{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lecture 5: Further Examples of Classifiers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This week we're discussing more classifiers and their applications. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Support Vector Machine\n", "\n", "The Support Vector Machine is another classification method known for its memory-friendly nature. A good way to think about all these machine learning algorithms we have seen is as a set of tools. Each one has its unique advantages and disadvantages, but these tools can oftentimes be used in conjunction with each other. An SVM is almost like a scalpel; it can navigate through complex relationships in high-dimensions, but is best used on smaller subsets of data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Basics\n", "\n", "We start by assigning each data point a set of \"coordinates\" called its features. In this way, we can represent the data in some n-dimensional feature space as a set of points. The basic goal is to find a **hyperplane**, that is, an (n-1)-dimensional plane that best seperates the data points. A **support vector** is the position vector of a point close to this hyperplane of seperation.\n", "\n", "![image](http://dni-institute.in/blogs/wp-content/uploads/2015/09/SVM-Planes.png)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a 2-dimensional case. This means that we represented the data in terms of two features. We want to find a separation hyperplane that separates the data points into two sets.\n", "\n", "In 2-dimensions, our hyperplane of interest is simply a line of the form $mx + b$. We want to try and tweek $m$ and $b$ to find the best line of seperation.\n", "\n", "![image](https://www.analyticsvidhya.com/wp-content/uploads/2015/10/SVM_21.png)\n", "\n", "It is pretty intuitive to see that in the above case, line B is the best case. The following case is a bit trickier, but still we can find that line C appears to be the best.\n", "\n", "![image](https://www.analyticsvidhya.com/wp-content/uploads/2015/10/SVM_4.png)\n", "\n", "This is because it maximizes the **margin** - the distance between the hyperplane and the closest support vectors." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The support vector machine does this process for us. It finds the best hyperplane to seperate the data points.\n", "\n", "![image](https://media.licdn.com/mpr/mpr/AAEAAQAAAAAAAAuSAAAAJDlhYzcwMzhlLTA0MjYtNDEyYS1hMWM4LTE3Zjk5NDlhNzVkMQ.png)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### To Reiterate...\n", "\n", "Pros:\n", "* Effective in high dimensions\n", "* Uses a subset of data, thus is memory efficient\n", "\n", "Cons:\n", "* Bad on large training sets, due to long training time\n", "* Sensitive to noise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1: Classifying Iris Species\n", "\n", "We will use SVM to predict the iris species. You can read more about the dataset here." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# import necessary packages\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.model_selection import train_test_split\n", "from sklearn import svm, datasets" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# here we use the iris dataset\n", "iris = datasets.load_iris()\n", "X = iris.data[:, :2] \n", "Y = iris.target" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SVC(C=1, cache_size=200, class_weight=None, coef0=0.0,\n", " decision_function_shape=None, degree=3, gamma=1, kernel='linear',\n", " max_iter=-1, probability=False, random_state=None, shrinking=True,\n", " tol=0.001, verbose=False)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# we use .SVC function to make the classification object\n", "model = svm.SVC(kernel='linear', C=1,gamma=1)\n", "\n", "# split the training and testing data\n", "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.3)\n", "\n", "# fit the model to the training data\n", "model.fit(X_train, Y_train)\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 1, 2, 2, 2, 2, 2, 1, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 1, 0, 1, 0,\n", " 1, 1, 2, 2, 0, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 0, 1])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# predict on the testing data\n", "model.predict(X_test)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.80000000000000004" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# test the score of the model\n", "model.score(X_test,Y_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Margins\n", "\n", "Given a dataset \n", "\n", "\n", "\n", "How do we separate the blue dots from the red dots? One way is to draw a straight line between the two classes, separating them. However, there are an infinite number of straight lines we can draw from this graph, so which line should we pick? \n", "\n", "One reasonable choice would be the line that gives the largest separation between the two classes. This separation is called the **margin**, and in **maximal margin classifiers**, we want to maximize the margin. In other words, we want to maximize the distance between the hyperplane (a line in our case) and the closest point(s) (filled in in the graph below) in each class.