cleanonegram.csv' does not exist", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mFileNotFoundError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtfidf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilepath\u001b[0m\u001b[0;34m,\u001b[0m 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compression, thousands, decimal, lineterminator, quotechar, quoting, escapechar, comment, encoding, dialect, tupleize_cols, error_bad_lines, warn_bad_lines, skipfooter, skip_footer, doublequote, delim_whitespace, as_recarray, compact_ints, use_unsigned, low_memory, buffer_lines, memory_map, float_precision)\u001b[0m\n\u001b[1;32m 644\u001b[0m skip_blank_lines=skip_blank_lines)\n\u001b[1;32m 645\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 646\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0m_read\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilepath_or_buffer\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 647\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 648\u001b[0m \u001b[0mparser_f\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", 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"\u001b[0;31mFileNotFoundError\u001b[0m: File b'Data/cleanonegram.csv' does not exist" ] } ], "source": [ "tfidf = pd.read_csv(filepath, index_col=0)\n", "# tfidf = pd.concat([pd.read_csv('Data/cleanonegram.csv', index_col = 0).loc[[\"NEW\"], tfidf.columns], tfidf])\n", "tfidf.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First let's generate a list of words and texts present in the DTM. The list of words is just all the column names of the DataFrame. The list of document IDs is the index (or the name of a row) of each row of the DataFrame." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:14.519246Z", "start_time": "2018-04-02T08:47:14.507718Z" }, "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'tfidf' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mwords\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mre\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msub\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'[^\\w\\[\\]\\-/]'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m''\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mword\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mword\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtfidf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#get all the column names (i.e. words)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"First 5 words: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwords\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Number of words: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwords\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'tfidf' is not defined" ] } ], "source": [ "words = [re.sub('[^\\w\\[\\]\\-/]','', word) for word in list(tfidf.columns.values)] #get all the column names (i.e. words)\n", "print(\"First 5 words: \", words[:5])\n", "print(\"Number of words: \", len(words))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:14.812524Z", "start_time": "2018-04-02T08:47:14.806510Z" }, "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'tfidf' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtexts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtfidf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#get all the index names (i.e. text IDs)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"First 5 texts: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtexts\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Number of texts: \"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtexts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'tfidf' is not defined" ] } ], "source": [ "texts = list(tfidf.index.values) #get all the index names (i.e. text IDs)\n", "print(\"First 5 texts: \", texts[:5])\n", "print(\"Number of texts: \", len(texts))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll also define a function to access document names based on indices. This will come in handy later." ] }, { "cell_type": "code", "execution_count": 216, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:15.238156Z", "start_time": "2018-04-02T08:47:15.234648Z" }, "collapsed": true }, "outputs": [], "source": [ "def id_text(index):\n", " return texts[index]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll also define a dictionary, and function that maps the document ID's (like c.0.1.1) to document names (like 'Ur III catalogue from Nibru (N1)'). Don't worry too much about how this works, just understand what it does." ] }, { "cell_type": "code", "execution_count": 217, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:15.741496Z", "start_time": "2018-04-02T08:47:15.729494Z" }, "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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name
id
c.4.12.2A hymn to Martu (Martu B)
c.4.12.1A šir-gida to Martu (Martu A)
c.4.29.1A šir-gida to Nuska (Nuska A)
c.4.29.2A šir-gida to Nuska (Nuska B)
c.4.08.31A balbale to Inana (Dumuzid-Inana E1)
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" ], "text/plain": [ " name\n", "id \n", "c.4.12.2 A hymn to Martu (Martu B)\n", "c.4.12.1 A šir-gida to Martu (Martu A)\n", "c.4.29.1 A šir-gida to Nuska (Nuska A)\n", "c.4.29.2 A šir-gida to Nuska (Nuska B)\n", "c.4.08.31 A balbale to Inana (Dumuzid-Inana E1)" ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" } ], "source": [ "idToName = pd.read_csv('Data/idToTextName.csv', index_col=0, names=['id', 'name'])\n", "idToName.head()" ] }, { "cell_type": "code", "execution_count": 218, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:15.975116Z", "start_time": "2018-04-02T08:47:15.969603Z" }, "collapsed": true }, "outputs": [], "source": [ "def text_name(doc):\n", " if(type(doc) == int): #if an index was passed in, turn it into a doc ID\n", " doc = id_text(doc)\n", " try:\n", " return idToName.loc[doc]['name'] #not all document labels will be in the DataFrame\n", " except:\n", " return doc #if not in the DataFrame, just return the argument passed in" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The New Text\n", "The ultimate goal of this exercise is to compare a new text to the existing texts in the corpus. We will first do this by categorizing the existing documents into \"clusters\", and then seeing which of those clusters the new text best fits in. Below we define a new text. " ] }, { "cell_type": "code", "execution_count": 219, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:16.314574Z", "start_time": "2018-04-02T08:47:16.311066Z" }, "collapsed": true }, "outputs": [], "source": [ "new_text = tfidf.iloc[0] #the new text, which is really just a row from the tfidf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now try to cluster documents that are similar to each other.\n", "\n", "### K-Means Clustering ###\n", "\n", "[K-Means clustering](https://en.wikipedia.org/wiki/K-means_clustering) is an iterative method to group vectors into $k$ clusters. It uses the following process:\n", "\n", "1. Randomize $k$ \"cluster centers\". These are preliminary estimates for where the clusters are going to be centered.\n", "2. Categorize each data point by which cluster center it's closest to. We should now have $k$ clusters, each vector belonging to a single cluster.\n", "3. Redefine each cluster center at the actual center of the vectors that were assigned to it in step 2.\n", "4. Repeat steps 2 and 3 until convergence (until the cluster centers aren't changing by much anymore).\n", "\n", "To see this process visually, consider the following two-dimensional dataset (our actual dataset is more like 4000+ dimensions, one dimension for each term):" ] }, { "cell_type": "code", "execution_count": 220, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:16.810894Z", "start_time": "2018-04-02T08:47:16.668014Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n0Kd8v/AAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = [1, 1.5, 1.5, 2, 3.5, 4]\n", "ys = [1, 0.0, 5, 4, 2, 2]\n", "plt.plot(xs, ys, 'bs')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's say we want three clusters. First we initialize random cluster centers (in red):" ] }, { "cell_type": "code", "execution_count": 221, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:17.184889Z", "start_time": "2018-04-02T08:47:17.044516Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cxs = [2, 3, 4]\n", "cys = [0, 2, 3]\n", "plt.plot(xs, ys, 'bs')\n", "plt.plot(cxs, cys, 'r^')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now assign each data point (or vector) to the nearest cluster center." ] }, { "cell_type": "code", "execution_count": 222, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:17.529806Z", "start_time": "2018-04-02T08:47:17.381413Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(xs[:2], ys[:2], 'bs')\n", "plt.plot(xs[2:5], ys[2:5], 'gs')\n", "plt.plot(xs[5:], ys[5:], 'ys')\n", "plt.plot(cxs, cys, 'r^')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here I've colored the ones closest to the (2, 0) cluster in blue, the ones closest to the (3, 2) cluster in green, and the ones closest to the (4, 3) cluster in yellow.\n", "\n", "Now we recenter all the cluster centers at the actual centers of the current clusters" ] }, { "cell_type": "code", "execution_count": 223, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:17.868706Z", "start_time": "2018-04-02T08:47:17.726830Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cxs = [1.25, 7/3, 4]\n", "cys = [.5, 11/3, 2]\n", "plt.plot(xs[:2], ys[:2], 'bs')\n", "plt.plot(xs[2:5], ys[2:5], 'gs')\n", "plt.plot(xs[5:], ys[5:], 'ys')\n", "plt.plot(cxs, cys, 'r^')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we repeat the above process (assign vectors to closest centers, then re-define centers) one more time, we will end up with the below clustering." ] }, { "cell_type": "code", "execution_count": 224, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:18.220643Z", "start_time": "2018-04-02T08:47:18.075758Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cxs = [1.25, 1.75, 3.75]\n", "cys = [.5, 4.5, 2]\n", "plt.plot(xs[:2], ys[:2], 'bs')\n", "plt.plot(xs[2:4], ys[2:4], 'gs')\n", "plt.plot(xs[4:], ys[4:], 'ys')\n", "plt.plot(cxs, cys, 'r^')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks about right! Even though this time it only took two iterations, usually this will take many many iterations to get right. Furthermore, since the initial cluster centers are randomized, and our dataset doesn't have extremely clear clusters like in this example, we will end up with different clusterings every time we run k-means on it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using K-Means Clustering for the Corpus\n", "\n", "Let's try executing K-Means on our documents using 7 clusters. I picked 7 arbitrarily - in the future we can try using the \"[elbow method](https://en.wikipedia.org/wiki/Determining_the_number_of_clusters_in_a_data_set#The_elbow_method)\" to determine a number of clusters, or we can try different options and manually inspect the clusters to see if they make any sense.