\n", "\n", "![image](https://qph.ec.quoracdn.net/main-qimg-312b52d9d056499a3c8893e22f6fee5e)\n", "\n", "These points are called **support vectors** and they help us find where our hyperplane lies. \n", "\n", "### Hard Margins\n", "Our hyperplane may not always be perfect, especially when our dataset is not linearly separable. In such cases, we want to introduce the **cost function**: \n", "\n", "$$-log(1-\\frac{1}{1+e^{cx}})$$\n", "\n", "It looks like an exponential function and the coefficient c will change how fast the value increases. This function dictates how much to penalize support vectors for being mislabled. If the penalty value (namely $c$) is high, then the svm is **hard margin**.\n", "\n", "Let's look at specific case. The graph below shows the hyperplane between two classes, blue are red. As you can see, the existence of one (red) outlier drasticaly changes the hyperplane. \n", "\n", "\n", "\n", "If we were to use a **hard margin** SVM, we would have a high penalty value and the resulting hyperplane would be dictated by that one red outlier. \n", "\n", "### Soft Margins\n", "You might have realized that, in the example above, it is better to allow one outlier to fall on to the wrong side rather than letting that one outlier dictate the position of our hyperplane. We can achieve a \"more balanced\" hyperplane that lies more or less right in the middle of the two classes, by having a low $c$ value. This is called a **soft margin support vector machine**.\n", "\n", "Especially in non-linearly separable datasets, it is generally better to use a soft margin SVM. In this case, we introduce the **hinge loss function**: \n", "\n", "![image](https://wikimedia.org/api/rest_v1/media/math/render/svg/53b729df53f32c7fbf933b1b034a8e368037d9b5)\n", "\n", "where $y_i$ is either 1 or -1, indicating the class to which $x_i$ belongs, and $w$ is the vector normal to the hyperplane.\n", "\n", "\n", "\n", "The regularization constant controls how \"soft\" the margins are. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Restrictions of Linearity - Introducing Kernels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having talked about the function of a support vector machine and the methodology behind it, we now move on to a critical limitation of SVMs: **linearity**. See, an SVM is a member of a class of machine learning models known as **linear classifiers**, an entire class of functions which fit lines or hyperplanes to classify data. Herein lies the problem: linear classifiers fit *straight* lines to the data, but quite often the underlying decision boundary between the classes is anything but.\n", "\n", "To illustrate why this is such an issue, imagine cluster of points of class A, surrounded by a ring of points of class B. Now, attempt to draw a straight line with a ruler so to separate those to classes. Such a task is nigh impossible. \n", "\n", "\n", "\n", "However, this doesn't mean that the two classes are inseparable. In fact, we can simply use an oval shape to separate the two classes:\n", "\n", "\n", "\n", "And here comes the problem, how do we find this oval that separates our two classes? " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One way to resolve this dilemma is to transform the data into a linearly separable dataset, as such:\n", "\n", "\n", "\n", "Now we can easily find the separating hyperplane! After finding this hyperplane, we can project the data back into its original form, alnong with the now non-linear decision boundary.\n", "\n", "As the title of this section may suggest, to achieve this goal we resort to using a class of functions called **kernel functions**. Kernel functions are used internally within the model to compare data points; each kernel function represents a different measure of similiarity, even simulating the similarity of two points in a higher dimensional space than the one they currently occupy. This is important to note, as while the data might not be separatable in their current form, a different perspective may make all the difference." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Radial Basis Functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, if you recall back to the example given early in the notes, you may remember the keywork \"kernel = 'linear'\" appearing. This kernel is the vanilla ice cream of kernels - the default flavor, not particularly interesting, but still good to have sometimes. The problem posed above is, as we've said, not one of those times. Instead we're going to reach for another flavor of kernel function, known as a **Radial Basis Function**.\n", "\n", "A radial basis function is actually a class of functions that all have the same property: the value they return relies **only** on radial distance from the origin (*cough* *cough* kinda like the definition of a circle *cough*). Plugging this into our SVM model will cause the decision boundary generated to take on curvature, even circular patterns if the data is just right. Let's take a look at an example of scikit's RBF in action:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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4DrOD61KvC3NEojhyPbl8teUrPD7/Emm53lwm/jZRh6gihyTvILKyCp7bPnky\nfLEUVbDEC9qw4cmcgoM3G8xBD1wAgv5iLIpNhzfRZ1YfarxVg0vGXcK7q94NWidaiKJoVq0ZTS5o\ngsVoyfe6QTEQb4nn9ktu1ykyURTBOiCnZbgywhRJZJLkHUSrVuANcpKiwwE33BDeeIriujrX+f3i\nOi3Xm8vlVS4v8P3VEqtRu1ztgG1mg5neF/cuUXzf7/yeZhObMX3TdP459Q8bj2zk0cWPcu2Ua3F5\no/ikABEx5veZz/Wp12M1WUmKS8JuttOkUhN+HvgzdrNd7/BEIZSzlitwh8tFyReFMZrII8k7iNNn\nvtps+V83GCA+Hvr21SeuwnjgqgcCHs5hM9noc0kfKjkqnfce73d53++XnMlgorytPE9e82SxY/Op\nPvp+2ddvJbDT7WTdoXVMXTe12PcW4rRy1nLM6zOPrfduZXbv2awdspbfh/1OnfJ19A5NFJJBMfDU\nNU/hMDv82uxmO/+59j86RBU5JHkXYNo0uOMOrSJPYqL236uugpUrI6+k3tlqJtXk+37fk1ouFYfZ\nQVJcElaTlb5N+vLeje8V6h6ta7Xmp7t/ouOFHbGZbCTGJdL/sv78PvR3KscXv7rBbwd+Czrc5XQ7\nmbB2QrHvLcS5aiTVoF1qOxomN9Q7FFEM9za7lweuegCryUpiXCKJcYnYzXZevu5lujfsrnd4upKt\nYoVw8iTs2AGVKkH16npHU3iqqrLh8AaOZx+nyQVNqGCroHdILN29lG7Tu3Eq91TA9ouSL2LziM1h\njkoIEcnSs9NZtncZRsVI29ptcVj8e+NlhZRHDaGkJGgahUfzKopCkwua6B1GPpdXvjzovLbZYKbD\nhR3CHJEQItKVt5Wna4OupfoMtxtycrRp0Uit4XE2GTYXYZVkTeKetHsCLhqymqw8dPVDOkQVOXI9\nufzvp/9R/c3qOF500OyDZizYJlvzzsftdZ+3foEQgezfD716aUm7QgWoVUurpBnpJHmLsHu1/avc\n1+w+7GZ73hzWRckXsfTupdRMqql3eLrx+Dy0+7gd/1v2P/Zl7MPpdrJ6/2p6ftGT99YUbq1CrFmw\nbQGXjLsE6/+sxP03jh6f92D3id16h5XPsj3LaD+1PcmvJlP/nfqMWTlGdlVEiPR0SEuDOXPA5QKP\nB/7+G+65B958U+/oCiZz3kI3Wa4s/jz6J0lxSdSrWE/vcHT3xaYv6P9V/4D7W+1mO4cePkS8JV6H\nyCLTzM3ojdd1AAAgAElEQVQz6fdlP7I9Zw5rNigGylvLs374eqomVNUxOs0n6z9h6NdD81UrtJvt\nNK/WnEV9F4WkZoIovhdfhBde0IbLz+VwwJEj/juOSpuURxURz2FxkFY1TRL3v6asmxK0MIXJYGLx\nzsVhjihy+VQf9y24L1/iPv36qdxTvLriVZ0iOyPbnc3wecP9ygw73U5W71vNV399pVNk4rQvvgic\nuEGrsLlyZXjjKQpJ3kKUIqfbybjV47hq4lVcOeFKXlvxGidyTgS8tqCTklRVDTrU6lN9LNy+kBd+\nfIF3V73L4azDIYk9km05uoWM3MBbDt0+N7M2zwpzRP5+2P0DBiXwr9hMdyYf/v5hmCMS5zKcJwOe\nr11PMmYjRCk5mXOSqz68ir0n9+YdrLDpyCZG/zqa1YNX+w3r9rioB7/880u+QxhOc3vdtKnVxu/1\ng5kHaftRW/Zl7CPLlYXVZOXh7x5mTKcxDLliSOn8xaJBBKwWznZnF9ge6NQzEV59+sCff0J2gP+r\nVFWr6xGpQvK5QlGUToqibFEUZbuiKI8HaO+jKMp6RVE2KIrys6Iol4biuUJEsud+fI5d6bvyJeNs\nTzaHMg9x3/z7/K7vd2k/KlgrYFLyf6a2m+0MuHwAF8Rf4PeeHp/3YMfxHWS6MlFRyfZkk+PJ4cGF\nD7Jmf9ldL9IguQGJcYkB28wGM70a9QpzRP5a1mwZtF6/zWQr9a1P4vwGD4YqVcByTjVpux3eegvi\n/AtVRowSJ29FUYzAu0BnoBFwu6Iojc65bBfQRlXVS4AXACmjJcq8j37/iFyv/y9vr+rlm23f+A2T\nx1viWTV4FZ3qdcJitOStxn+s5WO8c8M7fvfZemwrfxz8A4/qf+pSjieHN3+J8OWyJWBQDIy9YSw2\nk83v9aS4JB5p8YhOkZ1ROb4yd116l9+2yNMHpAxqOkinyMRpCQmwejUMGKBtFTMY4JJLYPp0GDhQ\n7+gKFoph82bAdlVVdwIoijId6AbklclSVfXns65fCURRnTIhCm9/xn7GrBzD/G3zOZEbeG77NKfb\nidVkzfdalYQqfH3712TkZnAi5wSV4ytjNpoDvn/78e1YjBa/RVugzYNvOryp+H+RKNDjoh582ftL\nHlv8GOsPrcdkMNG9YXde7/A6VRKq6B0eAONuHEeSNYlxq8dhUAy4vC6aVWvGlO5TCjx0Q4RPhQrw\n3nvaVzQJRfKuBvx91vf/AM0LuH4gEHFVJ1QVjh0DkwnKyc+UKIbNRzbT4sMWZHuyz7uPt6KtIuWt\n5YO2J8QlkBBXcAH9Wkm1cPvcAdsUlJhYxd+xbkc61u2I1+fFoBhQIqw0ltFg5NX2r/J82+fZdWIX\nFW0VA05/CFFUYV1LpyjKtWjJ+7ECrhmiKMoaRVHWHDlyJCxxzZ8PDRpAtWpa/fJmzUC2l4uiuuvL\nuziVe+q8idtutvNc2+dKnGgaV2pMg4oNMCpGvzab2RZT1eqMBmPEJe6z2cw2GqU0ksQtQiYUyXsf\nUOOs76v/+1o+iqI0ASYC3VRVPRbsZqqqTlBVNU1V1bSUlJQQhFew+fOhZ0/Ytk2rsON2a3MgbdvC\n+vWl/nhRRuw7tY8NhzegErjokYJCYlwiNpONJ695ksFNB4fkuXNum0PVhKp5xVssRgtWk5Vn2zxL\nixotQvIMIUTkCcWw+WqgnqIoqWhJ+zbgjrMvUBSlJjAb6Kuq6tYQPDMkVBX+7/8CbxNwOuGpp2Du\n3PDHpTePz8PcLXNZsmsJiXGJ9LmkD40rNdY7rIh2MvckFqMl4AI1gMS4RGb0mkGLGi1CWiWtZlJN\ntt+/nTl/zWH53uWk2FO4s8mdpJZPDdkzhBCRJyTlURVFuQEYDRiBSaqq/k9RlGEAqqqOVxRlInAL\nsOfft3gKU/6ttMujHjmiHfHpCjLKabNpSTyWHM46TMtJLTmYeZBMVyZGxYjFaGFo2lDe7PBmRA9N\n6inXk0vya8kB9+4qKHSp34W5t8fgJ0EhRJGEtTyqqqrzVVWtr6rqhaqq/u/f18arqjr+3z8PUlW1\nvKqql/37dd7AwsFk0nrfBbXHmjtn38meE3vykpBX9ZLtyeaDtR/w1RYp5xhMnCmOh1s8jMPsf86w\nzWzjmTbP6BCVEKKsiuDib6WvfHm4NEi5GKMRevQIbzx6O5BxgJ/2/BRwBXOWO4vXf35dh6iix9Ot\nn+beZvdiM9lIiksiwZJAij2FGT1nkFY1Ij6vCiHKiBjsW+b37rvQrp02PH66F240QlISPP+8vrGF\n2z+n/sFqsgadt420oxYjjUEx8PL1LzOq1SjWHliLzWSjWbVmGA3+q8GFEKIkYrrnDdq2sBUr4IYb\ntDnu+Hi44w747TftUPZYUrtc7aDlHAEaVGwQxmiiV5I1iXap7bi6xtWSuIUQpSLme96gDZ1/843e\nUegvxZFC53qdmb9tvl/v226283grv7L1Zc6BjAP8dfQvKsdX5qKUi/QORwghApLkLfKZ3G0yHaZ2\nYNORTeR4cjAbzaiqyjOtn6H9he31Dq/UZLoyuevLu5i3bR5WkxW3z02dcnWYeetMGiTLiIMQIrKE\nZKtYaSntrWIiMFVVWfH3CpbtWUa8JZ5bGt3id3xlWdNhageW7V2W77AQBYUKtgpsv3+71KEWIsb8\n/DM89hisXAlmM9x8M7z8MtSocf73lkRht4pJ8hYxb/ORzaRNSAt4wIfdbOfFdi/yf1f9nw6RCSH0\nsHgxdO2av4CX0ajtUFq3DqqWYl8mrPu8hYhmK/9ZiUEJ/KPgdDtZvHNxmCMSQuhFVWHYMP/Km14v\nnDgBL76oT1znkuQtYl5SXFLQ5K2gUNFeMcwRCSH08vffsH9/4DaPB2bMCG88wUjyFjGvc73O+FRf\nwDa72c7AyweGOSIhhF68XiioCrQv8K+KsJPkLWKe3WxncrfJ2E32fD1wh9nBbRffRquarXSMTggR\nTrVrQ4UKgduMRrjpprCGE5QkbyGAXo17sWLgCno37k39ivW5tva1fNLjEz646QM5jEWIGKIoMGaM\nVrTr3NcdDnj6aX3iOpesNhdCCCHOMW8ejBwJO3Zo37dpA++8AxeVcu2mwq42lyItQgghxDluvFH7\nysjQ9nlbrXpHlJ8kbyGEECKIhAS9IwgsJue8lyyBbt20muZ33QXr1+sdkRBCCFF4MdfzHjUK3n5b\nOwIUYNMmmDkTJk2C3r31jU0IIYQojJjqea9fr60iPJ24QdvT53TCgAHa3IYQQggR6WIqeX/4Ibhc\ngdsMBvjqq/DGI4QQQhRHTCXvI0e0nnYgbjccPx7eeIQQ/jw+D5muTCJ5G6sQeoup5N26tbbJPhCT\nCZo3D288QogzjjmPcdecu4h/MZ7yr5Sn2pvVGL9mvCRxIQKIqeR9551a1ZxzC2ZZLNrG+2bN9IlL\niFjndDtpPrE50zZMI9ebi8fn4UDmAUYuGskzPzyjd3hCRJyYSt7x8bBiBTRooPXAk5K0jffXXAML\nFxZcjF4IUXo+Wf8JBzIP4Pa5873udDt5/ZfXSc9O1ykyISJTzG0Vq18fNm/WVp7v368l8jp19I5K\niNj2+abPcbqdAdvMBjNLdy/l5otuDnNUQkSumEveoPWwL71U+xJC6C/YeeoAiqLI4TBCnCMmk7cQ\nIrhtx7bxzqp3+OPgH9SrUI/7mt/HZZUvK9Vn3nnJnfzy9y9kubP82txeN+1S25Xq84U4n1OnYM4c\nbVfSlVdCixb6TrVK8hZC5Jm1eRZ9v+yLx+fB7XPz898/M23jNF66/iX+r/n/ldpze1/cm9d/eZ1t\nx7aR683Ne91utvNM62dIjEsstWcLcT7Tp8PAgVo9ELdb251Uvz4sWgTJyfrEFFML1oQQwZ3MOUm/\nL/uR7cnOWzjmVb1ke7J5fPHj7Di+o9SebTVZWTFgBcPShpFgSUBBoV6Feky8aSKPtXqs1J4rxPls\n2KAlbqcTMjMhNxeysmDjRujZU7+4pOcthABg9p+zg84t+1QfU9ZN4T/X/qfUnp8Yl8joTqMZ3Wk0\nqqoWep47PTudH/f8iFEx0rZ2WxLi/I+BcnldLN+7nFxPLlfXuJpy1nKhDl+UUW+8oSXsc7ndsGoV\nbN8OdeuGPy5J3kIIAA5nHc43ZH02l9fF/oz9YYulMIlbVVWe/uFp3vjlDSxGC6DNj7943Ys8cNUD\nedd9tuEzhs8bnve9y+vi/mb38/L1Lwd8zj+n/mHlPyuJt8TTLrVd3r1FbFq3LnhlTosFtmyR5C2E\n0FHTKk2xmqxkujL92uLN8VxV/SrcXjdjfh3D27++zRHnEeqWr8tTrZ+i98XhP5Jv7OqxjF45mhxP\nDjmenLzXn1zyJDUSa3BLo1tYunspg+cOxulx+r23vK08j7d6PO81l9dF/6/6M2vzLOKMcfBvXv+4\n+8d0a9gtLH8nEXlq19YSeKBCfx4PVKsW9pAAUCK59GBaWpq6Zs0avcMQIib4VB8NxjZgV/ouvOqZ\nroaCQgVbBXb/325unXkrP+75Md+ebIfZwcirR/L8tc+HLVZVVan8RmUOZx0O2N4ouRGbRmyi9eTW\nLNu7LOA15eLKcfiRw5iNZgCGfj2Uqeunku3Jzned3WxnWf9lNK3SNLR/CREVfvwRbrgh/2mUoK00\nb9BAqxsSylXniqKsVVU17XzXyYK1GLQ/Yz8DvxpI4kuJ2P5no8PUDqzZLx+SYp1BMbD0rqU0rtQY\nh9lBgiWBeEs8NZNq8uPdP/Lrvl/5ac9PfsVUstxZvLriVQ5mHgxbrCdzT3Ii+0TQ9i3HtgDw+8Hf\ng17j8rnYl7EPgBM5J/h4/cd+iRsgx5PDS8teKmHEIlq1aQMjR2qltY1G7bX4eG2V+Vdf6bddTIbN\nY8yBjANcNv4y0nPS8fg8AHy38ztW/L2CBX0W0LpWa50jFHqqlliNdcPW8duB39h6bCs1EmvQokYL\nFEXhzV/eDLgPG8BoMPLN1m8Y1HRQWOK0m+15w9qBnF60lhiXGHAaALTTy5LikgDYcnQLFqMl3/D7\naT7Vx+r9q0setIha//kP9O4NkybBoUPaIVd9+gQ/6CocpOcdY/637H+cyDmRl7hPc7qdDPtmmE5R\niUjTtEpTbrv4NlrWbJm3qCvH65/YTvOpPtxed9D2ULMYLfRo2AOzwezXFmeMY9Dl2oeIoVcMxWqy\n+l1jUAy0qtmK8rbyAFS0Vyww/mS7Tpt5RcRo3Fhbef7JJzBkiL6JG2IweWdna5VyIniqv1TN2DTD\n7/CH03ad2MW+U/vCHJGIFt0bdCfeEh+wTUXl+jrXhzWetzu/TbWEalov/F8Os4P6FevzbNtnAXi4\nxcM0SmmEw3zmN63VZKWCrQITb5qY91rdCnWpX7E+SoDuvMPs4L5m95Xi30SIoouZ5P3XX3D99ZCY\nCBUragsNvv5a76jC79we99kUlKCJXYjuDbtTI7EGFkP+rVN2k51uDbpRr2K9sMaT4khh4z0beaPD\nG7Sp1YZ2qe0Yd+M4Vg9enfchw2628/OAn3mn8zu0qtmKtCppPN36af4a8Rep5VPz3W/aLdMoZy2H\nzWTLe81hdtAutR13NrkzrH83Ic4nJlab794Nl13m3+O22+Gjj6BXrxI/Imr0mdWH6Zum41N9fm3V\nE6uz94G9cgiECCo9O51759/LrD9nYVAMmAwm7rnyHv7b7r+YDKWzhMbldTFj0ww+3fApPtVH78a9\nuf3i27GZbed/cxEddR5lwtoJLNi+gHLWcgxuOpgu9bsUeHCKEKFU2NXmMZG8Bw3SknSgjfZVq8Lf\nf2s1a2PB1mNbSZuQRoYrI9/rNpONj2/+mJ6NdKz3J6KG0+0kPTudFEdKqRYxyXRl0mpSK7Yf3563\nWM5hdlAtsRorB67Mm7MWoqyQrWJnmTs3eIWcEydg587wxqOn+hXrs3zAclrUaIHZYMZitJBaLpVP\ne3wqiVsUmt1sp1pitVKvPvbMD8/w19G/8q1yz3JnsTt9NyMXjSzVZwsRyWKi512lChwMsgXVZoNN\nmyA1NXB7WXYq9xQur4uKtooyVB6jVFVl85HNuLwuGldqnJeMV+9bzeKdi4kzxXFzw5v95ofPZ8vR\nLRx1HqVhckMq2isWO76kl5I45ToVsM1qspI5KhOjwVjs+wsRaQrb846Jfd633grvvacVkj9XlSpa\n+btYJMcsxraF2xcyaO4g0nPSMSgGFEXhmdbP8O32b/n5n5/J9eRiNBh5csmTDE8bzhsd3jjvh7zN\nRzbT+4ve7DyxE7PBTI4nh9suvo3xXcYH3LJVEFVV/aZ3zubxecj2ZAddAS9EWRYTyXvUKJg2TTtE\n/ezhc7tdS+rS6RSxZtW+VfT4vIdfze/Hv38cVPCo2q4E778/MO+vfZ+0qmnccckdQe