\n", "\n", "We use scikit-learns convenient KMeans function; it does all the work for us, we just have to specify number of clusters." ] }, { "cell_type": "code", "execution_count": 225, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:20.482659Z", "start_time": "2018-04-02T08:47:18.818734Z" }, "collapsed": true }, "outputs": [], "source": [ "dtm_normalized_kmeans = KMeans(n_clusters=7, max_iter=1000).fit(tfidf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can examine the \"label\" of each of the documents as defined by this clustering - this tells us which cluster each of the documents is classified under." ] }, { "cell_type": "code", "execution_count": 226, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:20.677680Z", "start_time": "2018-04-02T08:47:20.607494Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([3, 2, 5, 5, 5, 2, 5, 5, 2, 2, 5, 2, 2, 3, 5, 5, 2, 2, 2, 2, 2, 2, 2,\n", " 3, 3, 2, 3, 2, 2, 4, 4, 4, 3, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3,\n", " 2, 2, 6, 6, 6, 2, 3, 2, 5, 3, 3, 3, 3, 3, 5, 5, 6, 6, 6, 2, 6, 6, 6,\n", " 6, 5, 3, 5, 5, 3, 5, 2, 5, 5, 5, 5, 4, 5, 5, 5, 5, 2, 2, 2, 2, 2, 2,\n", " 2, 4, 5, 5, 5, 5, 5, 5, 5, 1, 2, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5,\n", " 5, 2, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 4, 5, 5, 5, 4, 5,\n", " 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5, 6, 5, 5, 5, 5, 5, 2, 5, 5, 5,\n", " 5, 2, 5, 5, 5, 5, 5, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1,\n", " 1, 1, 1, 1, 3, 1, 2, 1, 1, 2, 3, 2, 2, 2, 2, 2, 2, 1, 2, 5, 3, 5, 2,\n", " 5, 5, 2, 2, 5, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", " 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 5, 5, 5, 2, 5, 2, 5, 2, 6,\n", " 5, 5, 5, 2, 5, 5, 5, 6, 5, 5, 3, 2, 2, 5, 5, 2, 2, 5, 2, 2, 2, 5, 5,\n", " 2, 5, 5, 5, 2, 5, 2, 2, 2, 4, 4, 4, 4, 2, 4, 3, 5, 5, 5, 2, 2, 2, 5,\n", " 2, 5, 2, 5, 3, 3, 2, 2, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 2, 2, 2, 3, 2,\n", " 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 0, 2, 3, 3, 3, 3, 3, 3, 3, 0, 0,\n", " 0, 3, 3, 0, 3, 3, 3, 3, 3, 3, 3, 3])" ] }, "execution_count": 226, "metadata": {}, "output_type": "execute_result" } ], "source": [ "labels = dtm_normalized_kmeans.labels_\n", "labels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It seems like a there is a nice spread of documents being assigned to different clusters. (what we don't want is something like 50% or more of the documents falling into the same cluster).\n", "\n", "Let's see what the centers of each of the clusters look like." ] }, { "cell_type": "code", "execution_count": 227, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:23.207779Z", "start_time": "2018-04-02T08:47:23.201764Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.00000000e+00, 2.77052924e-02, -1.08420217e-19, ...,\n", " 0.00000000e+00, 5.42101086e-20, 2.71050543e-20],\n", " [ 6.45082761e-03, 8.67361738e-19, 2.16840434e-19, ...,\n", " -2.16840434e-19, 1.08420217e-19, -2.71050543e-20],\n", " [ 4.40117818e-03, 3.15881856e-03, 1.07511997e-03, ...,\n", " 1.41651819e-03, 2.83007182e-04, 5.01722791e-04],\n", " ..., \n", " [ 0.00000000e+00, 8.67361738e-19, 2.16840434e-19, ...,\n", " 0.00000000e+00, 2.40189125e-03, 2.71050543e-20],\n", " [ 4.97035070e-04, 7.37797049e-05, 1.08420217e-18, ...,\n", " -1.73472348e-18, 2.90439073e-04, -1.08420217e-19],\n", " [ 1.94294611e-03, 1.30913345e-03, 2.16840434e-19, ...,\n", " 0.00000000e+00, 1.08420217e-19, 2.71050543e-20]])" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cluster_centers = dtm_normalized_kmeans.cluster_centers_\n", "cluster_centers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Interesting... We get a nice variation across cluster centers (i.e. not all 0s or anything like that), so we can move on.\n", "\n", "\n", "Below I now define a method that takes in a cluster number, and outputs a dictionary whose values are lists of documents that belong to a specific cluster. The idea is that someone familiar with this corpus could look at the output and determine if the clustering makes any sense whatsoever." ] }, { "cell_type": "code", "execution_count": 228, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:23.713124Z", "start_time": "2018-04-02T08:47:23.705603Z" }, "collapsed": true }, "outputs": [], "source": [ "def inspect_clusters(num_clusters, use_id=True):\n", " km = KMeans(n_clusters=num_clusters, max_iter=1000).fit(tfidf)\n", " labels = km.labels_\n", " clusters = {}\n", " for i in range(num_clusters):\n", " docs = [j for j in range(len(labels)) if labels[j] == i]\n", " clusters[i] = [id_text(k) for k in docs] if use_id else [text_name(id_text(k)) for k in docs] \n", " return clusters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's an example of a use of this function. This examines the documents that appear in a certain cluster given that we choose $k = 7$." ] }, { "cell_type": "code", "execution_count": 229, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:26.138580Z", "start_time": "2018-04-02T08:47:24.454598Z" }, "collapsed": true }, "outputs": [], "source": [ "seven_clusters = inspect_clusters(7)" ] }, { "cell_type": "code", "execution_count": 230, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:26.301067Z", "start_time": "2018-04-02T08:47:26.296555Z" }, "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['c.1.7.1', 'c.3.1.01', 'c.3.1.02', 'c.3.1.03', 'c.3.1.04', 'c.3.1.05', 'c.3.1.06', 'c.3.1.06.1', 'c.3.1.07', 'c.3.1.08', 'c.3.1.11.1', 'c.3.1.13.2', 'c.3.1.15', 'c.3.1.16', 'c.3.1.17', 'c.3.1.18', 'c.3.1.19', 'c.3.1.20', 'c.3.2.02', 'c.3.2.03', 'c.3.2.04', 'c.3.3.04', 'c.3.3.05', 'c.3.3.08', 'c.3.3.11', 'c.4.22.2', 'c.5.5.5', 'c.5.6.3', 'c.6.1.13', 'c.6.1.27']\n" ] } ], "source": [ "print(seven_clusters[0])" ] }, { "cell_type": "code", "execution_count": 231, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:26.455979Z", "start_time": "2018-04-02T08:47:26.450464Z" }, "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['NEW', 'c.0.1.1', 'c.0.2.08', 'c.1.1.1', 'c.1.1.2', 'c.1.1.3', 'c.1.1.4', 'c.1.2.2', 'c.1.3.1', 'c.1.3.2', 'c.1.3.3', 'c.1.3.5', 'c.1.4.1', 'c.1.4.1.1', 'c.1.4.3', 'c.1.4.4', 'c.1.5.1', 'c.1.7.3', 'c.1.7.4', 'c.1.7.7', 'c.1.8.1.2', 'c.1.8.1.3', 'c.1.8.1.4', 'c.1.8.1.5', 'c.1.8.1.5.1', 'c.1.8.2.1', 'c.1.8.2.2', 'c.1.8.2.3', 'c.1.8.2.4', 'c.2.1.4', 'c.2.1.5', 'c.2.1.6', 'c.2.1.7', 'c.2.2.2', 'c.2.2.3', 'c.2.2.4', 'c.2.2.5', 'c.2.2.6', 'c.2.3.1', 'c.2.3.2', 'c.2.4.1.1', 'c.2.4.2.01', 'c.2.4.2.02', 'c.2.4.2.03', 'c.2.4.2.04', 'c.2.4.2.05', 'c.2.4.2.21', 'c.2.4.2.24', 'c.2.4.2.a', 'c.2.5.1.2', 'c.2.5.1.3', 'c.2.5.1.4', 'c.2.5.2.1', 'c.2.5.3.1', 'c.2.5.3.4', 'c.2.5.4.10', 'c.2.5.4.11', 'c.2.5.4.a', 'c.2.5.6.6', 'c.2.5.8.1', 'c.2.6.9.1', 'c.2.7.1.1', 'c.2.8.2.1', 'c.2.8.3.1', 'c.2.8.5.a', 'c.3.1.11', 'c.3.2.05', 'c.3.3.01', 'c.3.3.03', 'c.3.3.09', 'c.3.3.10', 'c.3.3.21', 'c.3.3.22', 'c.3.3.39', 'c.4.02.1', 'c.4.06.1', 'c.4.07.1', 'c.4.07.2', 'c.4.07.3', 'c.4.07.4', 'c.4.07.5', 'c.4.07.a', 'c.4.08.09', 'c.4.08.10', 'c.4.08.20', 'c.4.08.29', 'c.4.08.33', 'c.4.08.a', 'c.4.14.1', 'c.4.14.3', 'c.4.15.2', 'c.4.15.3', 'c.4.16.1', 'c.4.16.2', 'c.4.19.1', 'c.4.19.2', 'c.4.19.3', 'c.4.22.1', 'c.4.22.4', 'c.4.22.5', 'c.4.25.1', 'c.4.28.1', 'c.4.31.1', 'c.4.32.2', 'c.4.80.2', 'c.5.1.3', 'c.5.2.4', 'c.5.2.5', 'c.5.3.2', 'c.5.3.3', 'c.5.3.5', 'c.5.3.7', 'c.5.4.11', 'c.5.4.12', 'c.5.5.1', 'c.5.5.2', 'c.5.5.a', 'c.5.7.1', 'c.5.7.2', 'c.5.9.2']\n" ] } ], "source": [ "print(seven_clusters[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Save clusters into variables (used later in the MDS Section)" ] }, { "cell_type": "code", "execution_count": 232, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:29.671186Z", "start_time": "2018-04-02T08:47:29.666700Z" }, "collapsed": true }, "outputs": [], "source": [ "cluster_0 = seven_clusters[0]\n", "cluster_1 = seven_clusters[1]\n", "cluster_2 = seven_clusters[2]\n", "cluster_3 = seven_clusters[3]\n", "cluster_4 = seven_clusters[4]\n", "cluster_5 = seven_clusters[5]\n", "cluster_6 = seven_clusters[6]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also choose to use the names of documents instead of their labeled id by using the `use_id` tag in the function call." ] }, { "cell_type": "code", "execution_count": 233, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:31.886210Z", "start_time": "2018-04-02T08:47:30.268836Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "['OB catalogue possibly from Zimbir (B1)',\n", " 'Dumuzid and his sisters',\n", " 'Inana and Bilulu: an ulila to Inana',\n", " 'A lullaby for a son of Šulgi (Šulgi N)',\n", " 'A love song of Šulgi (Šulgi Z)',\n", " 'A song of Šulgi',\n", " 'A balbale to Bau for Šu-Suen (Šu-Suen A)',\n", " 'A balbale to Inana for Šu-Suen (Šu-Suen B)',\n", " 'A balbale to Inana for Šu-Suen (Šu-Suen C)',\n", " 'A love song of Išme-Dagan (Išme-Dagan J)']" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" } ], "source": [ "seven_clusters_names = inspect_clusters(7, use_id=False)\n", "seven_clusters_names[1][:10]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see a high frequency of documents belonging in a specific \"genre\" (like c.2) per cluster, so perhaps we're onto something by choosing 7 clusters!\n", "\n", "And finally, below I define a method to classify a new text into one of the seven clusters. It does this by finding which of the cluster centers is closest (in terms of Euclidean distance) to the new text vector." ] }, { "cell_type": "code", "execution_count": 234, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:32.776551Z", "start_time": "2018-04-02T08:47:32.771539Z" }, "collapsed": true }, "outputs": [], "source": [ "def classify(cluster_centers, new_text):\n", " euclid_dist = lambda x, y: np.linalg.norm(x-y)\n", " return min(range(len(cluster_centers)), \\\n", " key=lambda i: euclid_dist(cluster_centers[i], new_text))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we test this function using the cluster centers we just generated with seven clusters, and passing in the second document of our existing corpus as a \"new text\", we see that our classifier correctly chooses the category k-means had chosen previously." ] }, { "cell_type": "code", "execution_count": 235, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:33.228253Z", "start_time": "2018-04-02T08:47:33.221738Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "5" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "classify(cluster_centers, tfidf.iloc[2])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### K-Means Visualization ###\n", "It's difficult to visualize the clustering of 4000+ dimension vectors (each term adds to the dimensionality of the vecotrs).\n", "\n", "Here we attempt to use feature selection - trying to pick out two or three of the most \"significant\" features (where features are terms in this case) and plot those features onto 2D or 3D graphs. Below we try two different selection criteria to determine which terms to plot.