951HmUlpNa\ncjLnJCpnRvRmbJqB0+1kRq8ZRYoxy51FQlwCp3ID97yT7cn5toAJEUtiYs67cmX47TetIo7Nph2k\nfs012kHqHTroHZ0Q4ffMD8/4JW7QerOnE/fZnG4nLy57scB7Tlg7gVxPbr7EDZDtyebrrV+z58Se\nQseX7c6mxYct/EqxnmY323m69dMy3SNiVkwkb4Dq1WHKFK24vNsNP/0ELVvqHZUQ+ljx94oiv2f3\nid0Fti/cvjBgbXAAs8HMr/t+Pe8zslxZjJg3gnKvlGPD4Q1B6xIMvHwgw9OGB2wTIhbExLC5ECI/\nu8ketOZ3MFUTqhbYXtC2LUVRSLAkFPh+r8/LtVOuZf2h9bi8rqDXOcwOmlZpKr1uEdNipucthDij\n32X9gm7zClQi1G6283CLhwu85+Cmgwucg26X2q7A9y/csZA/j/5Jrje3wOsURQkYYzCHMg/xzq/v\n8MKPL7Bw+8KABYqEKIwvv4SLL4aUFGjVClbreF5NSJK3oiidFEXZoijKdkVRHg/QriiK8va/7esV\nRZGDcUVMSM9O54ddP7Bm/5qIShpPtHqCagnV8q0ANxvMJFgSaJjcMG8Ft0ExYDfbueWiW857Yljn\nep3pWLdjvgR++v0fd/+YOFNcge+f89ecQo0GeLweOtbteN7rAN5b/R61x9Tm0cWP8uzSZ+n5RU8a\nvduIQ5mHCvV+IU675Rbo0UPbWnz0KKxYAc2awcsv6xNPiYfNFUUxAu8C7YF/gNWKosxVVXXzWZd1\nBur9+9UceO/f/wpRJnl9Xh5c+CAf/PYBccY4vKqXpLgkPu3xKW1qt9E7PMrbyvP70N8Zu2osU9ZN\nIdeby031b+KRFo9QI6kG3+34jgXbFxBnjKP3xb1pWuX8n7cNioEven3B9I3TefvXtzmcdZhm1Zox\nqtUoLq186XnfbzKYUFD8FrydzW62M+LKEVSOr3ze+63at4qHFz2c75jPTFcmO9J30GNGD1YMKPq8\nv4hNCxfC7NmB20aN0k4Zq1AhvDGVuEiLoihXA8+pqtrx3+9HAaiq+tJZ17wPLFVVddq/328B2qqq\neqCge4eqSIsQ4fbAtw/wwW8f+K2WtpvtrB2ylobJDXWKLHIt2bWEbtO7Be19V4mvwrNtn2VI0yGF\nmu/uPbM3X2z6IuCHAZvJxrph68J+mIqITs2bw6pVwdvvvx/GjAnNs8JZHrUa8PdZ3//z72tFvQYA\nRVGGKIqyRlGUNUeOHAlBeEKE16ncU7y/9v2A25xyPbm8uuJVHaKKfNfWvparq1+d71QvONPb3j9y\nP0OvGFrohWqbD28O2ou3GC3sSN9R4phFbAhWofO0f/4JTxxni7gFa6qqTlBVNU1V1bSUlBS9wxGi\nyDYe3hh0MZhX9bJ099LwBqSjg5kHGTh3IPEvxmN+wUyrSa1YtmdZwGsVReGbO77hiWueoJK9EkbF\nSK2kWrzZ8U3e6fxOkZ9dt2LdoAvb3D43tcvVLvI9RWxqep5ZIz22HYdiq9g+oMZZ31f/97WiXiNE\nmZAUl4TXF+QkHKC8NTZOwjqSdYSm7zfliPNI3n7tFX+voNOnnZjRcwY31r/R7z0Wo4WnWj/FU62f\nKvHzH7rqIRbtWOQ3AmJUjFyUfFHMTF3sTN/JocxDNEhuQAVbmCdmy4g334Q5cwK3mc3wwAPhjQdC\n0/NeDdRTFCVVURQLcBsw95xr5gL9/l11fhVw8nzz3UJEq0YpjYIuqLKb7Qy/MjaKi7z+8+scyz7m\nV2jF6XYy9JuhlPahSNfUuoanWz+N1WTNGwlJsCRQNaEqs3sHWX1Uhmw7to0rJlzBxeMupvOnnan2\nZjX6z+mfbwGfKJzUVK3I17kzNnFx2qpzPY6UDsmpYoqi3ACMBozAJFVV/6coyjAAVVXHK9ok1Vig\nE+AE+quqet6VaLJgTUSr1ftW0+7jduR6cnH7tBNxHGYHaVXT+K7vd5iNZp0jLH0136rJ36f+Dtjm\nMDtYM2RNWHq/O9N38un6TznqPEqrmq3o3rB7mf/fPz07nXrv1ON49vF88/5Wk5Ub6t7ArN6zdIwu\nerlc8MYbsG0btGgBAwaEPnGH9VQxVVXnA/PPeW38WX9WgRGheJYQ0eDKaleyYfgG3vrlLb7b+R1J\ncUkMSxvGHZfcUeYTx2kF7WtXFKXAqYVQqlO+Dk+3eTrv+6POo8z+czYZuRm0rNmS5tWal7lqbZN+\nn0S2O9tvwV6OJ4f52+ezM30ndcrX0Sm66GWxaFvDIkFMlUf1emHNGsjJ0RYgJBRcrVGIEqldrjZj\nOodo/0gU6tagGx/89kHeyMPZrCarLnPO41aNY+R3IzEoBtxeNxajhUsqXcK3d35LkjUp7PGUloU7\nFgY8eAa0/fS//P2LJO8oF3GrzUvLvHna2d3t20PXrnDBBfDUU1DK025CxKzHWz2Ow+LwW/FtN9t5\no/0bGA3GsMazfO9yHln8CDmeHJxuJ26fmyx3Fr8d/I1+c/qFNZbSVtAHEQWFhDjpuUS7mEjeq1fD\nrbfCkSOQkQGnTkF2Nrz1Frz00vnfL4QouhpJNfh10K9cX+d6TAYTZoOZ1HKpTOk+hX6XhT9Zvrz8\n5YB7711eF4u2L+Jg5nk280aRQZcPClpnXkWlfZ32YY5IhFpMDJs//7yWrM/ldMIrr8DDD2tzGUKI\n0KpfsT6L+mrbtXI9uZSzltNtfnnzkc1B2+JMcew4vqNQZVejQYcLO9C5XmcWbFtAljsL0HrcNpON\nD7t+iM1sO88dRKSLiZ73L78EHx73+WDXrvDGI0SssZvtlLeV13VhWM2kmkHbcr25VEsMWPQxKimK\nwuc9P+f9Lu9zZdUrqZVUi5sb3syP/X/k1sa36h2eCIGY6HknJsLx44HbPB6tXQhRto28eiRr9q/J\n64meZjKYuKLKFWWu4ppBMdCnSR/6NOmjdyiiFMREz3vwYLBa/V9XFGjSRFvIJoQo27rU78LgKwZj\nN9sxKtpiuXhLPFXjq/J5z891jk6IoglJkZbSEqoiLU6nVnt261btz6DNcdts8PPP0KhRiR8hhCgC\nVVX5ZP0nvP7L6+w7tY+6FeryxDVP0LVB11J/9vpD65m6birHs49zXZ3ruOWiW8571rgQ4VLYIi0x\nkbxB29v90UcwcaK2eO3GG7V6tFWrhuT2QpQpC7cv5Nmlz7Lx8EaSrEkMu2IYD7d4OGQLnQZ+NZDP\nN32ebwjbYXbwaMtHeabNMyF5hhDRSJK3EKJYPlj7AQ8sfCDftiqbyUaTC5qwrP+yEleIW7t/La0/\nah1w25bVZGXH/TuomiCfqkVsCud53kKIMsLpdvLgwgf9Emu2J5uNhzcyc/PMEj9j2sZpQQ/HUFCY\n/WfZPzREiJKS5C2EyPPDrh+CVj7Lcmcx+Y/JJX5GpiszaN1zj89Dtjt/UQZVVZn8+2Qajm1I/Ivx\nNBzbkEm/Tyr1U8mEOC0nB157DerUgYoVoWNHbQuyniR5CyHyuLyuAttDcZxkp7qdiLfEB2wzG81c\nm3ptvteGzRvGvQvuZcuxLWS5s9hybAv3LbiPYfOGlTgWIc7H5YK2beHZZ7WaIMePw6JFcP31MLPk\nA1HFJslbxKRcTy5r9q9hw6EN0oM7S6uarYImcLvZTs9GPUv8jC71u1A9sTpmQ/65c6vJSvNqzUmr\nema6b/ORzUxdN9VvGN/pdjJ13dQCq6YJEQrTp8PGjf5VOp1ObRuy2//cnbCQ5C1iiqqqvPnLm6S8\nlsJ1U67j6g+vpsZbNVi0Y5HeoUWEFEcKw64Yht1sz/e6UTGSFJfE3ZfdXeJnmAwmlvdfTud6nYkz\nxpFgScBqstK7cW++ueObfNfO/nN2wFPJANxeN7M2y7nUonRNnAhZWYHbfD5YsSK88ZwWExXWhDjt\nvdXv8fQPT+fryWW5s7h5ulY68uxeX6x6o+MbJDuSeW3Fa7h9bjw+D9enXs+EmyaQGBeacoQV7RX5\n6ravOJ59nIOZB6meWD3gvV1eV9Bzvz2qJyTD+GXRgYwDbDm2hWoJ1ahXsZ7e4UQ1Z+CTVfMEOjcj\nHGSrmIgZXp+XC16/gGPZx/zaFBQ61+3MvD7zdIgsMrm9bg5kHiApLkm3s65/2vMTN3x6g19JU9Cq\no827Yx6ta7Uu9v03Ht7Ikl1LsJqsdGvQjQviLyhJuLrLyM2g75d9Wbh9IXGmOFxeFxelXMQXvb6Q\n87uL6T//0U6fzAnwOdFqhX37oEKF0D1P9nmLMsHtdfPt9m/Zl7GPhskNaVOrTbEPt9iVvouL37s4\n4P5igMS4RE4+frIk4YoQU1WVayZfw9r9a8nxnvntaTVaaVq1Kcv7Ly/Wv4ccTw49Z/Rkya4lqKgY\nFAM+1cdTrZ/iyWueDOVfIazaTG7Dr/t+Jdebm/eaQTGQYk9hx/07cFgCHxMqgjtyBBo2hBMntGHy\n0+x2GDoU3nwztM+Tfd4i6v36z69UeaMKfWb34aGFD3HTtJuoP7Y+u0/sLtb9HBZH0CFYIOj5x0I/\niqKw8M6F3NnkTmwmG3azHZvJRp8mfVh056Jif5B78NsHWbJrCdmebHI8OTjdTnI8Oby47EXmbpkb\n4lssVOQAACAASURBVL9FePx+4HfWHFiTL3ED+FQfma5MPt3wqU6RRbeUFFi5Eq66CuLiID5e+3rk\nEXj9df3ikp63iEjp2enUGl2LDFdGvtcNioFaSbXYfv92DErRP3s2n9icVftW+b0eZ4zjoasf4sXr\nXix2zKJ0ZbuzOZx1mBRHit+CuqLIcmWR8loK2Z7Ak5XNqjbj18G/Fvv+ehm3ehwjF40Mug7g1ka3\n8nkvOYClJA4e1HrgtWsHPuwqFKTnLaLaR398hFf17yX7VB9HnEf4fuf3xbrvpK6TSIxLzLdNyWqy\nUjOpJo+1fKzY8YrSZzPbqFWuVokSN8C+jH1BC9EAbD2+tcD3q6rKoh2L6DOrD92mdeP9Ne+T5Qqy\nHDmMEuMSMRkCr0E2KAYq2EI4MRujKlfWhtBLK3EXRUwm7wMHtAUIQ4fCuHFw6pTeEYlzrdm/Jujc\ntMvrYtORTcW6b+NKjVk/bD1DrhhC7aTaNKjYgOfaPMfaIWt1W5QVCY5kHeHxxY+TOiaVWqNrMXLh\nSA5kHNA7rFJRyVEJtzf45tzK8ZWDtnl9Xm7+/GZu+fwWPtv4GXO3zmXkopE0GNuAfaf2lUa4hda1\nQdeg00JWk5UBlw8Ic0SiNMXcVrFp02DgQFBVbfWgwwGjRsHixXDllXpHJ06rXa42ZoM54B7fOGMc\nVeKLfwh7rXK1GHvDWMbeMLYkIZYZ+zP20/T9pqTnpOcVaBm7eixT1k1h9eDVpJZP1TnC0CpnLaft\nLNg2z+/fl8Ps4KGrHgr63g9//5Dvdn7nt9Uw15tLvzn9+L5f8UaEisKn+gJOGSXGJTK+y3iGzxtO\ntjsbFW1K1GF20P+y/lxZTX7BlSUx1fPeu1dL3NnZZ5b9Z2VpPe/OnfWrlCP8DWw6MOgQoKIoYTn3\nOVTSs9P5YO0HvLTsJRbtWBS0rrdeHlv8GMecx/JVVnN5XaTnpPPAtw/oGFnp+aDrB6SWT80r06qg\n4DA76FK/CwObDgz6vjG/jgk4IuTxeVixdwWHsw6XSrwur4vnlz5P8qvJGP9jpMobVXhr5Vt+/5b6\nXdqPH+/+kVsuuoV6Fepxbe1rmXbLNN7u/HapxCX0E1M97w8+AG+QxcYuF8ybB927hzcmEVid8nUY\n3Wk0D3z7AB6fB7fPjdVkxagY+bL3lyE7V7q0fbbhMwbNHYRBMZDjycFutnNB/AX8ePePEXHspaqq\nfLHpCzyqx6/Np/qYv30+bq+7xMeARppkezIbh29kzl9z+GbbN8Sb4+nTpA9XV7+6wBXshzODJ2eD\nYuBI1hEqOSqFNFZVVek6rSs/7fkpb5HdwcyDPLXkKTYc2sCkbpPyXZ9WNY0vbv0ipDGIyBNTyXvb\nNi1JB+JywZ494Y1HFGzIFUNoW7stE9ZOYGf6Ti6vfDmDrxhc4JxkJNl8ZDOD5g7Kt6o5w5WBM91J\nl8+68NvQ33SM7oyCDiNRVRW3r+wlb9AOQenVuBe9Gvcq9HvqVqjL0X1HA7Zle7JDnrgBlu1dxvK9\ny/1WxzvdTqZvnM7jrR6nfsX6IX+uiGwxNWzepEnwVYIWCzRoEN54xPnVr1if1zu8zuzes3m6zdNR\nk7gBxqwcEzAxelUvW45tYd3BdTpElZ+iKFxe+fKg7XXK1ynx6u6y5MIKFwZtMxvMLNm1JOTPnP3n\n7KCLN72ql6+3fB3yZ4rIF1PJe+BAMAbYIaIokJQE7duHPyZRdm04vCHgdjfQDufYeqzgLUnh8vL1\nL2Mz+U9D2M12Xm3/qg4RRSdFUdifsT/k91VVNW/xWVHaRNkWU8n7ggtgzpwzFXKMRkhI0PbuLV4c\nOLELUVx1K9QNWkjG6/NSq1ytMEcUWPsL2zP15qlUdlQm3hJPvCWeZHsy73d5n+4NZRHI2a6ocgV2\nU+CRCIvRQuNKjUP+zG4NuwU9/9xkMHFjvRtD/kwR+WKywlpWFsyapRWUv+gi6NIFTDE1+y/CYc3+\nNbSZ3AanJ/+Qp4JC3Qp12XLvlmKX9ywNPtXHpsObUFFpnNK4wEImsSo9O53ao2tzypW/OIRBMVAz\nqSY77t9RrMp/BVFVlWunXMuv+37NVz3NbrLTtUFXpvWcFtLnCX3JwSRCRIDRK0cz6vtR+FQfLq+L\neEv8/7d35/FRVXcfxz8nmWyTBAIYZF8ERLEuaBSpC6jgVhXFKtaFPmhLrcpjXVp3+9RatbZaLdYV\naxVxQcUKloqCG5a6EFoRpEAVN3YQJPsyc54/TiKQzGSbyb0zk+/79cqLmbk3d37HmPzmnHvO7xAM\nBFl44cKYJhmVVJWwZvsaCoOF9Mxv+5p3ab33vnqP7z31PapD1dSGa0lPS2fP3D2ZP3E+AwoGtMt7\nVtZWctPrN/Fg8YNU1laSn5nPFYdfwfVHXa8PWSlGyVskQazZtobHP3ycDaUb+G7f73LWsLPavNSt\nOlTNFa9cwWP/foyM9AyqaqsY0WcE08+YTr/O/eIcuUQTz93uWiNsw1TUVBDMCCbUqE2qWr8e3nnH\nTXQ+7ji3k1h7U/IWSUETnp/AnJVzdls2lG7SKcwtZNVlq8jPyvcxOpHUEArBpZfCX/7idhKrf23q\nVJg0qX3fWxuTiKSYNdvWMHvl7EbrfUM2RElVCdOXTvcpMpHUctNNMH06VFW5Cpw7dri5UpddBm+8\n4Xd0jpK3SJJY+MVCAibyzMqymjL+tvpvHkckknoqK10PuzzC0vrycvjVr7yPKRIlb5Ek0dx9zvxM\nDZmLxOrLL5s+/qH/tZUAJW+RpHHi4BOjFn3Jy8hj0kHtfDOugepQNbcvvJ3ed/cm+9ZsvnP/d5i5\nfKanMYjEW5cuTW9S1TVBtkVX8hZJEnmZeUw9aWqjcqXBjCDHDDyGsYO8KxEYtmFOfPJEfv32r1lX\nso6qUBXLNy9n0kuT+PVbv/YsDpF422MPOPLIyEW7cnLcRLZEoOQtkkQuHH4hc8+dy5i9xtA9tzv7\nFe7HPSfcw4sTXox7cZCmvPLfV3h/7fsRN8v4zcLfsKU88uYdIsngscegsHD3pWG5uXDYYW7SWiJQ\nXTGRJDNqwChGDRjlawwzPppBWU1ZxGMZaRnMXT2XiQdO9Dgqkfjo2xdWrnRJ/K9/dYl70iQYNy5x\nqnEmSBgikkyqa6NvIxomTE2oiZuGKcpay5ufvcn9H9zPhtINHNnvSC477DJ6d+rtd2jSBp06weWX\nu69EpORdp6oK/vUvyMiAgw7SJiUiTTlj3zN45ZNXKK0ubXQsHA4zZq8xPkTlH2stl/ztEqYvnf7t\niMQH6z7gvg/u49XzX2Vk35E+RyipRve8gT/+0d3fOOEEOOYY6NkTXnzR76hEEteZ+55Jr/xeZKRl\n7PZ6MCPIhO9MSJgd07zy+prXd0vcAFWhKkqrSxn/7HjCNuxjdJKKOnzy/vOf4brroKTEVdEpKYHN\nm+H88+Gtt/yOTiQxZQWy+OdF/+SsYWeRlZ5FTiCHTlmduHrk1Tx62qN+h+e5P33wp6hzAMpqynjn\ni3c8jkhSXYceNg+H4YYbolfSufFGWLjQ+7hE4ml9yXr+8O4fmLNqDlnpWVw4/EJ+dPCPGi05a62u\nOV2ZceYMptVM45uqb9gjuAeBtI75J2VD6Yaox4wxbC7b7GE00hF0zN+0Ops3w/bt0Y9rTxRJdiu3\nrGTkoyMpqymjOuQmmV234DoeLn6Yd3/0LnmZeTG/R05GTpt3SUsVR/Q9guL1xd/+N95Vdaiag3oc\n5ENUkso69LB5MOh639HkdOy/R5ICLpp9Edsrt++WVMpryvlk2yf87h+/8zGy1DJlxJRG9/8BstKz\nGN1/NIO6DvIhKkllMSVvY0xXY8xrxpjVdf92iXBOX2PMG8aYj40xy40xCTPxPj8fjjoK0iL8V8jM\nhIlapipJbEv5FhavW4yl8ba/lbWVTPvXNB+iSk39Ovdj7nlzKQwWkp+ZT6fMTmQHshk9YDQzz1LJ\nWIm/WIfNrwUWWGvvMMZcW/f8mgbn1AJXWWuXGGPygWJjzGvW2o9jfO+4eOghVzWntBSq6zonOTlu\nxvkvf+lvbCKx2FG1g0BagKpQVcTjkZZ5Sdsd3f9o1l+1nrc+f4st5VsY3mM4Q7oN8TssSVGxJu9x\nwOi6x48Db9IgeVtr1wPr6x6XGGNWAL2BhEjegwbBsmVwzz0wa5Zb5/0//wMXX+wW6YtEsnzTcu5c\ndCfvffUePfJ68L8j/pcz9jmjyV2/vNavcz8y0zOjzoIe0XuExxGlvvS0dI4deKzfYUgHYKxtPKTW\n4m82Zru1tqDusQG21T+Pcv4A4G3gO9baHVHOmQxMBujXr98hn3/+eZvjE2kPL696mQnPT6Cqturb\nXb5yM3I5Y98zeOL0JxIqgd/9z7u5+Y2bGyXwYEaQBRMXcHifw32KTEQiMcYUW2uLmjuv2Xvexpj5\nxphlEb7G7XqedZ8Con4SMMbkAS8AP4uWuOuu87C1tshaW1RYWNhceCKeqqqt4rxZ51FeU77b9pxl\nNWW8uOJFFqxZ4GN0jV1x+BVcc+Q1BDOCdMrqRH5mPoXBQp458xklbpE61rrVRfPnw5Yk2VOn2WFz\na23UOofGmI3GmJ7W2vXGmJ7ApijnZeAS9wxr7aw2Ryvis6aSc1lNGQ8XP5xQpUGNMdx09E1cefiV\nFK8vJjuQzSE9DyE9TfV/RQAWLYJzzoFt21xZ7KoqOPdceOABN3E5UcV6z3s28EPgjrp/X2p4Qt1w\n+qPACmvt3TG+n4ivtldup6lbTYm6FWZuZi5H9z/a7zBEEsqaNa4sdmmDuZtPP+3+fTSBiwXGus77\nDmCsMWY1MKbuOcaYXsaYuXXnHAFcABxrjPl33dfJMb6viC9G9B5BTTjyjlk5gZyE6nWLSNPuvtv1\ntBuqqIAZM1whr0QVU8/bWrsVOC7C6+uAk+sevwMkzgwekRgM6jqI4/c6nlc/fZXK2srdjmUFsph8\nyGSfIhOR1nrjDaiJsnttdjb8+98wdqy3MbVUh66wJtIWT3//aU4behpZ6Vl0zupMbkYuQ7sN5e3/\neZs9gnv4HZ6ItFDXrtGPhUJQEHXtlP86dG1zkbYIZgR59vvPsqF0Ax9v/pjuud3Zr3C/hFoiJiLN\n++lPYckSKItQCqGgAIqaXbDlHyVvkTbqkdeDHnk9/A6jXc3/dD5T35vKFzu+oKhXEVcefiX7Fu7r\nd1gicXH22fDkk2775/oEnpHhZpk/8wwk8ufxmIq0tLeioiK7WFt7ifjiqlev4qHFD31b4CXdpJMV\nyOKp8U8xbp9xzXy3SHIIhWDmTLj/fvj6azjmGLjySthrL3/iaWmRFiVvEWnkg7UfMPrx0ZTXNN7s\nPi8zj01Xb+rw24CKtIe4VVjr6EIhmDMHfvMb+POfYUfU2nAiqWPakmmNZtPXMxj+tvpvHkckIrvS\nPe8mfPopjB4N27e7+yE5OTBlilvAf9ppfkcn0n42lm0kbCNvdh+yIb6u+NrjiERkV+p5R2Gtq7yz\ndi2UlEA47BJ4ebkrpaf9UiSVjeo/imBGMOrxw3of5mE0ItKQkncU77wDGza4pN1QKOQmN4ikqknD\nJ5GVnoVpUF8pMz2T4T2Gc1CPg3yKTERAyTuq1atd7zuS6mpYutTbeES8VJBdwMJJCxnUZRC5Gbl0\nzupMdiCbUf1H8fK5L/sdnkiHp3veUfTvD2lRPtoEAjB0qLfxiHhtv+77sWrKKpasX8KG0g3sW7gv\ne3Xxaf2MiOxGyTuKY46B/Hx3v7uhjAxXmUck1RljOKTXIX6HISINaNg8irQ0eOUVV/s2L8+9lpXl\nitX/6U/qeYuIiH/U827C/vvDF1/As8/CBx9A374wcSL06eN3ZCIi0pEpeTcjNxcuvNB9iYiIJAIN\nm4uISMqyFqZPdyOpXbvCwQfDc89FX02ULNTzFhGRlPWTn8BTT+3cNWzbNpg0CYqL4Y47/I0tFup5\ni4hISlq61G352XC/7rIyuPde+OwzX8KKCyVvERFJSc8844pqRWItzJrlbTzxpOQtIiIpqaLClbOO\npLbWHU9WSt4iIpKSjj9+Z52OhrKz4dhjvY0nnpS8RUQkJZ1wAgwaBJmZu7+elQXDh8Phh/sTVzwo\neYuISEpKS4M334TTT3cJOy/P9bjPOcdV0DSm2UskLC0VExGRlFVQ4KpkfvON2+a5Vy+3b0WyU/KO\ng+3b3azGTz5xNc8nTEiN/zlERFJF587uK1Uoecdo/nw3JGMtlJe7cqpXXQV//zt897t+RyeSHELh\nEGkmDZPM45giHtI97xhs2+YSd1mZS9zgHu/YASefvPM1EYls3n/ncdCDB5Hx6wyyf5PNuS+cy9od\na/0OSyThKXnH4MknIRyOfCwUghde8DYekWTy3PLnGD9zPB9u/BCLpTpUzczlMzn44YPZVLbJ7/BE\nEpqSdwxWrYq+yL+0FNas8TYekWQRCoe47O+XUV6z+/BUyIbYXrmduxbd5VNkIslByTsG++wDwWDk\nY3l5bn2hiDS2YsuKRom7XnWommeXP+txRCLJRck7Bued59YRRhIIwPjx3sYjkixsM/sxWpJ8v0aR\ndqbkHYOCApgzx/Wyc3Pda3l5bjnCvHmQk+NvfCKJaljhMLID2RGPZaZlcvawsz2OyPX4Z6+czUOL\nH2LRl4ua/YAh4ictFYvR6NGwbh3MnOnucQ8ZAmedFX04XUQgPS2de0+8lx/N/hEVtTsnjqSZNDpl\ndeKq717laTwLP1/IuGfGURuuJWRDGAwDCgbw6gWv0iu/l6exiLSESeRPl0VFRXbx4sV+hyEi7WTO\nyjlcM/8aVm5dSZpJ47S9T+PuE+6mf0F/z2LYWLqRwVMHU1pdutvrgbQA+3Tbh6U/Xar15wkqHHbl\nT5ctc5XTTjnFlT9NZsaYYmttUXPnqectIr45deipnDr0VKpqqwikBUhPS/c8hkeWPEJtqLbR67Xh\nWtZsX8O7X73LyL4jPY9Lmvb55zBmjCt5WlPjNh9JS4O//tWNiKY63fMWEd9lBbJ8SdwA7619j8pQ\nZcRjFsuyTcs8jkiaYy2MHetuVZaWQlUVlJS4+uWnnOISeqpT8haRDm1A5wGkm8gfHAImQI+8Hh5H\nJM15+21Yv94Vw2ooFIJp07yPyWtK3iLSoV1cdDGZ6ZkRjwXSA5w4+ESPI5LmrFgROXEDVFZCcbG3\n8fhByVtEOrT9uu/HrcfeSk4gh4Bx04CyA9nkZebx0jkvkZGe4XOE0lDv3q6WRiSBAAwc6G08ftBs\ncxERYPmm5TxU/BCff/M5h/U6jB8f8mO653b3OyyJoKYGevS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "# Let's generate some data to use\n", "pointsA = np.random.normal(size=(60,2), scale=.2)\n", "theta = np.expand_dims(np.linspace(0,2, 60) * np.pi, axis=1) \n", "pointsB = np.concatenate([np.cos(theta), np.sin(theta)], axis=1) * .7\n", "\n", "data = np.concatenate([pointsA, pointsB], axis=0)\n", "labels = np.zeros(120)\n", "labels[:60] = 0\n", "labels[60:] = 1\n", "\n", "\n", "colors=[\"green\", \"blue\"]\n", "\n", "plt.figure(figsize=(8,8))\n", "plt.scatter(data[:, 0], data[:, 1], c=labels, cmap=matplotlib.colors.ListedColormap(colors), s=50)\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SVC(C=1, cache_size=200, class_weight=None, coef0=0.0,\n", " decision_function_shape=None, degree=3, gamma=1, kernel='rbf',\n", " max_iter=-1, probability=False, random_state=None, shrinking=True,\n", " tol=0.001, verbose=False)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's train two SVMS, one using a linear kernel and one using RBF\n", "clfLIN = svm.SVC(kernel='linear', C=1,gamma=1)\n", "clfRBF = svm.SVC(kernel='rbf', C=1,gamma=1)\n", "\n", "clfLIN.fit(data, labels)\n", "clfRBF.fit(data, labels)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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OPjeffjq0agVPPBH/miLJQMsS1SFz/zOBaQ/8C3B0PvI0ug05J+iQpJry8vwQ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\nztqXW+NwmSj5v8/pvXoAt1JvpefmzpU7M7vLbLe5XMi5bE4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xzvp3KPxlYcK+CKP9/Pbs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\nM3yw5QOmdJyS5TWal2vO1sFbs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2DsWNGqrIARuVllr7wCa9ZA585Kbm7XDhYsgM8/Vzuy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Now