\n", "\n", "This one sees which word has the highest tf-idf values across the clusters we choose to plot." ] }, { "cell_type": "code", "execution_count": 236, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:33.803784Z", "start_time": "2018-04-02T08:47:33.798771Z" }, "collapsed": true }, "outputs": [], "source": [ "# gives the features with the largest magnitude (summed across given cluster centers)\n", "def largest_selector(clusters, num_features):\n", " size = []\n", " for feat in range(len(clusters[0])):\n", " size.append((feat, sum([c[feat] for c in clusters])))\n", " size = sorted(size, key=lambda t: -t[1]) \n", " return size[:num_features]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This one sees which word has the highest difference across tf-idf values across the clusters we choose to plot." ] }, { "cell_type": "code", "execution_count": 237, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:34.357757Z", "start_time": "2018-04-02T08:47:34.351241Z" }, "collapsed": true }, "outputs": [], "source": [ "# gives the features with the largest difference between clusters\n", "def largest_diff_selector(clusters, num_features):\n", " tot_diff = []\n", " for feat in range(len(clusters[0])):\n", " tot_diff.append((feat, sum([abs(c1[feat] - c2[feat]) for c1 in clusters for c2 in clusters])))\n", " tot_diff = sorted(tot_diff, key=lambda t: -t[1])\n", " return tot_diff[:num_features]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below I've defined two functions that take in a list of cluster numbers, a selector function (one of the two just defined above, and a new text - a text that is not yet in the corpus that we want to compare.\n", "\n", "Each of these functions will use matplotlib to plot a scatterplot of the clusters selected (in different colors) according to the frequency of the terms that were selected by the selector function. They will also print out the terms that were selected.\n", "\n", "Don't worry too much about how these functions work. We'll go through a couple examples below.\n", "\n", "Also, just for the sake of consistency, I'll be loading in a set of clusters that was previously generated so I can adequately explain what is going on with the plots, since K-Means will tend to produce a different set of clusters each time." ] }, { "cell_type": "code", "execution_count": 238, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:34.951336Z", "start_time": "2018-04-02T08:47:34.946323Z" }, "collapsed": true }, "outputs": [], "source": [ "labels = list(pd.read_pickle('text_to_cluster.pickle')['cluster'])\n", "cluster_centers = pd.read_pickle('cluster_to_center.pickle').as_matrix()" ] }, { "cell_type": "code", "execution_count": 239, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:35.503305Z", "start_time": "2018-04-02T08:47:35.441640Z" }, "collapsed": true }, "outputs": [], "source": [ "def plot2d(clusters, selector_func, new_text=None):\n", " selected_features = selector_func([cluster_centers[i] for i in clusters], 2)\n", " selected_features = [f[0] for f in selected_features]\n", " \n", " selected_dtm = tfidf.iloc[:,selected_features]\n", " mask = lambda i: [lbl == i for lbl in labels]\n", " cluster_vectors = [selected_dtm.loc[mask(i)] for i in clusters]\n", " colors = iter(['b', 'g', 'y', 'c'])\n", " cluster_numbers = iter(clusters)\n", " for cluster in cluster_vectors:\n", " X, Y = list(cluster.iloc[:,0]), list(cluster.iloc[:,1])\n", " plt.scatter(X, Y, c=next(colors), label=\"cluster \" + str(next(cluster_numbers)), s=20)\n", " if new_text is not None:\n", " plt.scatter(new_text[selected_features[0]], new_text[selected_features[1]], c='r', s=40, label=\"new text\")\n", " plt.legend()\n", " plt.xlabel(words[selected_features[0]])\n", " plt.ylabel(words[selected_features[1]])\n", " plt.show()\n", " return selected_features\n", " \n", "def plot3d(clusters, selector_func, new_text=None):\n", " selected_features = selector_func([cluster_centers[i] for i in clusters], 3)\n", " selected_features = [f[0] for f in selected_features]\n", " \n", " selected_dtm = tfidf.iloc[:,selected_features]\n", " mask = lambda i: [lbl == i for lbl in labels]\n", " cluster_vectors = [selected_dtm.loc[mask(i)] for i in clusters]\n", " cluster_numbers = iter(clusters)\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111, projection='3d')\n", " for cluster in cluster_vectors:\n", " X, Y, Z = list(cluster.iloc[:,0]), list(cluster.iloc[:,1]), list(cluster.iloc[:,2])\n", " ax.scatter(X, Y, Z, label=\"cluster \" + str(next(cluster_numbers)), s=10)\n", " if new_text is not None:\n", " X, Y, Z = new_text[selected_features[0]], new_text[selected_features[1]], new_text[selected_features[2]]\n", " ax.scatter(X, Y, Z, label=\"new text\", c='red', s=40)\n", " plt.legend()\n", " plt.xlabel(words[selected_features[0]])\n", " plt.ylabel(words[selected_features[1]])\n", " ax.set_zlabel(words[selected_features[2]])\n", " plt.draw()\n", " plt.show()\n", " return selected_features" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try using these functions now. First, 2D.\n", "\n", "Below I pass in `[2, 5]` as clusters (meaning we want to visualize the documents in the 0th and 1st cluster). We are using the largest_selector function to pick out two features." ] }, { "cell_type": "code", "execution_count": 240, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:36.547594Z", "start_time": "2018-04-02T08:47:36.367603Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "selected = plot2d([2, 5], largest_selector)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that cluster2 (in blue) has greater variation across the x-axis and y-axis (more across y-axis), or the terms 'Ninurtak[1]DN' and 'ursa[hero]N', and generally has a higher frequency of 'Ninurtak[1]DN' as compared to cluster5 (in green) , which has less variation across each axis. \n", "\n", "Let's try passing in the exact same thing, but also add in a \"new text\". Remember `new_text`? We defined it way way above in the notebook." ] }, { "cell_type": "code", "execution_count": 241, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:54.029664Z", "start_time": "2018-04-02T08:47:53.851190Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "selected = plot2d([2, 5], largest_selector, new_text=new_text)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our \"new text\", marked in red, seems to stay around cluster 5, so we might predict that our new text is most similar to cluster 5 documents.\n", "\n", "Let's try passing in the exact same paramenters into the 3D function." ] }, { "cell_type": "code", "execution_count": 242, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:55.730045Z", "start_time": "2018-04-02T08:47:55.444788Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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Lks/NFNLNNyPddx+Sz4fkckV/33cf0s03p91nss91aGiIHTt2cMMNN9DT08Nf/dVfKboo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "selected = plot3d([2, 5], largest_selector, new_text=new_text)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see the same results as before, except we now see that cluster2 (in orange) has variation across the third term our selector chose, 'mah[great]V/i', whereas cluster5 and our new_text (in red) seem to not vary across this third term much.\n", "\n", "We can also throw in more clusters (than two) into the function. Here I call the same function, but also include cluster3." ] }, { "cell_type": "code", "execution_count": 243, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:57.656548Z", "start_time": "2018-04-02T08:47:57.316109Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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z2WWXxbzYLF++nKNHj0bsz5e+9CXa29sxm82cOXOG6urqCA3mDRs28Ktf/Yra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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "selected = plot3d([2, 5, 3], largest_selector, new_text=new_text)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see that cluster3 (green), like cluster5 (orange), doesn't vary much in the x-axis, though it does have more variation in the z-axis than both the other clusters. Our new text still doesn't look like it fits any of these too well.\n", "\n", "If you look at labels up above, we could see that it's actually classified into cluster5. One might have been able to guess this from the plots just by where it is in comparison to the clusters.\n", "\n", "Below I write out a couple other usages of these functions. See if you can explain in words what they are visualizing, and what the differences between the clusters seem to be." ] }, { "cell_type": "code", "execution_count": 244, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:59.586293Z", "start_time": "2018-04-02T08:47:59.186730Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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IAB/+8If5/Oc/z/z8PB/96Ef1bc6cOcP09DR33nknEP+s77rrLt74xjdmfc2r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BMuYnoQSfiX/p8luAsYrChKErAO6KMoylfW3b1KEQOEKooSqCiKIzAM2Fxmmc3A04oJ3YEcIUTq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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "selected = plot3d([1, 5, 6], largest_diff_selector)" ] }, { "cell_type": "code", "execution_count": 245, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:47:59.933717Z", "start_time": "2018-04-02T08:47:59.699093Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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WCQeKmZllwoFiZmaZcKCYmVkmHCjWr6RDkf8gZ/pySdek72dImt5F//GSpuRM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\nsSzW0zEAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "selected = plot2d([2, 4, 6], largest_diff_selector)" ] }, { "cell_type": "code", "execution_count": 246, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:00.466694Z", "start_time": "2018-04-02T08:48:00.161358Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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yhUceeQSAm266if379/PCCy/Q0tJCaWkpP/rRjwD4v//3//LUU0+xbds2du7c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\n1Vdf5Z577sFqtWIymXjkkUfijoUsyz5Jkv6GWB7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WVVVVDBw4kEmTJjFp0iSntU1feOGF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\n0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RS0AcZhWh4D/BX4CEAI0dDyvyuAfS2BMA74H6YvdSwmCqMeU9bci1MMQogKTJ/7nYqi\nHML0mf9DBmNtDaMXzoPioGSlF39CtHzJ+mNSRhxubzshhFAU5RPgbSHEF4qiVGAKuOuA34EFwGhM\n3PNR4G3gX0ApcBMm/rkJWCGEqHTiYfXCDiiKEgZ4CyHSW24rjlrR9KJj9FIWZzBavmglWGStLYFa\nadnGCPgrivI8kICpkAZwIaZC2SxMhbXvgDlCiExFUcZh4oszhRB5LdX4EOCfmKiNXpyiEEKoXT+9\nwbj70RuQe9EKLV9C7RexDpP+dDMtMjghxD5Msqs1ALKw1xLMPYEyIYS0d8sFLgCKhRBN3XMUvbAX\nvcG4+9FLWfSiS9BwioosJLaVUSmK8hdMRaPZcinci170ojV6A3IvHI7epW4vetE1/H9J3B7Dgxao\nQQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "selected = plot3d([2, 4, 6], largest_diff_selector)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hierarchical Clustering ###\n", "We'll use \"agglomerative clustering\" here, a variant of hierarchical clustering.\n", "\n", "In agglomerative clustering, each document starts as a cluster.\n", "The algorithm will look for which clusters are most similar and will pair them up (\"link\" them) to form a new cluster. Now we have one fewer clusters (because two clusters just became one). This keeps happening until *all* the documents are part of a single cluster.\n", "\n" ] }, { "cell_type": "code", "execution_count": 247, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:01.349145Z", "start_time": "2018-04-02T08:48:00.950850Z" }, "collapsed": true }, "outputs": [], "source": [ "dtm_normalized_hierarchical = AgglomerativeClustering(7).fit(tfidf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check the number of \"leaves\" as a sanity check. This should equal the number of documents." ] }, { "cell_type": "code", "execution_count": 248, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:01.472976Z", "start_time": "2018-04-02T08:48:01.468966Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "357" ] }, "execution_count": 248, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dtm_normalized_hierarchical.n_leaves_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also check the labels of each document. Like with k-means, this represents which cluster this method would place each document in." ] }, { "cell_type": "code", "execution_count": 249, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:01.846469Z", "start_time": "2018-04-02T08:48:01.839452Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([6, 1, 2, 0, 0, 0, 0, 1, 1, 1, 0, 1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 6,\n", " 6, 1, 1, 1, 1, 1, 3, 3, 2, 1, 1, 6, 1, 1, 1, 6, 6, 6, 1, 6, 6, 6, 6,\n", " 6, 6, 0, 0, 1, 1, 4, 1, 2, 6, 6, 6, 6, 6, 2, 2, 0, 0, 0, 1, 0, 0, 0,\n", " 0, 6, 6, 6, 6, 6, 6, 1, 6, 6, 6, 6, 3, 2, 2, 6, 2, 1, 1, 0, 0, 1, 1,\n", " 1, 3, 0, 0, 0, 2, 0, 0, 0, 5, 1, 2, 2, 6, 1, 1, 2, 6, 2, 2, 2, 2, 2,\n", " 2, 1, 6, 2, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n", " 2, 2, 3, 2, 6, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 1, 0, 0, 1, 2, 2, 2, 2,\n", " 2, 0, 0, 0, 0, 0, 2, 0, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5,\n", " 5, 5, 5, 5, 4, 1, 1, 5, 6, 1, 4, 4, 1, 1, 1, 2, 1, 1, 1, 2, 6, 2, 2,\n", " 2, 2, 1, 2, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n", " 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 0, 1, 0, 0, 0,\n", " 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 6, 1, 0, 1, 1, 1, 1, 2,\n", " 1, 2, 2, 2, 1, 2, 1, 1, 1, 3, 3, 3, 3, 1, 2, 6, 2, 2, 2, 1, 1, 1, 2,\n", " 1, 2, 1, 1, 6, 6, 0, 1, 1, 4, 1, 4, 6, 4, 4, 2, 6, 6, 1, 1, 1, 6, 1,\n", " 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,\n", " 4, 4, 1, 4, 4, 4, 4, 1, 4, 1, 4, 4], dtype=int64)" ] }, "execution_count": 249, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hierarchical_labels = dtm_normalized_hierarchical.labels_\n", "hierarchical_labels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Like with k-means, we see that there is a fair amount of variation in the labels.\n", "\n", "We can also look at the \"children\" attribute. This tells us how the documents were linked together." ] }, { "cell_type": "code", "execution_count": 250, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:02.791005Z", "start_time": "2018-04-02T08:48:02.785490Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[116, 243],\n", " [ 66, 67],\n", " [ 42, 43],\n", " [ 3, 4],\n", " [134, 138],\n", " [ 94, 95],\n", " [ 6, 360],\n", " [129, 130],\n", " [ 29, 30],\n", " [ 60, 61]], dtype=int64)" ] }, "execution_count": 250, "metadata": {}, "output_type": "execute_result" } ], "source": [ "children = dtm_normalized_hierarchical.children_\n", "children[:10]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first pair of the array indicates which two documents were linked together first. For example, if the array looked like what's below:" ] }, { "cell_type": "code", "execution_count": 251, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:03.247720Z", "start_time": "2018-04-02T08:48:03.240701Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[115, 242],\n", " [ 65, 66],\n", " [ 41, 42],\n", " [ 2, 3],\n", " [133, 137]])" ] }, "execution_count": 251, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array([[115, 242], [65, 66], [41, 42], [2, 3], [133, 137]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This would mean that documents 115 and 242 were linked together first, followed by documents 65 and 66, etc.\n", "\n", "Note that this means the children array should have length one less than the total number of documents. Think about why this is." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hierarchical Visualization ###\n", "Let's draw a dendrogram! Here we're going to use scipy's function.\n", "\n", "First we go through the agglomerative proceess (called \"linkage\")." ] }, { "cell_type": "code", "execution_count": 252, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:04.454430Z", "start_time": "2018-04-02T08:48:04.058375Z" }, "collapsed": true }, "outputs": [], "source": [ "Z = linkage(tfidf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we plot all the documents in a dendrogram. A dengrogram looks has a tree structure, meaning that it starts with a root, and splits off into more and more \"branches\", which then keep splitting until we reach \"leaves\", which in this case are documents. Leaves on the same branch as \"similar\" to each other as decided by the linkage function." ] }, { "cell_type": "code", "execution_count": 253, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:06.616682Z", "start_time": "2018-04-02T08:48:04.843965Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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C6VUcLxZlvE798VoG6NLGF8gLl9/F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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(25, 10))\n", "plt.title('Hierarchical Clustering Dendrogram')\n", "plt.xlabel('document index')\n", "plt.ylabel('distance')\n", "dendrogram(\n", " Z,\n", " leaf_rotation=90., # rotates the x axis labels\n", " leaf_font_size=8., # font size for the x axis labels\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is way too crowded, since it has all 394 documents. Let's try it on some subset of the documents - maybe the ones from a specific cluster.\n", "\n", "So first we select only the documents from cluster 0." ] }, { "cell_type": "code", "execution_count": 254, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:06.769588Z", "start_time": "2018-04-02T08:48:06.747529Z" }, "collapsed": true }, "outputs": [], "source": [ "# select only documents from one of the clusters\n", "mask = [i for i in range(len(hierarchical_labels)) if hierarchical_labels[i] == 2]\n", "dendro_labels = [text_name(i) for i in mask]\n", "selected_hierarchical = tfidf.iloc[mask]" ] }, { "cell_type": "code", "execution_count": 255, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:07.192211Z", "start_time": "2018-04-02T08:48:07.182184Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "72" ] }, "execution_count": 255, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(selected_hierarchical)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we go through the agglomerative process." ] }, { "cell_type": "code", "execution_count": 256, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:09.315496Z", "start_time": "2018-04-02T08:48:09.295401Z" }, "collapsed": true }, "outputs": [], "source": [ "Z2 = linkage(selected_hierarchical)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And now we plot!" ] }, { "cell_type": "code", "execution_count": 257, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:10.849062Z", "start_time": "2018-04-02T08:48:09.905037Z" }, "collapsed": false }, "outputs": [ { "data": { "image/png": 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6EVIDAAAAANCNkBoAAAAAgG6E1AAAAAAAdCOkBgAAAACgGyE1AAAA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vFdJ7KDkNhK1Vb40vJXLRbytau99dE1OT6QLIzNeyvdTfCBwpaTnCrmCwHVryezYp24TWnOgP\nRM74cGDpsp9awvbJkgbPdLHdF1htC6xu+5pSDF3Q+fLPbO8GIOlgQnh1UNm/zBc/1MNEVNkLeY7V\nihWA3W3/TdJGik7QQ8v7f0dFvG420z2MChCPsL2DpIsGxsourqSeVz08zfZsIa6kbRkVMGswke5I\n2Vm584KBpnq/zn4aeILthzTEPQZ4n+3rJa1CnOD7A6fafkplzG6oz/NblACSvmj75bWvH4vV2Rt8\n2/azJV04lFTOhqSrCAXOUUWBfobtatWt5rQ6mI1KsmkiUHjqrQ/80vbt8/r9GWKsUR4a+Jvtvy1E\nazucGFDzLqId5++2XzgwRqqvr+aiaq1Rz/Xint1XMEr61hCVgqS3E/5aKwF72P5WuQ6dYHuwV3Ym\nOnWapGcQCVmLOm0iKArDX9Bru7V9VWWsOVrHJkT6D4ai/f8NRBJzP6IoWE1yKNpG9yWI6luA9xcS\ndkiMLF/2fszziOTvy4SF1J5usASQtN/YU65Rao7FPK9VLatQrz+HeP87BWmL137635kBSUcRZPz3\nxp5/lu2hm4KFEr17lYhutdmtvDX3qhJzG2IjuzahXPlIIT8WGLLztRLzfIdfYpeXVsUsqqqXEEOI\nz2RE6tv1VmNpSCK8+/GeSxS6lmV0P6i95qbFWphRyIMpQ7hrr7mSdrVdNcBxLM77iI6JdRm1m9eK\nflL3P5J+QLR0n0W8b7MLZUNzwMxcUtLKhahdjCA1u0GYp9oerBrv5TFvtH3U0NePxcp8z2Z3W0h6\nOrA1YXtwC/D6oqCtWWNTriBpdeAPjlk3byIKl/sRXu9H296xYk190dXsp8vaFuiAyLG9Y1dgBIbt\nHSU9DXgtQUp/gui82Nf2rh0/U7m+ieZYardfnUisyv//WYT489eSZhH3glkE2Xqu7Sr7kFJQ6RdX\nHmH7VwNjTOK8WowQlnbXosWI6+QQxfhMsTvl/rOJToCm7sj/70nqSUHhTfYs23dKWgr4tu2ntFw0\nEtd2HnEzv4K4MFZfsBVq1sOJi+RuwPdtDxrOMQmoQ7UuUwAAIABJREFUKNCJyv86xCCqKgX6GMlk\nYjjeHsBfFmTSnZk8lgRjplg1bbITJfYlPcQVVhOSXtv78Z3AIYw2FrMq4h3PyDd0K6KK3SVB1ZtY\nSccR7ZSXEeT+Eh6oLFXYB/yjKwqUKvESWYWHWii8gV9B3MQ7dRqw0Axlm4MwlHSK7cFtt73XP4qp\nm9jBKtm5FFRbiIQfAdvYblULLdSQtDJRbFieOObOs315RRzZtkZD7Wajtcgi6STb2zfG+A5wBiNf\nyKrrWi/ewzw2VMbtw1uakU3GZ0LSFgSpvBrRzntzzfk5dq+agsbPVMR58GcvJAl8Zr5W4n2ByEk/\nSCi0H+2GOQ+SnumRF+wiC0mXESKY5vtBZqxsSDrR9g69n49wmQdSEesUxoZw92MvSEh6k+2mDrXp\niuwdaortknYGXg48hchvYZTHDCrSZuaSncBK0um2XzTktTPE+yFBHP4XY4N4hxYZM9+zEm/G17ix\nU6rcX7p78mACvf8jU4nbmsLDGjP9m+0q7+0slL1jh24PCQP3jpIebPvW8vglRIHlIKILen/bVR3H\nExA8zGHnZbu2G6M51iT2U73Yizs6tQU82DH7Z8jrU4srmedVyUt3JHiJy0q8uwmrjo8OXVsv7rhy\n/7Plnz5pu1q5/38k9QxQDCt7ByHPF3GTOgP4d9st01sz1jbHhbvmgl1OwNfa/kzGuiYF5SnQtyBa\nt/6X8I67NGmJtevpJ48fIZIhYHjy2Is1h82E7V0W8Nqmu2B3saqr4Z3aqvb1/4R4TwbWJIbPDVKj\nLsxYmNVp6rXdMnXgxe898ikcGnMOP2TbLd7saVAMu9nb9l8a40yX8AHQQKAfbvutkrYH3gZ8y3at\nbUUKJH3Y4VvXDYqEts2igMNs19oDjcdr3mBr6lCZL9jeXNKHCZJ/61pVSCayyfhMFNXbFoRf6IsJ\ni7dWv77WNU3kHjoJZOVrJVbXwXWl7ZZW9lQoWm5XZLT5b7VVS0E5Tv7LCVZ2mbGyIGkD4ElEN0FH\nHC5ODN2rvU913aTd9xSSc1GHEroAMnNJSZ8i7Mma1ecl3qqE5+17iSGdfQK96l6V8Z6VOOOq5w6u\nESWVmPsQ97tbqS869POq2U/XxPpXgpJU2WMxU3IszWnntZ0r7bwyY2Ujk/TOLq5M4ryS9A7bh/Z+\nbirka0LK/f8jqf8/hKRlgdczamc61sWztiJWmnVIL+bDGJFzC1yFoWi7fTXwXeDjbpygPglkEaRq\ntJmYxNp6F2wBJ9MbSNpSDR9Xy7YiM55ikMa7CQ/v1wA72Z7vIXSd4jNjLZNCtjpt/G9ueQ+U1HZb\nYnUKnfMdLehfaSGpNdWio3pYbYl1MfAQgoDsumoWipZsSecWgvREh7fbxbZrh3xMDJJWdIO6WNLH\nCVuU6nudRp0rGxFDXKv9z8v991DgVOCt5dg9wfZrtBDYeUEOGT8p9M7z84lW6gttP3UBr2mhVZRl\nowhEXgw8jPCTPdX21xfsqkZQdB9uSXTkXU0M/K224JK0DlPVbtUDYSXtTrQC/6I8VX0/yIyVBcWg\n9/WB1xG+3iJ8RP+ngcw5hxiM9WngSuDFtjccGGNiHTr/CsjMJSUd6LGZDo3xHrgwFcgmhYU1P/tX\nQJYqeyxmVkdBmp1XZqz/QxvG+Y6Efe1EuiMXucGJRdlU1aoyFmc9ouVz5V68haUS+CUiQfsqMSH4\ny9QPW1leMdW62ToEQNJeZS2XAxuUDd8HauMlYV+CxNmMmJQKDRX2CSGLkPy9wk+9s5m4LiFm09r6\nm+j/x955x0lWVdv/uwgSTKigD0RJJlSSooKKRBXRhxF5PkDhJ2J4KmZByUEQDKCIIOA4gqKiKBgA\nJYPw5AESDMgDRFEE9ImAIAKyfn/sc6du13TPTJ1zirpd3evz6U9XV3ft2dNd99xz9l57LUn/KCxM\nN91O0TOpKWFLNMUhAatLmsdCGLQ41IcvE3qOR9r+l6Q3EcYMi4pziPfql2zvUpDH0FCzQJ3waYJx\nO9XXi4xaBeqEB9Lh82+S3kyYC5bgYOBVtm9e6E8uBB0/VCymMAxuigcD60IOC5K+Yfs/JL0PeIWk\nWwvue88Bzpd0K/mNgjPT57MW+FOLhtqmMtXQWm9rmZEOA3PT7+pzhPnlyAukzT1zMoLCKPOqDUnv\nBZ5NGFHdDDwR2E3S6i4YRU2xiyWbEl5te8MW8zZ7slLSDwhjpOZeYPIMVxvsAKxk+76CGMOIVQUO\nY9oriWu0XdxfmXzTpxom3M1e5Sz6ikxkns3SWbbKlE6K9RZ3dGq25l6yZoE6xRv7AnXCDyW9mon3\n5JHL96X37ofbrM9xgyuajNfeY9l+mpKcV9rPP0PSpmTIedWMNYs8aH6TXxGydv9TGPp0+pj7NTA2\nTGpVGFXpi3cxsD1RWHobwYT8eI1cS9HffZJ0mu1XZMaqIh3SineBW9qBki60/eLceOOMvoLrCsBt\nFBbPJS1PsNhXB37rTJmJmrm12CViolj/yFkmqqzX14rbsPHOtr3ZoGz0dHi9k2isNC7XnTAMGRYk\nPdv2L1pfP932b0aZU8qjXw/5rHRYzo1XRaIjxVoL+ATwKOAOYA/bVy34VQ8NJD2GkBw6jzDmeIEz\nzVHSxmpHevJbpff35rpsWN4X2X5hbrxZLBqGtd52GZNco3vmrh+J9Xk0UahbB3hnh8gTxUgNlc3s\nCRM1ixNSQSXXezXJplZx+kdEw/ELttfKjPVDVzArasU7FDge+CW9wkTWHqtmrNqYrLjvAWUOUsN5\nUtRggNWAKkzptGJVmZpVz6BwPtPxLhQ1u45akxOpeLtWrf2epK8QpLz2NTVyc1kASV8FdrF976hz\nadDV9WPYeyzVlfMqipWugbldPBN3vbki6d9tf79ivKFMR44Tk/qVtp9XMd4/bV+vcNK9TlK2acsQ\nsLikMwi27DoE028/yOqUmZAleARhVLMTgzE++3Gfwqn558To8v0FscYaLjACWgBOsL0lhV2xyrk1\n7JL2143u1kgP2EMsjJwt6ShgJUmH0ys0LxJsv0rSSsAngT3oMXM6hYrsNAjmYvv9cADhdJ2b26OY\nKKmRqxt6B/AK4mDxf8Sam12kJvSyfyrpz+nrkomOIwk9zt9JWhU4gXCRHxi1NnySdrI9h2CWGdik\n9e1cB+93EEbGte4n90j6MnB5+n//a9AAkna3fZAm0Qse9aZZQzSVKcF0KERL2pMY/7+nea6wEFzt\nGgXus31SenytQspsnPBAu0AN4JhEKi2Oru2eZNP2kk4uiLWrQpP6g4TZeAnT9R+SPstEtttApmx9\nWD99NCjZY9WMVRtyucF7s6faGvgLPR+XRwNZRSaFqX0b9xMM70/bvi4jZI0pnQa1pmZ3IOSk+hnL\nJhh6Wai8l6wGSY8AtmVibrm6z9UmJ2xb0oGExm8NrOSWVGQu0n7qtHQOrYV1iCnh39AdWbvq60cN\nDHuPZft6wg/g0IX97LBjpWvgT5JeQPz+H0zP5zZmq02vpNyeLWnpGs2VIVxX9yXSwxOIqfvDbL8n\nI6+hTkeOU5G69qjK6YqRz69LuoJwq+wKPtF6fFphrFJZgn7sCHyU2MBcR+jxzuKhw82SPsrEBbvI\n7bkUpd3W6Qjb+yfGxFnAtTnMOds3S9qR6DQ/hRjvLjZdqYXJ2GlkbLinGD8ycFNBbl8CVmHiYSD3\nAHUGE8eYihoGrivRsQS939MfCMZyFipu+C5Pn8/se75kbOsCYE1JtVh9rwWeZPsGhdN4znujKSbt\nUZDHAiFpoxz2+ZAaoDMFL7O9QcV41a5R6hIUuoi1EmuuDQHPKoxbTbLJ9pUtNuR3KFvX+plMpdJq\nm6b1bAUXyknVjDUEFBf3nUzEJG3bLnhLKjlTXQKcTMgdrkP4r3wTmEvskwZC5b1CFUmBFjNwd9u3\nNM9LenpuzFp7yRRrC0Kqc2XivXF74f3w28BJxJ7hSMKUOBc1mitt3C3pi0zcr+U2uf4kaVcmXlMD\nnx3TPvJ/JW3bl1d2Pcb2OrmvHRZqrh9dZWVPEzw/fTTIbqam9+4yzbRIhdyqNVeGcF3tSUxq/zjV\n/nL3WDWlCufDOBWpnwJsRJ2iBLYPTg+PlvRdFxgr1UblTtnitq+JJg0A8xl/DIg32n5384VC560z\nuomSnkcq+DlTCqNiLsMwx/sdsDS9DbGBgTcaQ8qtCmp2O1vx3uIKen1TbDbWkbRO5mbjq8S47WUE\nq+kE4E0FKdZEFXZaYt3OUUWzQ2A1FxqGtnC77YNKg0g6olkbJe1h+4D0+HjbO2SG/QJwsaTfAU8m\nDlElKN7wtRoy/wNsTmu0lXy91eemj+y8oMd+JgrMVsufgAEaqokR2xQeN7M9J91b9gHmEOvwwEhF\noZcS7KgVgV+Rzz6fNsgtxg8Jv6hMeDiCuEZvJBpnXyiIVZOg0EVMZVBZ2gjajtjbvpOQbMpdb2uz\nIZtCx8MIM8bXUsDCk/QWQqbw8ZKeA3zDdtY0Us1YQ0C1MWWCUbY7PR+Xkmmdl9jeDUDSpcDhtj8o\nKSumwlCtf7Ig91z7V2IiqSE8HJUZp8Exkna2fWtqbO9DTJzloOakwyeALYBTCQnQAwtiASxl+zhJ\nb7Z9rKRsczHqT07UvAfcQOzVmimfrLNjwiMI0+GG9VnKsl8Z2J3ee/cg29kklsqosX4MnZXdsT1W\nNQyBBFdtemUIzZWa19W/0odTDSSLfDVs5v44FamrjKo0UM9Y6f3AliozVuoyimQJGigMfR4HvCFt\nMEQwhrahI0VqSYcRHfrLgLdJ2iFnvKEiqpvj2d63Rhw6bNxXu9uZ4m0FfKU8u+qbjZVtb5cenyGp\nS+PytQ0FT5d0JD1TsJKN6M01WCEJtcaY2p3qzQg5EwjGTxZsnyDp64Ru/J8L2cW1N3z9DPRstPNK\nG6pcZlQt9vPDgC9JOpEo5MwB3gPsTBRQvj1IMElvJArTyxK/t6fZ3jw3uS43GaHzxfilgdekDyg8\nYBOsyg1J1yhlLN7zJK0LPIbe6PlIJ6VqwgV+KAvBIakReAvwmbTX3TUzVhU2pKRHAq8iCnsbEiPP\npfqVO9veKBX7/iXpcR2JVRsnEGeLFYAvEnusXGxDXOvrEPuOzxTE+qrCz+j3xH19rkJT/XuZ8fZJ\nn0XIhG1SkNvXgG8Qxdv1ga8T779cvB04VtK3id/fGwpi1dxL3m37TkkG7qWM+Qxwm2Kq+urUNHhk\nQazakxNzKxKvrgJ+6ApGqbZ3Su/7xwO32R5YTq0PXwH2Bi4l/p5z6Y70UPH6MYypjo7vsapB0maE\n0fIDRM1pH9v9U5yLjJrTK7WbK5Wvq0MI9vOaxJnjkwWxhoZxKlJXGVVp4fHp83Nsv1zSRaUJDgsl\nHTJXkCVI2JhYqFclxggE3Ed5t74m1rW9SXp8dAcKfn9PBaZN1RtxLTLHk7Q9wZZYE/gbwQJdf8Gv\nGn5uqbBUU0+pplYfVNLrG8Jm44+SPk5IKKwP1BhBqoV+dlppE28O9TaiNVkhtW7eUx1IBj6oaAo9\nZElFesiVN3xVGOgpryUJdtTW9DbcA7MXbd+aHt4PvJ6JLO9BdCafBNxOvM8eLuklwF0OQ6m7B82L\naFhcQOjCXSbpNQt7wULQySZj7WL8MGB7JwBJa7uOKdXnHZrWt6a4B5KptS/p+wSLt7kPlKxrYw9J\n6xF7hfXV0+9egrKiZjEbUmG6eDfwXeC/gG/ZrkHmeEChoWtJy1BWBKsZqzZOIAx532T785IOIu4P\nA8P2/ZIuJxoYAjYgnxl/lKRjCJPlv7SKCIdlxms3bW6U9JGcOAmPtv319Pg3krIaLZqog38JwVQ+\ngNBtzmUFV5t0IBoDSxMeJ+cDPyiIhe1tASS9l2DKXlMQq/bkRE3i1ZOBUyXdTDQzzswlPUj6T6Jp\n/1tgdcUU4QmZeQEsbfun6fGFCk+ArmBJ4J/EPXkZQuIn929azMqeDnusyjgAeLntuxQ+RGcwv9Tg\nIkN1zei/QsXmSs3ryvYP0z5keYJQV1UisBZzf5yK1DWLElDBWGlYqN0hs321wuzqpIX/9JQxTgFO\nkfSkDo3h9OMuSdvRK/j9fZTJeDjmeO8lWDlnEZv2LH3x2rkltnI1PaWa3c6EKnp9LdQaId2B2Miu\nDfwaqFL0K0EqyDV4avp8KXFTL0G1jWgzUZDW7qz3rqT1bP+cMg3ZNlZST3N7hdbj5TNiDUsPueaG\nr5iBPsQN9ykE4yV383mO7bNSju8n2JD7p8PxwKPKtp8maW3gdZL2Ap4haVPgItv/zMivegO0EmoX\n44eJwyg7UPRr7Tco2R8tY/sdBa+fNqjEGHqQaLj9ld4e/l7COyUXNaQmLiaKoRsSTYdaxsgfJaY4\n1kyfd+tIrNpYIRWE31gaSBX0kIfYNG4McAUsRUwm5eKKVEC/nJDOyr33ta/F3wMfT49LmhjVJh3c\nk+37bvooQrov70i8RxYjc7JGw5mcqEa8sn04cLikVVJux0v6JvA5D276+W5gI9sPpHrF+URjKRen\nJqLPVQRj+dSCWLVRbWKQOlMd02mPVQMi1RPS59J7aU2j69rNlarXVZq2/DOEBCXROMvCsJj7Y1Ok\ntr2vpH8DVgNudLkMQA1jpaoYcoeshFkyDx0uUEN063chCrnX0QFtX9c3x7s7jWbeT7hRr9uh3Krp\nKVXudkJ9vb72ZuMGMkdI0+F8IOmAhwCN9MLziHvI5cT6cS/5msMA3+/biGYXA9IN99XAXfQ0hwct\nOK1NNBn6O8xZDVDbzxj0NQuI1TCCj3VLe1shP1GyrtXc8NVgoA9rw/072yfmvrjNMLJ9MVF0anB4\nZsyrSIUDSWsQ6+5e9K63QWINowFajCEU44eJUuO5YWjtH1/K4p0OSGSChjG0Wi5jyGFyeBWwRcNi\nLMipkRcrPnjZ3j/FXJU4ayyeSDEXpPdNbtxL6O2vSnOsFmsIuC0RHpaR9FrKJsxq6CEPq2m8qe0H\nmi8kLTtogFaz/WNEw2EN4Cjbl+Yk1L6O1DMQzSYCUHnSQdKewCuBe1o5l0hDzCWmHf5YkNOwJieq\nEa8kPZPYO25AMOT3Sd/KMf18kChU3ZQ+5zKyX2H7NOIMNJeY1P5Ma//bBVSbGKQCK3ua7bFqYA9C\nKrJp5u1ZGK+m0XXt5kqV66omhs3cl7srWzgQJH2YOMxdSdzgznbPhTgn3mG236eQT/gg4YD50TrZ\nZud0LbFBPjId2H9ke6tKsbcoGOueFpB0qO0Pt76eZ142Skj6GhPN8Z5tO6vQJOnlxBjk8wiH6++W\nHHpq5pbiVdFTSgyTCd1O27ndTiSdSoy4Nf/PN9ku0esbe0j6oe1XTvV1ZswnEBvRG0s2opIuHgLb\nvjNIm87NCKZ9s4ldAniR7Y0L4m5OHE6aDd9+tgfyKWgOxQrpkAlwhgRXs+Em7utrAW+lcMOdmK0P\nJ7r9KbXx85xI6+2EJmPJulsbrWL8Vq5vgJOTT1VT3tpQyM59n1YBvbT42kWk/+dL2oyhkvVc0sHE\nhMPl9Ka4BjrgSfqI7UPUM7NrCnN2vpldO/4TgFeXFK80v1zTvoOu38OIVRtpYmVnouh6DXCM7Xsz\nY51NTB1+hygifsj22pmxftLfNC7cLx9PmHo/KOmxxD53oDOfpJ/afpGkswuLtf1x5zMQtT2IZBaS\n1iGINLvQ8y66H/hvZ05ZSrrAdrXR9XQG2tF2tqFmKpxvQBBWvg3s7gLpQyk8JxTTbrvQ83E5xvYd\nmTGPJN5fF/U9/2LbFw4Ya21i7XgMIYu2t+0rMnK6hGCxnkHsd+c1QwZdv4eF1ID4J+WeNc25dgIr\nu0JztVN7rFpQb3rldbZLjFb7425HEBlvJBld2z5+wBivsH2apNWJ5tSqFJ5pU9zi60rS/sw/9SLg\nP22vkZHT0OqSMF5F6gk3JkkXFhatzrK9uaTjbe/QlaJHrQP7FG9UIH+BTXHXBRrG4DU5N6baSEXM\nNYBPEQ0HiILOx0sKOrUg6bx2Hv1fjxI1c1OfnhKQraekMKd5Udq8L0EwkEoOsf3/z/NdpnE99kiH\nu2PoSZq8PWcTpJAamjPZmlSw2dsDuJqJG8eBDj2SzkmvfQxhgnQt8DRis1FqxlMExUjmqsx/uPuF\n7Tsz4lXb8El6i8PQZ+++bw18iJ0kdpUNd/r99SdXxbRNHXJRr91knAmQ9AXgAFcw5a0NSafYfvWo\n8xg2JF1INIpvkvRk4ETbg7L52vHO6XvKuQW7VoFIBBngqtwCaW2k4v4EuabcfVHNWLUhaSPgwtbf\n4cW5a66kFYmR5+UJPeSzMw7+w2oab0qc8fYmpvt2tf2rBb9qvhj7EgSutelJfDTST9l73BqkhBRH\nwFcdch/FkPRF4HQK9n598a4iDDobyYvs35t6kxNbEWzIrMkJSefa3kQVPSckPZx4D89jxtseiMUr\n6XDbu0p6l+0jK+T0VuCNwPOJcwb03rudME6UNN/1bTtLdkXSqba3Ls9q/KHwEdiNmBb8YPt7mWSY\n5hz6QuC/KTCjr91cqXldTfZ+beWW+76tTiRqMDZyH4QG7AuJhWx98jVgGyymGJVobm4PLOiHHyq4\n3khwVda0gsm+IVHI+W16+k3pd3ix7UNr/nsDYhViwWg0y0W8P3YfYU5tFJvjSXoQuIIwS5z3NOU3\n85rGfTX1lI4ALpZ0I6nbWZAX1NPrmxS5hStJLyV+b8uR9PA6VDx/PcFmegmxTr4+M87l6XPNNekp\nhEzHPJYPA0rLNEVQhS7fi23fnTbyWTrvbajQkT0VVH8HnJfuAysR9/N1yZNc2UbSZcCektprSM6G\n73hJixEd/6qwfT2hl5h1P1FvfHSycbQs2QR120V9ZdvbpcdnaPRmwdMBtU15SUW+R9M7/P8+M1Sx\nzvs0wbuAIyQ1jKF3lQSrzCA7k1g/9iOmwlYm5AW6gJpyTbW1PmtiH6eR4lSo3pt848RmT3sLmbJs\nxP7nQYJ8cVZ67n7g4JxgiYEHcY8/J8XckZBUGwi29wb2lvRftkv3yW0UG4im11jSHyU9n4JJhxaW\nJqT2GmmwbFnBlEcWq36KWDcCnwU+qzQ5kRlqMs+J5t/InQg7nXJt5RdK2gV4j6QJ79XM98ZxwHGS\nXm+7RGpyaLDd3oOXrpEz5f5eA28l5KjadR3I96N7j6SfAp8mmpUiTNFzmlxHExNv69K7H+TKTkLF\n6yq3EL2QmNWkCvsxTkzqJxFGH2sQHc9DCw4CpM1xc+BfAnh+V9hRtdG/wNoeuMghaW1PoQm8oO89\nlJC0pAtGtoYFxUj2a+mNbH3PLR26RYyxDXFQWoZYoL9r+7Yu5NaKVcyOqtntTPEaaYKH09Pru96Z\nen2tuPMVrmx/LCPOzwnWaCdYfZIWd5ILkLSu7SskPZ44QJ1qO8v5PLFpTnPBCGRfvB/bzjaB6It1\nGbC17T8qdH6/b/u5BfHajuzrA/c605Fdk5g+2X5dRpz1iA3fLsAcmDDKPugIb8NAb+OJwFNs1zKh\nzIKkl9s+Q9Jb+r/nAccqNb8W27bumIt6Osj+kl6T8Vm2/2O0Wc0sSPoS0Uhtj8XnejFUY211GZK2\ns/211tevtZ1tgjbZmlTApD7H9qbqTVmWTm0WNSz7YhXLNQ0jVm0oJuk2tn2fwozqPNsbjDqvWlBI\nykyG7LWjNia5h3pQ5m0rVrVJh9qQ9AhgWyaekYsmwmpAEz0n5sGZE2E1WLySnkiQVvYiTN7bDNKx\nk6WCenvwFGtG3N9rQtIaibxSGucVRGNra+A0KJfzqtVcmYnXVYOxKFKnAkdVHUGFbMXehDHby4Dd\nbB9YK35XULHI8QjCtfhXtn9ZN8tZLCpaxdF9gbNsd8aRXXX0lC4nzCTm0ut2Ankjfaqs11e7cKXQ\nJHy/7b+U5lYD6eD6SsIB+WiHJNJRhA76e10mufJ54EKieNuwaXJ1CecShbk2IyGnu94UEfYkOvZ/\nI6QAsosJSqOara9LJHTOd8/0aVNJJ+dukFO8Khu+Vrz1gV0J/ecv2D5rIS8ZKloMtfkw6HtNQ9Zi\nq4GaTcZxh3qSN8czf0EzW69cfTq1JZD0aOCdxD3048CWtn9QI3ZXkN6zZ9Ibk12ceN9WYSunfcg2\ntrMMltK9ZSViD/INYp+Vu35Xa1jOJCgMdD9GMI2fBBxs+3ujzao+pO5Jy0havyFxSFrZ9h/S481H\nfX9PeWxB+PGsTOwjb3eZrMnpwEmE4eGRwPNsv71Grl2AejJ761NPW/nhtu+ulmSHMYw9OIWkwVnk\nQ9KLbP901HlMhpl0XTUYC7mPdBNfRj337Ro4nOiqnGz7XwoTkbErUlPH2RrCtfRHwBslXUOwLu5v\nNln10p3FZEgHu02I9+y/Ad9KHyOHkp4SIZlQqqf5cUJ/alWicNge8cnpdp6pMFFbO30GivT6DiAK\nV4elwtVrFvaCheAS4BpJv05f5+ZVC38kmlpPBpZJLKalbJ8o6R2FsR9BsHkbNnXJmOYN9MbAmlhZ\nRWrb/0N012uhmiM78IBCWuNvkt5MMPKyUYmRIKIw+jZC/mmfmoXvQrQLU8196QXA0xlwP+Rp4KKe\nph6+Peo8pgmasck9FvhTg+NmSbtSoWFGyGN9AfiYQzbrfcDYFKkTO3NHemOyAu4j9pa1cA3wciau\nBYsM22+RtET6/YtoSudi3VbD8mgVyvFI2ooo3jZmhwfb/uGoY9WG7e9JOoXeJF32GUPSTsR77l9Q\nV+9WGTJvkrYkCu9fISQYuiYtcwi9kfWvth5/nN5o+0CoOekAfIKQfjmVkNMoPbcvZfs4SW+2fayk\n7AIk1J2cqIRGZq9ag6FWIa2p6UxGLsglsAwB1fbgk5EGyZPvm0UmulqghnrX1XTCWBSpE55D6HPe\nRh0dQdm+XVJz4xyn31UbtRbYJW1/CmjMDk6WdBJx2PhAnVTLoDDL2o0eq+wQ279d8KumDW4j/k+n\nENrUBjZX6Cllaa1WRE09pdOA0yR9tcbNxJU99jWNAAAgAElEQVT1+oZQuNoBWMn2faW5VcLdwNsc\nhpVfI95ve0tamp4WfRZs71QjwYSrgB+W/N5aB6clgScQ5korALcU3lu2I2Q13ktIU5UY2W1HaJW/\nk5gsyGZ8VsQNxPtkDsE837gZYxz1WtS8x9I973VEIf0sMrUhPUQttlk8dFAYWt2UvtzMISn1PELu\nYA7B2MxFtYYZsIzt0yV9JH3dJZ3gYqTR1bmSnpeag1Ug6QJ6shXQM5sdJEZjXnQB4KhPz9OZzL0f\n1GxYQrxfN7F9j6RlgXOB3MJyzVhVMNW0Q9rn5t773kEQKIqlAFXHn+A8wvfifuLeDrCqk7RMRk4r\nEfuDDYi9DETj5xLgi7b/OGjM2nBLM76ZdCgId7ftO9PZ/V6CgV6C29L+9mqFDMsjcwP1TU68TdIO\no56ccLflJHYgmiL9DcUinfHKqLkHr0UaHHtImvLvP+pzRgOFrOkEuECGeCZi2hdelTRqgQ9V7oDM\nTZ361SV9iziojCNqLbA/kLSa7d86mR2k57M0yoaEE4nR8yuJ4vnXgBeONCNAdczxhtIIqJTba+gd\n4h6gwsG6drezRoG6Fatm4eo8otD9S3osvFxDmWLYvqn1+AtMNKzcsSR25THNJwOnSrqZGMk+c9Df\nm3vGiV8mtNT/IGllMhl4Lexp+8PNF5L2IBj4OXix7ZOAWxQmRm8gmlRZUMhcPSN9eY0HlONJ2Cf3\n3x82FAZ2OxNFhO8TY/931ojtQlPHWYwUDwO+JOlEYHtiv/ce4r3yfQrY6Lb3hXkTBqX3vmslfRR4\nrKT3E3rjY4eaBeoUb6MKMXatFauFmg1LiPfDY4B7iD1b9r2gcqxaODd9Ppjygn6DC4A1S/ZYml/m\n7WnOl3l7LiGFd52kTSX9hDiPLkGwvQfFe4AT3CdvI+lZhITFoF4pK6UCkfoer5iR22QomnQgfldL\nA58jWKhFkya2twWQ9F7i3Jjlu5JQbXJCIb23NbFfc8rrB7ZrGpAPmlPjGdRIiMyDM6RDbB+SHu5u\n+5bWv/P0skzrwXWMVxtUnYwcc+SshYsE1ZNc2bcJCTyLkDnN9kpSR/Xxh4lpr0mtyhq1fbEfR7g1\n/9Yd0YStDUn9RaD7gRs9oGyKpIdNxVpc0PceSqSmw2tsO90IvudCo4hKeXXKHK+NmrlpBuoplULd\nNpRpmMaLAU8FbradzVqRdAl9Y5q2312Y4ypE0XBj4JvA52xfN2CMS4GNbP8jMcrOt71+Ri6rElMc\nnyIkayAaxR93vqbpBC11SWflHI4lfRjYkJDnaBjxqxN/14ttj0XhVdKdwO+J99i/aB2kcg5RXUel\nJuPYIx34X0Fojn4d+AjhJ/BfKtCMT7H3INazu6ggJyDpVYTJ729sn5obZyZBIenwFpLXARQZJ66d\nYi1H76CYa6x0aH/D0nZuwxKFoeDywF+BxwJ/IYgBA1/3NWPVgip7iKSYxXssDdGfQBOlZR5Zq6la\nkM98psMNnGniNcmkw1zbx+bEqo10ve9IyDA099Dc6/37BGmimZz4D2do7Uv6KmEcfw4xqQOxX9sM\neEHBVEH738iRqlnH9pWa3wDQBYW+5ve2s+1bJb2AkJB7RW68rkLSisTE5vJEPevsTKLI2ENDkoJR\nRSPMSWKfZDt7SkRjro8/GaY9k5r6GrXAvBGpNxJMAqVxsrE7xBIM3CUJdvHapI2CpJ/3d94XgiMl\n/ZW4ad6YnluVuGkuR4xVjwSt0cDHAb+QdDWwFnDrqHLqwy+I5kAXUS232gXqGt1OaZ4xzWL93xsl\nY7mVw6ZphHQF2zePOp82+kY0lwKOKQxZbUxT0jMJVtoGxFjrPulbc4nNxyDYB/iJpAeJ99q+C/7x\nKbEKMfLfjP6LuLZ2z4wH8DBJj3FIUz0WWDozzhlTFaLTIW1cUKIfOx1xCB1tgHYM5ziZfiWG8iuA\n/RMjr3Tk9pUlzbs2JB1vewcSO1A9v4exQ0U2E8Sk4IsrkSXmEofEbJmEVsNyC4XfDcR57KXkT9Xg\nAuPiYcaqiH4PkXnnvdzCed8+RsDATHlXlnlrFW2bryFTWiY1ybYG7gA+YPvqQfNpI7cQvZCY1aYT\nJO1J6Hbf04pf0tAovt5bqDI5MUUR+tfpI2sqVBWkamxfmR4+wfY8T6REgihZv98OHCvp28Rk7hsK\nYnUWlVnZ445hScFUk1xp3dsh9jKrFeQFlfXxpwOmfZHalTVqWziFWCR+XjFmF7FEu5PbMAASi2KR\ni9S2d5b0FOBV6QOClfcl2/9bNePBUdsIqTa6Zo7XRidzm6zbSd4m6NNEo+YseoeC5jAwcsZyYq1s\nDzxe0nOAb5R0Ymuir4O9ItHkKkHNMc13M/mI60cHDWT7B4W5NHHOI3wTPuEK+pcJHwW+lw7XDxJy\nKTm4QdI2wK9sT5AQcMjXjAXcbf3FYaDLDdDOoN2QtH0xcHHr24cXhv+hpFcz0ThxIKaPpPUI35X1\n1dNiXAJYrzC3TqLi/b3B+dSTzfoV8D+Fa/gwGpZjD1f2EIF5xbktiEJuU5wb+L3mijJvNYu2RJPs\n+QqpsuMUvk0nAc+yfVDFfycbNScdgJfZ3qBKYoEa13uDKlJvkl5OSFdeBexfQgBSXamaBi9KBKBv\nSjoU+L/M3NrFxksIE8wDCMmDrugO1zT9nMUiwkkKxnW9jKCu5EqzjptoEr62MLdq+vjTBdNe7mNY\nkPQD269a+E9Ob0g6GziKuNmtDbzD9maSzu9CMbImUiFnMyayc0auma2QOajC8pG0FuFu/ShiUdyz\n1d0eSW6qrFOWYp7f6nZuKunkkpEcSY+w/ffW10+wPXKmvaQLbG/U+n9WG3MtRbpJQu8G/FXbnWjq\nSXo4vSmOrGtdfUZZ7e+N4dp4NvAj4AWEtuF+tu9vJg0yY1Zdi2YxOCS9B9ibYFhBR5qMMwmSvkIU\nv5pJmIHHxSWtQ+ih7kLP9O9+4L9LRlu7iiHc36vJZkm6ijDQbWSjsq8pSUtWbFjOGKSmzV7EveVl\nwG62DxwwRn9xbtsKxbnOQTEivlPD0pS0AmGcuHQX9rhQ/Qz0ReB0CpqCffGKr/fW5EQVqTeFBN2W\nRBPvw4SHwiXAyom4N0isoUjVKEwinwmc6PANy4kxlbSMu3B270eaptimnxwzi/qY7FxGT04te4+r\n+SVXziqsoSwFPJ7eObTYODEV0dclfIPuWdjPT2dMeyb1EHFCuhH8mt6NrljnqYN4A2EOtCmhbfWG\nVMwdWCdrGuBbRAHm9cQI7yp0w9ixpjnekcD2tn+XNkYnEEydUeZ2efpc09CjtsHE8ZK2t313Yggf\nTYy+jRoPKMwSLGkZ5r8pjwxNBzutF8VmmJXHNE8niq7ZEikejlFWFUxRQC/ZoC1p+1Mp9luBkyWd\nRGyEck1Za69FsxgcOwAr1Tj8z1QoQ5uzDyvZzjbLgXlj1FcSo+czAVXv725JOpTCdjX5o9oFakmL\nA9sQRbUjgec404SyZqwh4DBi7P9k2/9KY9UDFakJRuYFwGGpOPea2kl2BK9lIkP5z+nhHSVBKzeh\na046LE28N5q/Z9H4f6XrvfbkxD+AO22fkqaeNwYWp/V3XlS4olTNJPvRpwHLJKLSwPtSt6Rl0vtt\nHumkoygy/ZxlZS86hngu28ghVXML8BmFVE3WuiZpN6KJ+gzgeuCfxNROFjSJPj5l0iadx1gwqVOR\n5DTbW1aMeSXwDlpFDtu/qxW/K5D05P7nanR6ughJ59repPX5VHfDOLEmy+di4EW2H1S4gV/gAm3B\nyrktC2xOAbu1Fat2t/NZxCHns4Tb+Zu7wDKR9HxgP2Adoti/T1cOiuppHf4dqhiCXVBr4zGMa1vS\n123/Z4U4qwC7Ecya64FDbP92wa8aLhQyKN+qmUfttWgWgyON2h4P1Dj8zwhoEm1O2x8riDeXWLvb\nzL6zK6Q6tpjk/p5lIFWzmTeMibDakHQiQSx4s+0XSjrTdtahuGas2mgx7c92TH5mmZs2xTlCNmct\n4K1k6kgPC5L+jdAyHdjQPr3+IEL67Jd9zz8b2M52VqE0XVMTmtC2s5rQNc8ZtTDZdd4g93qvNTmR\n3rd/znk/LELsRqpmq5rNvRJI+gGhCd6eRtpvhCnNg4Zk+jnLyl40SHoZUat7NL26Qsk59HDiHjBP\nqsb2wZmxLra9Yavm9E3b2xbk9nP69PHHsS7ZxlgwqW1b0v9K2ha4jNRNLBnxIeQvLp0Bo3j7Egvs\nYsCzgNuJzk8WuliAaeGBNHrxx9QxfuKoE4Lq5nhHABdLupHo3hfp9lXO7QwK2a0t3EGYWy1H6J2t\nQ0a3UxONDc4GvkaYmjyLDhhr2r6EGOvrIl5p+/mlQdTTtv6FyrVbm4PFEpK+2xertJCwYuHrG5xI\n6AleSTCVvwa8cJAAaf2aFJmb989OxbaV9LBMJm7VtWgWWVg/fTTohNZ+F6HhaHNCTKg1DDqIv8Fs\nkXoS9N2P10yfrwAemxOv8jRM9YmwIeyXV7B9VHovl6JmrNqYK+kUYHVJ3yLkDgaGK+pIDwOJxbcZ\ncQ2sp5C/+eSAYT4PvFPSBsCS6bn7gZ8R9+hcLAHclB7/gWDyZqFGMVSTj/838XOmy2pOfjZ51Kon\nrAbMZ4CZCHtb2z4lN7Dt64FD00cWUoH1LUwkJJUwPmX77QWvHwrS7/vLzpQzWQiKWNkzCAcDr6pQ\nnwBizyDpsDRRmi1Vk9A0O++R9BJC/qYENfXxpwXGokid8AiimNMUdEpp8OsAv5dUrDvXZbhPdD6N\neJeguAAzRGxp+wFJuxCL/3GjTgjm6W7VMse7AtiQGNH8M4VjspVzu931jFr6C965I2D9h9djCEZN\nJwoJ6dC+P/AAcQjY1/ZPRpvVPBQbgiW0N2GlY5rNweKsjDwWhndXivNnogFqhaTUXzJiNAaAOxMb\nl8sINthTM3M6UtJfgXOAG9Nzq9LT9X5bRsyqa9EsBkflJuO4Y1jj/1cBP8xs9EyApMNsv0/S9oS2\n6Y9tD2wG22FMVUzOuh9LmqphZ4cJ3yB4XF8RvQZq75dvS2SdZSS9FihhWtaMVRW2j5P0PWB14Abb\nWcZsfTGLi3NDwNbtBoukC4GBitRp3R9Goau4CV1z0qHWFF4rXpdNlpcAviPpPqBhUq5KNCG+Nqqk\nWphLH+OzEP+Q9FkmnjVGbpyY9vCvILNJ1o9JWNlfWsCPzyJwKb1icDYmWYOKpGoSdk3EyA8C7wQ+\nVJjmWsyAumQbYyH30UDSEwlTvEuBZV3geDtT0LfpXhF4v+31p/r5RYh3CvCatHgvBnyv9th9Rk5T\naom7A+YLqmiO1/9aSScVFJWr5NZit65P3EyK2a0ajpzDo5g4MjRy2RtJFwEvt31Xyu8Md0QyQRUM\nwfriPcr2na2vH227SDexBvrGyRYjcxRV0vHE+3514DEEE2Yt4NaC6/3HbundSvqJ7SwtdUlPAV5F\nr9B9LfAj2/+bGa/qWjSLwdFuMgKlTcaxxzDG/yXtSkz93Ax8AzjTmZIrks6yvbmk423v0IyT5uY2\n7pDUloAwoQ25KzHCO6jcR7uobaJQ9HrgSbYflZlf1f2ypKWJxuWaBBPvGNv3jjpWbQyBqdlJSDqL\nKDD/nNg/71eDdVwDCom8X9NqQtu+drRZdRu1JyckPYZe8/8627eXZ1kOSV8DdqzF+NT8Boruwtkd\nYp9LXANXEvcFO8O/LLGydxwSK3tsoZAVfAyxBkEHC7eSngQsZ3u+6YdZLBhjw6SW9DHg2cDTiZv5\nt4mDwSwWjKb7bEJCIYs91CrAPI4Y259XgKmRZCGaruTWBGuxYR0+mm4YJxab40naiWCdriXp/Na3\nbpriJQ9ZbgyH3VpVzkHSl4AnE4UE0R1DAtEzQ3mQfMb4MFBsCNaHk5loKvEdCkwmKuJgQtqklEm2\nR41k+nCTpKOJQ+y6xNhtFmxfRxhSFWGIa9EsBsfOrSbjvyQ9btQJdRnDGP+3fThweCpQHEqY9H4T\n+Fy65gbBYgqpn+vT1w/k5tVlqGcg1TCabrb9vEHjNGxISVsA7wLuJDSWL8uItW+K9WhisuTfgS8D\nA+uPDnG//AzbR0h6PGGwtCpRYB51rNqozdTsKnYEPkoUqq8DBi5+DRGfT03oWwEkHUgYbS4yKk86\nTAdUnZxIRelOeNT0oQrjU9L6ti+1PVfSyrb/kJ6vIcNVCzst/EcWjtqs7JmC2k16SbvZPljSloQc\n7tdsf27AGO8mTMv/SdQ9ngncJel+2+8syG1GNGfbGJsiNfDSxPQ8J13sDxt1QtMBzca7gaRjCfbE\noBhGAaYKnByCJW3rlq6VpNNGl9UEfJRoqqyZPu82aIDUfZ0j6W22j+lYbs1BsWZ3c1BdvoVhtVwG\n6pCxB3C6pObA3iV9sj8llmAtQ7Cl+r5euiDWBEjayPYFmS+/FCge1XcyuEiMic2IqZ+m6ZDVLLP9\nVknPIzQKv+zQMB8phrgWzWJw1GgyzkjUGv+X9EzgTcAGwCXAPulbc4EXDRiuYXmfn8ZIsw0du4w2\nWzT9P7PWEUn/D9gO+CnwTheYIaemxa4Ec/FYYBPnj6IOa7/8acKcej9CEmoOIbk06li1MVO0Od9o\ne57MmEKqcCAJAEkr2v6Tet4f8+AMebbKTeg2cWXCpAOQXaROe6KnANeX7olSQXQ/6kju1ZB66zxs\nr10p1CH0PDS+2nr8cYYj6ZeDO4C302PHl0h0LJ8alkWs7JkASUc0a6OkPWwfkB4fb3uHgtAvJYhJ\n2xE+IhcBAxWpCUPaF6S9yy9sPzXlViohNFOas/MwTkXq+xRyH5b0BOpo1LyAKCScAqzchfH/hwCr\n5LxoGAWYIeA+SbvTYx12YoPriuZ4tYtCNXOjx0YT0WkHOH+Kn10gbJ+XDo3t91kJbq5ccK0C22fR\nnc1YP/oNwaBMx/tcSScQm4INgXNzAyl0eF9KsN1WJA61uUXqtYCLJN2Wvi4dJ/sWwUh7PcEeX4XM\nNVLSkwlJgkcCb5a0sys4i9fAbIG6EyhuMs6iGO8GTrA9ocEoaZG1pJPUhIEjWvelB8hf0zqNvoLa\nSkBu0WNPojC0KbBJbE/zNG8J+aNrCAPF1wKvSfEYtJAwxP3ysulgvJTtEyW9oyOxamOstTklLUew\n7N8g6WTivbE4wVQetAi2A1Hs6yc4ZE0L1mxC15x0aCDpMML89jLgbZJ2sP2egjT3p09yDxioSN3x\nSeNq6CsWztuLSjrU9odHm93Q8G3gaOC7hJfZd8g3p67Cyp4heFbr8WaEpwjAyoVxl1FIxN5m+35J\n/8iI8Q8A2/+U1G7e/aswt5nSnJ2HcSpSv4vo/D+GGFkuMrmSdATwd2Az299NDOOao+0jhUL/br6n\nK4SuVoAZArYh5EzWITqenxltOgF12ByvZm6TsPZPLcjrCEKu5UVEUXNZMgveCf0F164YJ25FsOWa\n3//Btn842qwC/X/PCvH2lLQuMd79KdtXDhpD0huJwvSyxGHiabazRgNToftptcfJCBO7bRK7e4+S\n64AYN383cGSSc3gTGePnDRLrdltaRRPbU43kzqLjqNxknEUePgxsJmkHetfUV21fOECMr6TPI9fo\nf4jQFNQM/I3Mw7vt1aplFF4CtVF7v3wCQarZW6Epna13WzlWVVRkanYVGxNnlVWJa0HENNdRgway\nfUh6uLvtW5rnJT29JMEaTeiakw4trGt7k/T46ArsxRqSe0OZnJC0J/BK4B56zbfa5q6DoF0s/E96\ne9HnZsZbKb1H1Pd4xaIs6+I+2yelx9emHHNRk5U97phqiql0WnAH4CX07ntHZMRYKU2ZCFih9Xj5\nwtzGujk7GcapSL2B7f9ovlC4UQ88ytTCmg6DmnPS14sXZdc9nMX8F7MmeW5Q1CzAVEXqil0O3EL8\nXzegrLBZCwdQ2KlvQ3UNAKvl1nfzXgl4bEFea9t+SZL32T6xTXJyWtn2H2zvK2kJ2w+k55+1sNc+\nRNiHGCu+R9KyBLu4E0VqVdINbcP2FcAVBSEOINiFh9m+TFKWxn7CN4D/arFg5qFwBO+BxFD7o0Jf\n9okFsRa3fU3D6COMHUvwbeAkgil4JFD096y8Fs1iQHS5ATqDcDrwI3oGswOjxbx9c+tab77XFRJA\nNdjeSaH9/OhR59Kg+RtURpX9siQl6ZEvEoXM5n41cMGkZqxhITWz9wYeRZCHdrN94GizqgfbpwCn\nSHqS7VpeDsckduutaUp4H0bv21Rz0qHBXZK2IyYe1ifIZiXol9wbuOA8xMmJl9reoOD1XcdBUzw+\n+KFOpB+S9ifWxsUlnUFvQrtEGrAmK3vcMaxC8IsIxvPrcgPYfkZhDlPFHffm7HwYiyK1pMWBnSV9\nnd5Y1M7EhZ6Lv6cbOZLWY8wYLB6eQ3TNAkxVDIF9WwvVzPEUBoCr0DsQlxoA1jTua0ZdDFxNmUnb\nA2ka4G9pNOcpC3vBFGjrnP249fjzdGNz8EtiOuQeguldUsCtilq6oTVh+2kKc4nXpfXnGZI2BS6y\nPagE1HeJMfPaLJgtbT+g0Jd8OXBcQayzJR1FbNgOp6C5lbCU7eMkvdn2sZKyN2pDWItmMTiqNkBn\nkYXbbR+08B9bJKj1eS1gBbozqVYN6q6RcW3U2i9/GvgAPfJJ8z4xg+9jasYaFg4nmMYnpwmizYCx\nKVI3qFighmBoHivp28Tv7g05QZomxmTTuLYfnOw1U6HypEOD7YBdgPcSZpNvKg1oe6PmsaRBfQTa\nqD058UtJr2aiTGEJOa8Uz2kVC9dqPX52TjAnP6mO4sz0uS3HWOpzVZOVPdYYViGYDu+xZuKk67Qv\nUkt6C+GAvC6xWDRjUaVsw7cS+o33ANsTN71ZLBw1CzC1UYV9OwTUNMerbQBYnFs6QMD8xirPJ19S\nYzuCNfpOYqws1yhBi/B4lHgGodX8V4J5/hdJF9CBMR9N1A1dkXzd0MliPw+42va9g77W9lXAVSnO\nGkRHfC96muiLil8B19r+u6THA+8n3heDmmiQcnlz63H7W5uTb5y4v6S1iHvftTkSKX24LY24XS1p\nDqF1nYuumpHOJNRsMs5iALSYVktI+i4TCwl75cTsP7RL6sRUzRBQfe1QXTO1xYHHE7qVJTqTVfbL\ntj+QPheTT2rGGiJk+/a0L4UxOMsOC32FrkuIYv4BRLHjyxkhu97E2LOtfyxpD3oSFDnoN+n7ICFP\nkoPak8ZLEw2HZmJwpM0828uN6t8eAe60/fPW+TYbQ2JlzyIDHd9jVZ10nQ6Y9jf29IaaK+kjLe2t\n0m4ntv8iaT+CvQjBup3FFBhGAWYIqMW+rQrXNceragBYKbeGhdDe0DZf5+Z2BzGquBzhBL4O4Yg8\nKB6TNhnqe9yJzdYQ9JBroq0begeFph+SzkoSS/sTBYCVCb29bNi+Hjg0fQyKI+hplJ9AFBD+DMwh\nCgqDonnvb024ul8GrEdMdwy0RrbX2xbWkbROyfi/7W1T/PcSm+RrcmPRUTPSGYaaDdBZDIbJmFZF\naB1moZ5pcGfQOvBXXTtU0UwtSQm8h9BoXk3SEbZPGDDGUPbLktYhNNBXpMe0yiqi1Iw1BMyVdAqw\nuqRvEffksUOSNWkYg9ckObRB0W6i/J4oukKmtGNXmxiSViW0fLdorSNLEAbaAxepJe1EFHzbjOAH\ngf8pSLPqpLHtWaO90WFtopi8Ud/zOefaYbCyZ5GB2nusms1xKk66ThcopMemPySd3d5ASTrZdumo\n8oRxQ9tjM3ohaUoWpu2BJTASox0mKcDY/s+sJCtD0opEkWl5gn17duamrypU0RxP0t59T7lkHKRW\nbkmL7VDbH8rNpS/eBfTpfOaMhk3y+5oHVzYGHBdMMuY5T8t+0HHPvrjn2N5U0vG2d5B0oe0XL/yV\nw0Ern8cB5zR6YP33moy4P7K9Vevr02wPpA05rPVW0krAGwmJmaYwkcX6rL0WzWIWMx2SNk4PG0PB\nqz0um3gWeD8u3cec656ZGpLOs73xAl6yoFgXAS9JDOglgfMHbSYPcf2+mJj8PBZ4G7CT7Y8v+FXD\njzUMpPvy6sANtv9v1PnUhKQPAxsC19IzrFwdeCpwse2cpjtp6mo5evf2bLlDSf2FuPsJH6hP275u\nkpcsLF5RMSetjZsQk9VziP/j/cC5ti8aNF4r7r/b/n7u6/tiLZHWjYcTRIef2f5jQbwtiEbSykQB\n/fZRT1gOA+l9+wlCg/4Ogi1fOjVYmtOU/i+DnoMkrTcVK3uW2LFwVJ6Sau+x7gCuyt1j9TXH1wfu\nzW2Op3jfBN4CfAp4OPCUthTROGLaM6mH1O2E8R9VbrrgzyPeB5cTm+R7ydBpbgqEkra1/fbmeUmd\n6Qba/lN6eAvwmVHm0od9qGSO1xRWU1G4BsuqSm62LWkZSSu2/g4lqKLzOVuIzsJkpqtPJDYJJQaz\nv5P0E4IltQQTGUCjwN3p/rIhMWJFyqt0quY+SbvTG+m7f9AAQ1xvTyHWxp8XxhnGWjSLAVGzATqL\nTmB123PSoexgYlz/2yPOqRr678eSXmb7xxVC1zRTe5BgF9+UPg/cmB3i+v1P29dLWsz2dZJKDrA1\nY1WFpFUIOcY1gOslHWL7twt52XTCGVMVohWeGwND0g+APzLRI6LEk+cSQlf5CmKS8T+AbwJzCd+f\nQXIrnnSwfR5wnqRP2B54T7WAuMUF6mFNThCF2y2AU4FX0yFddkn/BqwG3FjhzHcksL3t3yXG/An0\nphxHhZrnoJqs7BmFWlNSmlr/+znkT+qs22qOHy3pvMw4wKSTrr8piTcdMO2L1LbnAHNqdTs1pHHD\nrqFVQPih7S2b51Wuv1NcgJmBqGaOp9BfezVwFz2Ga8mIZk3jvucA50u6NeXlgq5/NZ3PLkOhfbkN\nYd5wJPAc26UNuCJ4omHi+sCuBKvvXYVxd2wxTRYjWGajxJuANwMXA8en51YiDgYl2IbQEFwHuJ6y\nhlnt9fZW2ycWxgCGshbNYnDsQ6UG6J6AwpcAACAASURBVCzqQKFHekHmy7cnDkzvIXxTvs8YFakn\nwW6EoXEpapqpvQs4QtJjgNspu+/VXr9PV3gKfF3SFcDPOhKrNk4k9h1XEr+3rwEvHGlGdXGDpG2A\nX9n+ZfsbDs+NHKjdEKmAl9jeDUDSpcDhtj8oKec9XK2YU7NAXRHVpN76cLftOxVyXvfSEY3aNAmw\nGXFeXC9NJX6yIOQS9DyN/kAZGaYKKp+Djk9nnv0rpTeTUGvtaJOiTHhAvQ1YhvwidZXmuCZKkLRh\nYMpp8HHAtC9St3CfpDOBJxCblsMyafXbA78jxpaWo9etG9eO1jKS3kRvk1zKEqxZgJkpqGmO90rb\nNTcq1XIbdCR2ISjZ8EwnnACcB7zJ9uclHUQwJ0aGxIx9LXEDvxbYx6H9nBtvDrG+7m77Vpg3LndH\nhXSzYfsu4At9z/2e0HUsiXu/pMuJiQ4BG5DPaGqvtzdQvt6ekA6cv6bX/JlM/3pRUHstmsXgqNlk\nnEUGkiTES4F/J5i3vwJyi9QPV0i13WX7T5LurpRmV3F5pTg1zdTWsv3qVqzXkueHARX3y+m+fIvD\nbPjo9DHyWEPCn4FL04TepUThb5xwKiFn90ZJ1wD7pX2DCuR9/iHps0wkduQYJzb4qkIS5veE3MTc\nRKr4XkasmpMO1ZFYwdi+Jef1Q5ycmJsaSZ8j9pA/KIxXC1u3ZQgkXUjZme0I4GJJNwKr0LcvHwUq\nn4OGNZ06E1Bl7Whdo08lGg5rAHsB3y3IrVZz/MzWYxN1mV0JP66xLlKPkyb1hYSExY8dOqJZuqG5\nr5uuSGyQnUnabsBxtv9aGHMNWoLzJbpnNZFG93ckOmaNzvhY/a3T4etqJm5EbxhpUgmSVgbezsT3\nxkA671qAk3LJpEPK7WOk8VHgINs3LfhVw4ekM21v0axLzdcjzum3wN1Ed/lvtDZXhYeeGQFJRxAM\nmhcBFwHLusA/oSYkXQm8g4la77/LjNXZtWimIBURlgfmNRkJ6Y+SKZZZLAIkvZEoTC8LnAFsa3vz\nwpgbEobBRxJr79ttH16aa9cg6cl9T91PTHkMqvW5KnFP/xTwwfT0EsDHnaFJnYpwZxIsQREFhO/Z\nzjb4rblflvQt22/Mff2wYtWCpOOJe8nqRPPtamAt4r0xNnt5SRc0RT5JbyUaGScRrMEPZMZ8S99T\ndoHJcoq5OHF/+YvtbHk2SY8iijlrEMWcY2zfmRlrghQMkCUFo5BUehfRWPwrcX0+ltgbHZkz0Sjp\ne8REQkMKe6HtUU8MVoekswiT5p8ThcP9XGC0KelZBHFiBaJB9RTb19bItSCnoZyDWqzshwNfsF3N\neHkcUWvtSLWFdxFF7s/ZLm6QSzq0vzluO7c53mjQvwu4E/i87ctKc+w6xolJ/a/04dThytXAfI5C\n27qNpqA5doc627dLOoNgWQE8mwKdsskKMCXxKuMdwIs7Og5WC08hdK3aunNdMfz8GrAfMdK0F7DV\ngn98Ukyli1g66fAVoiN5KTEyN5duSBPcJmlbYuLhtUANPe9S7FMzWOvgOeFpYs3NZfF2GWvbfkka\ngdxe0smjTqiFqwiGWo01sstr0YxA5emVWQyGAwjG9GG2L5P0mpJgaV+7d1ueDRi7AnXCl4mCxC+B\nZxFFoqUkfdX2UQPEWYWYhmymIhsztd0HTSgV+XYkiktnpVj3EYzXLAxhv7y8pKsJZncjqZZ7D60Z\nqxb2GPG//1DhB5JWs/1b28cBx6XnBy4qS1rf9qW250pa2fYf0vNZDTNJu9s+qH/fJqlk6qrmpEMt\nKZgNgPfb/lv7SUnLATuQ53tVddI4TbU+nmg+Lw/cSkwgHmj7v0tiF2JH4KNEofo6QjavBJ9PTahb\nASQdSPwuR4l9agWqPZ06w1Br7TiTuCZvAQ5PEjpZtb9Wc3yLFrFuCWKibuDcFHrZ2wE/Bd7ZTBzP\nBIwTk/qVwIeANYmD9mdsn54R55ySjt90gyYx03CZi/r5rQLMppJO7hBL8FPEJu+X9Jh9A5vedBmS\nfmz7ZaPOYzK03hPNe2TkrOAGki60/eLW1z+1PZD5yzCQRvl2Jta1a4gu8b2jzaouEvNlUuSyeLsM\nSWcTki3fIUbJPmQ7ywxpktglerdIuoooDl2XnspuznZ5LZrFLB4KKEzOXkfoj65F6EhfZPufmfE+\nD1xIaJo+COM5naDwm3i97QcTW/M7xO/xZ86QEJK0ZC1ygqTn5bAop4hVdb882b20YBKmWqxZDAZJ\nD7N936Dfm+Ln500HT/V4wNyeYPvWGu+P2pMOKeYpwGtsW6Hz+71ctrKkFYD/q3lOrDw5cTSwr+2b\nJa1EFE73If7Pzy/PNjuvD9r+dOvrXWx/KSPOTgSxYS2irtPgJtvblWfaDcxOpw6OYawdtSBpY2AT\nolkzh15z/FzbF2XE+y0xQfBPeu+NsSXPtjE2TGrbP5T0I9LoEVMzLmcxEbXNNBrTs78pHI2fUjF2\nKZ6bPhp0wshLdc3x/qSKhp+Vc7syFV3PlnQO3dKdO1WhD3cVwXIoNmGthGfYPkLS44kb3qpEsXqc\n8Ezbp2lyd+Vx3KBtBywGvBP4TwpYJqqrd0utYnlC1bVoFrOYbnCYnF0F84oTryOmiHKJEI8Atkwf\nML7TCSsCz01M3rWBx6eC9T05wWpOz9UqUCfU3i/fQUiqNVIHAxeGhhRrFoPhSIUPzDnAjem5VYnz\nynIE43IkaLH4jrX90uZ5SScyuOZqzUmHhtn9OOAXae1Yi8S+zYh3NKEL/FhJe9v+SU6cvpi1Jyee\nS0yZQJi4rpsK1lnrZCkSy/xxwBvShGAjibQNGeuH7TnAHElvs31M1WS7hX1GncA0RLW1ozZsnwec\nJ+kTNfYetlerkNa0xNgwqfuRy+KS9KgcPZvpCknfJlxzq5hpSFqR6PgsTxRgzrbdObOmNF6zUUkX\nu2IuJxLmeG+2/cIShrGkfhH9UmZ8tdz64j4WuN0dWYAkPY5o2q1KHAr+2T/mNwpIOsv25pKOIv4O\n7x23EX5JL7d9hubXTJxnZjGLiVBlvVtJO9meo0lcpG3vlRmz6lo0i8FRuck4i1k8JJC0OjEZuRrh\nlfJpwtB8ddv/O8rcaqL2fllhHn80IXWwDjEanEXEqBlrmFBoB189hhNmTwFeBTw1PXUt8KNB3/8K\n48VDiCLOh1uPP2R7zYy8NiWK5TvQkx9ZAnhRAfu5eNKh9kSeki64pEcSxn0rEkbmz7W9a2aOtScn\ntgY+Qs9n6VBCfugNtr+ZG7cgn1cTciZbAqfRk0T6se3vPNT5zGL8UXNKahbdw9gwqWthJhWoE6oy\nRm03mrm3UKi3VRuJdbgFsDU91uHIi9TACraPSoWnUlwF/HCQccCFoFpukg6z/T5J2xPjOT8mdMty\nYtU2OjzJEzXPvgV0wTRoWUlLAUvZPlHSO0adUANJawGfAB5FsK72tH1lRqj/TUWJbAbwDERVvVvC\nGRsmukiXovZaNIvBcQLR3HqT7c9LOoi4B85iGkHS4bZ3VWiQjv24Z5Iwedck38oqUKuSmVorXpWR\n/SHsl++zfVJ6fO0U00mjiFUVreb9/oQm78pAtnllF2H7OuCwCqEOmuLxwZnxbiCkhlYntNkhGIy5\n8apMOjSF6ERA2ozW9UmGljcxCbZaWifaBIoSs8mqkxO2TwVOneRbD3mBGsD2KcApkp5UeB6bNqh4\nDppFBoZRoJb0b0SD/MbWPXoWI8C0L1JPxvwibkxrjCCdaQeHmcZSxEYv12yy05iEdfi0EtbhEFDT\nHO/JhHTFzcA3gDML9dRq5rZW+vxy2+tJurgg1leoYHSY/k+vA54pqc0KeVRBbjVxAnAKsHeSSsk+\nWA8BRwLb2/5d0gc7gRi7GhR7TvH8uI6yF8P205T0biXtBTwjMZyy9G5tX5kOd7t7ojFbCWqvRbMY\nHDUboLMYERrmnu0ZIWOXGtnvILwY/gb8zfZzF/yqBaKWmVrXzcEXVxih/5xgPz8gaT/ImoipGas2\nFkufV7W9g6QLR5pNh1F7Gi0Vg39HND+7iG8RknivB04mZAEGLizbHsY9s5rUG4CkdQh2/Ir0GmYj\nn3YYRoFa0guIxsMpwMq2f1/738hErXPQLDoASR8maglXAOulqYdPZsaq2hxPMZ9HNLeut31JSazp\ngGkv96EQKJ8USRdmFguApN2AlwHPIC6if9aQc+gSJF1LsA6PTKzDH9neatR5NdAQzPHS4ngosDHR\nVf9cYmaMLDeFDvU5wOK2927G6TJjVTE6lPRoQtNqF3qaafcDt4yyoCZJ9jzjFzHRSKMThb7UZHiR\nQyt0CeCCcZMiGQYUZjA70hvRdOnBQj29261cYPyrIRiz1VqLZjE4JH2dONS9jxjzfp3tHUab1Sxy\nIellhE7wcvRIBfcSk0BzRpZYZUi6BNiQYGpuQejf7lgQr6aZWpfNwaudh7p8tpL0FUIveC7RAD0r\nV2piFqNHzWKOpHNtb9L6fGrOta7QpD6VMDu7Oz33cMJP4FW2Rz7VmPbg2wPHEjrlO9n++Gizqo/U\nGPw7sJnt56tDptw1z0GzrOzBMYQpqQl1if5aw4CxLmJic/ww21nN8RTvMKIpfhmwPnCv7ffkxpsO\nmPZM6lFvlsYAr7a9YeuGXjQmNIwCTClqsw6HgGrmeJKeSZiXbABcQs+QYS7B/BlZbkQRbT3CUOBh\nhFxHLqoYHdq+g9gMdG1j92ngA8Qh3fQKEp0w+0w4ArhY0o0EW+ULJcEk7QlsBfyDjqwdQ8I7gBfX\nHFOzfT1RCD60MFQ1Y7YhrEWzGBz/j2gyXk6MxI/McGsWVXAwUSC5uXkiNZLPJVzkxwV32/6XpPsJ\n9ty6OUFU2UwtodrIfu39cs3zUJfPVrZ3lLSE7eZvkdVw6DqGwcQbFiRtZDtXsq3apANxfS4F/DGd\n956YGed9BNv5eIWHDoRJ4Y+IvXkX8E/b10tazPZ1kjoxaSNpXYL4BnCNy32p1kzyPuekrxcvjFcT\nNc9Bs6zswVFz7QC4T9ILiQmi9QnSWi7+DFyamuOXAn8piAVhjLpJeny0pM7eo2th2hepZ1GMpkh7\nj6SXAM8sjFe9AFMDtq8iCppt1uFeRFd81Pg0sDmwHzFCN4dgEeXg3cAJtidIKEjK0n6umZvt29NC\nvS1xqHgc8NIFv2pKHEcUu1YltBy70GyoBtsfSJ+78P6cClcQ74UViJtxkb4e8LIZwsS+AFhT0i/p\nmdV2gh1veydJTyQKQ5cSXftc1F6LZjE4ajYZZzF6XErfvc72vYlZOk44OBXf9yWKAIdnxtmjXkrz\nUHNkv5P75a5C0hzinrm77Vth3r3zjpEmNjzUlKmpytJUePy8lJBSbDx+covUNYs5W6bmxS7Ay4mz\nwsCw/Y/02qzXP0Q4Pa2TX5d0BfCzUSaTpBI2JEw+m2bKm1Kz4GLbuSSKvye5DyStR7eu95rnoCWA\nRirlD3SrGN9V1C4E70h4Ze0JXEfG/X1IzXGAuyRtR5BO1iemC8Ya017uYxZlSJpW1xAmGO8kjK7O\nKIj3KUL/q3MFmK4ijQttAhyVikTn5Y4upnG0zWiNA9vONvqokZvChODVhKzMXcCzgY2bEbrMvM5u\nM44kfStXQ06SgA/bPiQ3n2FBHdWcg0n/BifZ3qYg3heB04Ff0Fs7iqQmuogWG6RBZxjjkj5GXJ9P\nJzZBP7L9isxYVdeiWQwO9QzGjiKajO+dIY2gsUS6Hz+WOJiZMTVOlPRvtm+RtAxRBDvX9m0F8eYz\nUxt0LZI05Rpt++zMvIa6Xy5ktw4t1iwWDZVlai6gj6WZM8au+T1+tnWmx0+rmLM68BhgXjFn0D1R\nmmqYFF3Zd3Rx0rgmJK2dCGEDfW8R4i5PTBQ0spMH2S4tRlZBzXNQKkC+F7iRxMq2fXyVRMcMNdeO\nvrgftP3p1te72P7Sgl4zSYxVpvqek8FrZm6PIqRJ1yAK6MfYvjM33nTALJN6hqPVSf81sTiW4rnp\nY94/QXfkCbqKmuZ4pxPjaDcv7AcXETVyuwn4MrCj7bsknZZboNYQjA7TAeDZkpZ2oRb4EHAUfZpz\no01n3kb7/wFrSWobRpWapSwNvCZ9wJgaJ7bZ8al40okRzYSXOnRWz0nXxcMKYtVei2YxOJZNo89L\n2T5R0sh1NGeRj3FuMEjakjBB/iLBGN0cOJAoyP8XoWmfixpmalOt0wayitRU3i/XZLdWZspWRYtR\nPQ+2x2avMCQmXi2W5gHE++Awh8fPaxb2ggWg5qRDI4m3NcGmvIyQF3w0GcaJQ0KVyYlEADiAkDps\n5AAvB/YuIf9UwA2StgF+ZfuX7W/kFKhTYwZCZuUjFfKrhiGdg2pPp44zqk5JSVqOWG/fIOlk4ppa\nHNiGnl/VIqEpRE/WHKdsLdrT9odbOe9BrANji9ki9SyqouMFmE5BCnM84lB2FL1Nd8lm+3bbB3Us\nt9WB1wJzJf0fsLykh9m+LyPW2cRm7Pf0GR1mxGpjHeAmSb+hWwy1zmnOOQy65kh6m+1jSuMpaUva\n3qnv+eVLY3cR6fC/BXGYag7/5y/wRQ8d7ktyH5b0BMpkdKqsRbMoQs0G6CxGDE1inDhGTLwrCPmM\nlwBLpueWt/0BSVnTHC2sYHubxAbeQ9KpgwawvW9hDpPFrLJfnoTd+rQCdmu1WEPEPumziOLtJiPL\nZDgYhkxNFe1cV/T4qVnMsT03xdrW9tub5xXeNUVQSES2pzBy92u1pN4+CVxi+/2tHLdPz787M7ca\nOJUgJrxR0jXAfrbvb50nB0Xbk6d5ffN41F5XVc9BCZ9P9/NbASQdSBRJZ9GHIRSCNyYIUqsSUh8C\n7iPqH7mo0RwnTb6sAWzRmuhagmgij3WRelbuYxZVMVkBxnaJQd7YQtJn0gHsHPrM8TJG3fZPMdYn\nCkttyYS9RplbX9zlCemPVwKPcEccmrsKSbsBhwFvIeR4ftbegI8D2uNykr5t+w39z48Dao7JDgvp\nMHYgIfdxDbCHw5RxkBhV16JZDI7mUJiYSO0D3qz81jSGpMvpM04cFyg0c39v+w5JnyAYZYcA5wCn\n2H55QewziT3Hl4HfEIbhz13wq6aMtT3BiFwT+BvRjFs/M1aV/bKka4kC2JGJ3foj21tl5lQt1kMF\nSRfYHnkDvzYmK8DkSldIehYxMTuPpWn72go5Nh4/WznTQ0XSSfQVc2zvkBnre4Q2888JHe8X5kqk\npHhHEGzsFwEXAcvafl1mrCpSb5J+Yns+P5+pnn+o0L4OJb2VKPqdRBi+dcVssnNos7JJ3lkJN9ne\nbjRZTQ/UXDtSvCfZLp0KbmKda3uT1udTc9YiSRsTjdgdCV8wEeS8c21fVCPXrmK2SD3DIWllYsPd\n1rwdmC07HQow44y0iE0Kd9SlXdIjbd816jyAxo16b0I25GXAbrYPHHFOAt5i+yujzGPYSNISmy7o\n8ThgOh7+czAd16Jxw7CajLMYLSR9iTCN+79R5/JQQAU6pn1xlnCYqT2cMFP7me0/Zsa6hCign0UU\nmI+1veOAMarvlxt2KyFxsBbwVjLYrbVjDQMKfeVmXVuK8E7YZ6RJDQGVi7dVPURqolYxJ8VakiiO\nrg7cQDS4cqY2m3jn235Jsx+VdHJukbovroCNcljZSl4Ti/r8QwWFKfa3bFed2FKHvXlqojIre0ag\n5tpRGzWb4ynekp5hJsuzch+z+BqwH7A/sBeQWzSpqVM2o1DjBjys4s8wNwe5Beq0uattdHg4sbE9\n2fa/0kjNSIvUiQm5FfCVUeaxICiMHB5N773x+4wwy0haDVgMWLr9uFqiHYArjskOC5J2BHYG5rFt\nPaDszWwhevRoWEvj1OSZBRAFw4skNSaCHvT6nGY4jDKN5je3Hre/tTn52pB3pz3C/QTDdd2MGNX3\ny6mYfxVMYLfuBQy8BtSMNQyMI2t6ChTL1Gh4HiI18YDCO+GPaW/0xNxADnmJywkJQAEbUCan9kCa\nSPpbWk+ydYInm5zIzO2JfX9LiP/rqCXyPjtVQ0D5Eo/QQW+eNiqdg5gtUGeh2toxBGyZmuO7EM3x\n40qCzbQCNcwyqWc8Wt3hplt8pu0tMmN1mn3RVUi6mL4bsO2PjzarQFdzU5gm7uJKRoet9//Ztv9/\ne/ceJllZnvv/ew+YABoFxRgIBhQlkmwOKsQDJ0HAACpoghgdBTzEU4zZCSgYQUS2mOBvB92IAUw4\neCIeQEEREIbAKARE5OhWBBTZAYkkAyKE8/37411F1zQ9Qlet6ndNrftzXX1RVT399jNM96q1nvW8\nz7ODpPNtjzOoqRWSllC2Z17BTK/sFU4xX0hNVd/6zAzG84i7MI5f0ec8q0/1NGljm2zbJH0X2Gqc\nyqPojr5UIMV0kvRZ24vH+Pq9m4ePGKZm+3Ujrvky4HzKkMf9gVNd+pPOd52cL4+o2QH6NpZvgzE1\ngxMH2qzE63KVZss7HVprz9Gstw6lPcralJ75S2xfPs81erHTWNKnKUMOzwN+2ry8AeVG45q23zri\nuoMq2fNtbze4Xmsj5nG1dR0Uo2nz2NGstznwnObpD+f7u96sscJrdI/YrqmvkqTuOUlHAgc0H9sB\nv7L9ihbW7VwCpqsm+QbcVGCMPJG9zdiaC4v3UwYAXA8c7hF7P0m6gnKB0sqgQ5X+aa+kDFC8hLJ9\n9IRR12uLpPVnv+ZmYERtqtz/Lton6f8AxwHjDvaZa+2xjkUxf129yRjzI+lA24dL+gxD/cUBunLT\nsi3NTqkjbO/X4prLtVaS9E3b4w5jbE3Ol+dH0vnM2gHqKex523YCpmsmkcxpqz2HZgaUzRXbknmu\n1YtWbwCSngW8HHh289K1lOupH4+xZmdn87R9HdRWVfa0a/vYIWl/Shuva5kZMP5Mys/xRbaPmMda\nrd8cb9Zdn5KrG+RQ/r7t1jpdk3YfPWf7r5qHh0h6MrCspXWvB45oPuLXO1PSasDnJV1OGfoxkmY7\n2U6Uu/aD7WTjJIZai43StuKDwKWUKqQTGXErr+3NxohjrvX+SWXgyjOBn9i+rc31x3AHpWJo8KZ0\nbN1wlnOzpPew/GC8eZ28R+fcTplIfTOMN0V9AseimL97bV8vaZHt6yT1ZZv8tPnn5r8fqBrFAmja\nXK0uaR3bt7S07H2SDmRmmNrI22YlfQ94OvBjytb/m4D/piTW592OAXK+PIKHbJ8r6YO2z2mSWFNj\nQm1qumjwl3tEMofR/55ttedY0XulgXmd564Mrd7aYvs6SkK5zTU/2jw8pvnoktaug+aqyqa06olH\navvYcdaKEtHN7+5jZvvE5uv2Gr6ZIumbI8Q17AvAeyg7qzentOt98ZhrdlqS1D0naWfgvcDTKD/0\nnwDeXTWoHmmqhn7etK0Y+Q14ju1kG427nayt2IasZvs7zeNvN32kRo2t1UGHks4FvgWc3KEENcCX\nKf/fT6VUeX+FMXp0tuwGYE1g6+b5vE/eo3NeYvs5j/7HVmwSx6IYWZs3GaOe3WYlq4b984o+sRJ7\nHnCBpFtpYacUsCdl5sRmlJu9/3uMtX5EGXh2t6Q1KH0m30zpLTtSkjrm7YrmuLZEZThsJwZwt2gS\nydvOVWlOKJnzespMk3dQ2nOMtNPE9ofGiGGu9SbS513SlpRE/PW2Lxk3zi5Smc3zfuABYBXgo7a/\nUTeqh7V5HfSM7E59bCZw7LhB0p7AD2xfM+t7jTq8ubWb441fAJc2N/Ivpbw3TLW0++g5Sd+mvEme\n3WyNWm4CdEyepC/afs2Ya0xkO1kbsQ2t9V7Kz9qVlIvFfx26Qz7ftc5nZtDh9hpzqrWkVShVKntR\nqj6/SZlSfeuoa7ah69uU4eGbGYOLnnm3hkj/ru6QdDQlsTxcFXLDPNfozdbWLmt+L/fuQtuiGM/Q\n9lEov5dPprRvWd32M+tEtXJpEkPDPYxHGqbWVFK/3PYtKv1qT7O95aA1WmsBx2My2AHqKbyYbfP8\nb64qTXekd26zi/FiZpI5L7b9yrpRFZIWA28HNqbsNFtme4u6URUq7TrXoNzE2AK4x/bUFZlJuoRS\nQDG4Mfivtv+odlzDxr0OatY4EbiM7E59zNo6dqjMfzoDeAHwQ+BQlyGsGvW9pdlNugdlh/YNwNc8\nwryfoTZvzwTWAq6izLG4ddrzdamkjgebDw8fZGNBrS3pKsYYjjfB7WRjxzbknygtPjagVDKNE5ds\nL5M0ePMY61hm+0FJ36EMKdyLstXvhZJurdzrcBVJZ1HegDejbGU8FMD2wRXjQtIHgN0pVUzjtIaY\nSNVQjGR1yknVHs3zeW837NPW1i5rqi12pbRZipXYUNXQsynbPTekVOGdWjOutmlCvbc1xzA1SuXz\nKN4JHNtUpd4BvKu5yV31/bgPJD2VUh37S+AbwEcoF+2HU9rITZs2K/G6XKXZ5k6Htv0lpVftucCO\nlPkOXbH50I2xY5rinerUfu/cayi/53dTqpbnPcxuUlq8DoLsTh1FW8eOx9n+GDw8o+oUSV+iHHdH\nygE0Se7LgJ9TfjZeyGjnHVPf5m1FUkndc5J2A/aj3CW+EvgH2+P2zYl50ASG46mlQTxtxja7Sn+c\nKm21POhQ0smUBN0plOrsO5vXj3HFAR2StlvR52xXPSGVdJHtF7W4XuerxmP+2joWxfw11SFPpZ2b\njFGJyhCvdwK/Aj5h+7LKIU2EpKfZvrXtcyK1NEwt6mrash1HueFwAGVA2y+Bz9ueun77bVXiNWt1\nukqzrZ0ObRs6ZnyL0tbnNNub144LQNLpwMmUf9ctgNfa3q1uVCDpQpbvnXuk7Xn3zpW0lPKz+jjK\necx/UnYR/WKU9Sah7eugZs2xq7L7pI1jh6T3UXZPtzaIcK6b4+OcdzQ/Fzuw/N91qgu5kqSOwQ/+\n2sBt07hlruskrcms4Xi2WxlgOa42YpP0KkqSaifg7OblVYEn2/7jMWJ7Ci0NOpT0O7Z/Ps4afdNU\nEFzFGK0hZq3X2S2ffSFpR2B/7TNqvQAAIABJREFUYD3gIcrW1nF6wUZFk7gBGgtP0kOU99/Be5Rp\nqram5fdT0gbATc2upn1tH6/Sb/UQ4HjbXx5j7SWUKsivUKrP97M9r2FIQ2vtA7yFcnwEYFr+Dbpu\nuNBB0tJBYnrcdm9d1mKbmg/Oesm2Dx0zvFa0mcyRtC+wD2WH8OAYOfKWeEk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(25, 10))\n", "plt.title('Hierarchical Clustering Dendrogram')\n", "plt.xlabel('document index')\n", "plt.ylabel('distance')\n", "dendrogram(\n", " Z2,\n", " leaf_rotation=90., # rotates the x axis labels\n", " leaf_font_size=8., # font size for the x axis labels\n", " labels=dendro_labels\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now clearly see (if we go from bottom up) the progression in which the documents were linked together. For example, documents 10 and 11 (near the right) were linked together pretty early (meaning they were deemed relatively \"similar\"), this new \"cluster\" was then linked with document 7, then 8, then 9." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## Section 2: Multidimensional Scaling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## MDS \n", "Multidimensional scaling (MDS) is similar to factor analysis, which reduces the number of variables one has to work with and detects structure and patterns in the relationships between variables. It helps classify variables. The end goal is to analyze and be able to find a group of variables that results in clear similarities and dissimilarities (distances) between the objects using the variables that best describe them. “In factor analysis, the similarities between objects (e.g., variables) are expressed in the correlation matrix. With MDS, you can analyze any kind of similarity or dissimilarity matrix, in addition to correlation matrices.” (More information: http://www.statsoft.com/Textbook/Principal-Components-Factor-Analysis and http://scikit-learn.org/stable/modules/manifold.html#multidimensional-scaling)\n", "\n", "\n", "A simple example of MDS is a map of cities. We can use 2 dimensions to describe the location of the cities. MDS arranges the objects (cities) in a particular dimension (2-D) to demonstrate the observed differences. “As a result, we can \"explain\" the distances in terms of underlying dimensions; in our example, we could explain the distances in terms of the two geographical dimensions: north/south and east/west.” (More information: http://www.statsoft.com/Textbook/Principal-Components-Factor-Analysis and http://scikit-learn.org/stable/modules/manifold.html#multidimensional-scaling)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:15.479063Z", "start_time": "2018-04-02T08:48:11.420141Z" }, "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: datascience in /Users/stephkim/anaconda/lib/python3.6/site-packages\n", "Requirement already satisfied: folium==0.1.5 in /Users/stephkim/anaconda/lib/python3.6/site-packages (from datascience)\n", 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nbformat>=4.2 in /Users/stephkim/anaconda/lib/python3.6/site-packages (from plotly)\n", "Requirement already satisfied: decorator>=4.0.6 in /Users/stephkim/anaconda/lib/python3.6/site-packages (from plotly)\n", "Requirement already satisfied: six in /Users/stephkim/anaconda/lib/python3.6/site-packages (from plotly)\n" ] }, { "data": { "text/html": [ "" ], "text/vnd.plotly.v1+html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "!pip install datascience\n", "!pip install plotly\n", "\n", "\n", "#a bunch of import statements for the functions we'll be using\n", "from sklearn.cluster import KMeans, AgglomerativeClustering\n", "from scipy.cluster.hierarchy import dendrogram, linkage\n", "from sklearn.feature_selection import SelectKBest\n", "from sklearn.feature_extraction.text import CountVectorizer\n", "from sklearn.metrics import pairwise\n", "from sklearn.manifold import MDS\n", "from mpl_toolkits.mplot3d import Axes3D\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "import seaborn as sns\n", "import plotly.offline as py\n", "import plotly.graph_objs as go\n", "py.init_notebook_mode()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Read and process the file and data (Do not worry too much about the code used)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:34.307254Z", "start_time": "2018-04-02T08:48:33.828981Z" }, "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'pd' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfile\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread_csv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilepath\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mindex_col\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhead\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'pd' is not defined" ] } ], "source": [ "file = pd.read_csv(filepath, index_col = 0)\n", "file.head()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:36.628405Z", "start_time": "2018-04-02T08:48:36.624932Z" }, "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'file' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mwords\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mtexts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'file' is not defined" ] } ], "source": [ "words = file.columns\n", "texts = file.index" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:40.858998Z", "start_time": "2018-04-02T08:48:40.853984Z" }, "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'words' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwords\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#print out the first 10 words as a sanity check\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwords\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'words' is not defined" ] } ], "source": [ "print(words[:10]) #print out the first 10 words as a sanity check\n", "print(len(words))" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:41.273098Z", "start_time": "2018-04-02T08:48:41.267083Z" }, "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'file' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdtm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0mdtm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'file' is not defined" ] } ], "source": [ "dtm = file.as_matrix()\n", "dtm" ] }, { "cell_type": "code", "execution_count": 263, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:42.771098Z", "start_time": "2018-04-02T08:48:42.766586Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "357" ] }, "execution_count": 263, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(dtm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create the distance matrix (dist_matrix) which compares every text to all other texts using cosine distance. We convert this matrix to a pandas dataframe, so we can work with the data more easily." ] }, { "cell_type": "code", "execution_count": 264, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:43.178681Z", "start_time": "2018-04-02T08:48:43.118020Z" }, "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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c.4.12.2A hymn to Martu (Martu B)A hymn to Martu (Martu
c.4.12.1A šir-gida to Martu (Martu A)A šir-gida to Martu (Ma
c.4.29.1A šir-gida to Nuska (Nuska A)A šir-gida to Nuska (Nu
c.4.29.2A šir-gida to Nuska (Nuska B)A šir-gida to Nuska (Nu
c.4.08.31A balbale to Inana (Dumuzid-Inana E1)A balbale to Inana (Dum
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" ], "text/plain": [ " Full title display title\n", "text ref \n", "c.4.12.2 A hymn to Martu (Martu B) A hymn to Martu (Martu \n", "c.4.12.1 A šir-gida to Martu (Martu A) A šir-gida to Martu (Ma\n", "c.4.29.1 A šir-gida to Nuska (Nuska A) A šir-gida to Nuska (Nu\n", "c.4.29.2 A šir-gida to Nuska (Nuska B) A šir-gida to Nuska (Nu\n", "c.4.08.31 A balbale to Inana (Dumuzid-Inana E1) A balbale to Inana (Dum" ] }, "execution_count": 265, "metadata": {}, "output_type": "execute_result" } ], "source": [ "names = pd.read_csv('Data/idToTextName.csv', index_col=0, header = None)\n", "names.columns = [\"Full title\"]\n", "names.index.name = \"text ref\"\n", "names[\"display title\"] = names[\"Full title\"].str.slice(0,23)\n", "names.head()" ] }, { "cell_type": "code", "execution_count": 266, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:49.381202Z", "start_time": "2018-04-02T08:48:49.331570Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "text ref\n", "c.4.12.2 A hymn to Martu (Martu \n", "c.4.12.1 A šir-gida to Martu (Ma\n", "c.4.29.1 A šir-gida to Nuska (Nu\n", "c.4.29.2 A šir-gida to Nuska (Nu\n", "c.4.08.31 A balbale to Inana (Dum\n", "Name: display title, dtype: object" ] }, "execution_count": 266, "metadata": {}, "output_type": "execute_result" } ], "source": [ "labels = names[\"display title\"]\n", "fulltitles = names[\"Full title\"]\n", "labels.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the clusters from the K means results above." ] }, { "cell_type": "code", "execution_count": 267, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T08:48:49.877021Z", "start_time": "2018-04-02T08:48:49.873513Z" }, "collapsed": true }, "outputs": [], "source": [ "clusters = [cluster_0, cluster_1, cluster_2, cluster_3, cluster_4, cluster_5, cluster_6]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make a dictionary of colors. We will use each color to uniquely label each cluster." ] }, { "cell_type": "code", "execution_count": 281, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T09:03:32.421847Z", "start_time": "2018-04-02T09:03:32.415819Z" }, "collapsed": true }, "outputs": [], "source": [ "dict_color_cluster = { #define unique color for every cluster\n", " 0: '#2c4ff9', #dark blue\n", " 1: '#db0f12', #red\n", " 2: '#000000', #black\n", " 3: '#3FB230', #green\n", " 4: '#ff54f9', #pink\n", " 5: '#630AFF', #purple\n", " 6: '#F5770D', #orange \n", " -1: '#00ffff' #cyan\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the MDS function from sklearn.manifold, we run MDS on the data that we processed and grouped. When we call MDS, we used \"precomputed\" since we are using cosine distances we already calculated (in the dist_matrix). The output is the points that we will use to plot each text." ] }, { "cell_type": "code", "execution_count": 282, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T09:03:38.155177Z", "start_time": "2018-04-02T09:03:35.676084Z" }, "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.17061923, -0.08740414],\n", " [ 0.78848158, -0.10479215],\n", " [-0.02287633, -0.62204817],\n", " [ 0.20120709, -0.56470676],\n", " [-0.28317329, -0.57406227],\n", " [-0.188623 , 0.75038584],\n", " [-0.14670863, -0.6968594 ],\n", " [ 0.11473336, -0.66631904],\n", " [ 0.7814253 , -0.15693786],\n", " [-0.64083933, -0.41901616],\n", " [-0.37358358, -0.67691921],\n", " [ 0.31919244, -0.53404101],\n", " [ 0.26501496, 0.35391037],\n", " [-0.20123137, 0.40171282],\n", " [-0.0683872 , -0.07086821],\n", " [-0.34928297, 0.18443367],\n", " [ 0.53504492, 0.04088804],\n", " [ 0.12436799, -0.0127533 ],\n", " [ 0.27518697, -0.03879568],\n", " [-0.19164743, 0.19387329],\n", " [-0.02624566, 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0.19487315, 0.30283475],\n", " [ 0.54413929, -0.01564063],\n", " [ 0.73968017, -0.01071915],\n", " [-0.12976547, 0.58601435],\n", " [ 0.3877851 , 0.35888906],\n", " [ 0.0352073 , 0.75799459],\n", " [ 0.09142646, 0.50608576],\n", " [ 0.1381669 , 0.42637313],\n", " [ 0.41270353, 0.18257481],\n", " [ 0.15824761, 0.2210137 ],\n", " [ 0.22749656, 0.18792507]])" ] }, "execution_count": 282, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mds_cluster = MDS(n_components = 2, dissimilarity=\"precomputed\") #use MDS\n", "embeddings_cluster = mds_cluster.fit_transform(dist_matrix) #the points/vectors of the texts obtained by MDS\n", "embeddings_cluster" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a function that when given a text (input), it can output which cluster it is in or if it's the new text we are analyzing." ] }, { "cell_type": "code", "execution_count": 283, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T09:03:38.160691Z", "start_time": "2018-04-02T09:03:38.156681Z" }, "collapsed": true }, "outputs": [], "source": [ "def clusterpicker(label):\n", " for i in range(len(clusters)):\n", " if label in clusters[i]:\n", " return i" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make a table (pd dataframe) of all the data we want to plot or use as labels. " ] }, { "cell_type": "code", "execution_count": 292, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T09:06:57.834347Z", "start_time": "2018-04-02T09:06:57.809782Z" }, "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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xyclustertitlefulltitle
id_text
NEW0.170619-0.087404-1NEWiddindaganAB
c.0.1.10.788482-0.1047921Ur III catalogue from NUr III catalogue from Nibru (N1)
c.0.1.2-0.022876-0.6220486Ur III catalogue at YalUr III catalogue at Yale (Y1)
c.0.2.010.201207-0.5647076OB catalogue from NibruOB catalogue from Nibru (N2)
c.0.2.02-0.283173-0.5740626OB catalogue in the LouOB catalogue in the Louvre (L)
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" ], "text/plain": [ " x y cluster title \\\n", "id_text \n", "NEW 0.170619 -0.087404 -1 NEW \n", "c.0.1.1 0.788482 -0.104792 1 Ur III catalogue from N \n", "c.0.1.2 -0.022876 -0.622048 6 Ur III catalogue at Yal \n", "c.0.2.01 0.201207 -0.564707 6 OB catalogue from Nibru \n", "c.0.2.02 -0.283173 -0.574062 6 OB catalogue in the Lou \n", "\n", " fulltitle \n", "id_text \n", "NEW iddindaganAB \n", "c.0.1.1 Ur III catalogue from Nibru (N1) \n", "c.0.1.2 Ur III catalogue at Yale (Y1) \n", "c.0.2.01 OB catalogue from Nibru (N2) \n", "c.0.2.02 OB catalogue in the Louvre (L) " ] }, "execution_count": 292, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plotdata = pd.DataFrame(embeddings_cluster, columns = [\"x\", \"y\"], index = file.index)\n", "plotdata[\"cluster\"] = [clusterpicker(i) for i in file.index]\n", "plotdata[\"title\"] = [\"???\" if i not in labels else labels[i] for i in file.index]\n", "plotdata[\"fulltitle\"] = [str(i) if i not in fulltitles else fulltitles[i] for i in file.index]\n", "plotdata.loc[\"NEW\", \"cluster\"] = -1\n", "plotdata.loc[\"NEW\", \"title\"] = \"NEW\"\n", "plotdata.loc[\"NEW\", \"fulltitle\"] = \"iddindaganAB\"\n", "plotdata.head()" ] }, { "cell_type": "code", "execution_count": 293, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T09:07:01.447987Z", "start_time": "2018-04-02T09:07:01.443475Z" }, "collapsed": true }, "outputs": [], "source": [ "size_dict = { \n", " 0: 11,\n", " 1: 11,\n", " 2: 11,\n", " 3: 11,\n", " 4: 11,\n", " 5: 11,\n", " 6: 11,\n", " -1: 33\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot our findings using MDS. " ] }, { "cell_type": "code", "execution_count": 294, "metadata": { "ExecuteTime": { "end_time": "2018-04-02T09:07:04.919241Z", "start_time": "2018-04-02T09:07:04.873117Z" }, "collapsed": false }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "data": [ { "hovertext": [ "iddindaganAB" ], "marker": { "size": 10 }, "mode": "text", "name": "Cluster -1", "text": [ "NEW" ], "textfont": { "color": "#00ffff", "family": "sans serif", "size": 33 }, "type": "scatter", "x": [ 0.17061922819308709 ], "y": [ -0.08740413643544977 ] }, { "hovertext": [ "The marriage of Martu", "Letter from Aradŋu to Šulgi about Apillaša", "Letter from Šulgi to Aradŋu about Apillaša", "Letter from Aradŋu to Šulgi about irrigation work", "Letter from Aradŋu to Šulgi about the country", "Letter from Aradŋu to Šulgi about Aba-indasa's missing troops", "Letter from Aradŋu to Šulgi about the fortress Igi-hursaŋa", "Letter from Šulgi to Aradŋu about Aba-indasa's letter", "Letter from Puzur-Šulgi to Šulgi about 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