lets plot the decision boundaries generated by both models and see which worked better\n", "\n", "# Ignore, drawing decision boundaries is a pain :(\n", "h = .001\n", "x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1\n", "y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1\n", "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n", " np.arange(y_min, y_max, h))\n", "\n", "plt.figure(figsize=(16,8))\n", "plt.suptitle(\"SVM Decision Boundaries\")\n", "\n", "plt.subplot(121)\n", "Z = clfLIN.predict(np.c_[xx.ravel(), yy.ravel()])\n", "Z = Z.reshape(xx.shape)\n", "plt.contour(xx, yy, Z, cmap=plt.cm.Paired)\n", "plt.scatter(data[:, 0], data[:, 1], c=labels, cmap=matplotlib.colors.ListedColormap(colors), s=50)\n", "\n", "plt.title(\"Linear Kernel\")\n", "plt.axis([-1,1,-1,1])\n", "\n", "plt.subplot(122)\n", "Z = clfRBF.predict(np.c_[xx.ravel(), yy.ravel()])\n", "Z = Z.reshape(xx.shape)\n", "plt.contour(xx, yy, Z, cmap=plt.cm.Paired)\n", "plt.scatter(data[:, 0], data[:, 1], c=labels, cmap=matplotlib.colors.ListedColormap(colors), s=50)\n", "\n", "plt.title(\"RBF Kernel\")\n", "plt.axis([-1,1,-1,1])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the Radial Basis Function kernel was far superior at separating the classes for the non-linear decision boundary. This is an extreme example, of course, where the classes are quite literally oriented in a circle, but RBF would still be the superior choice with any curved decision boundary. However, there is an exception to that statement." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynomial Kernels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The exception mentioned above is simply when the decision boundary could best be modeled by a polynomial curve - in cases like this, the best option is to use the \"polynomial\" kernel in scikit learn. More on this can be found here: http://scikit-learn.org/stable/modules/svm.html#kernel-functions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting Parameters - GridSearchCV\n", "\n", "We previously talked about two parameters: gamma and C. The question then becomes how to determine these values when training a model. This is especially true because different values can give vastly different models, as seen previously. The manual way to perform parameter fitting would be to iterate over all possible combinations of C and gamma. Luckily, there is a sklearn function for this: GridSearchCV.\n", "\n", "Here we will revisit the Iris Species Classification from above:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model score for hard coded parameters: 0.577777777778\n", "Model score for grid search parameters: 0.777777777778\n" ] } ], "source": [ "# import necessary packages\n", "from sklearn.model_selection import train_test_split, GridSearchCV\n", "from sklearn import svm, datasets\n", "\n", "# here we use the iris dataset\n", "iris = datasets.load_iris()\n", "X = iris.data[:, :2] \n", "Y = iris.target\n", "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=0.3)\n", "\n", "# here is a hardcoded C and gamma\n", "model = svm.SVC(kernel='linear', C=0.01,gamma=1)\n", "model.fit(X_train, Y_train)\n", "model.predict(X_test)\n", "print(\"Model score for hard coded parameters: \", model.score(X_test,Y_test))\n", "\n", "# give the grid search options to iterate over\n", "Cs = [0.001, 0.01, 0.1, 1, 10, 100]\n", "gammas = [0.001, 0.01, 0.1, 1]\n", "param_grid = {'C': Cs, 'gamma' : gammas}\n", "# create the GridSearch model\n", "grid_search = GridSearchCV(svm.SVC(kernel='linear'), param_grid)\n", "# fit the model\n", "grid_search.fit(X_train, Y_train)\n", "\n", "# we use the grid search parameters\n", "model = svm.SVC(kernel='linear', C=grid_search.best_params_['C'],gamma=grid_search.best_params_['gamma'])\n", "model.fit(X_train, Y_train)\n", "model.predict(X_test)\n", "print(\"Model score for grid search parameters: \", model.score(X_test,Y_test))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model performed better with the grid search parameters than with arbitrarily chosen parameters. \n", "\n", "Additionally, the parameter options to iterate over must be given to the grid search. This means that if you give the model more values, you will get more accurate parameters. However, grid search will take longer to run then." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }