{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Chapter 10\n", "### This notebook and the figures below are made by Yeseul Lee, under the guidance of Steven Skiena." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy import stats\n", "from scipy.spatial import Voronoi, voronoi_plot_2d, ConvexHull\n", "from astroML.clustering import HierarchicalClustering, get_graph_segments\n", "from sklearn.cluster import KMeans, SpectralClustering\n", "from sklearn.linear_model import LogisticRegression\n", "from sklearn import neighbors, datasets\n", "from matplotlib.colors import ListedColormap\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import math, random\n", "import pandas as pd\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.2" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12,3))\n", "\n", "ax = plt.subplot(141)\n", "x = np.linspace(-1,1,100)\n", "y1 = 1 - np.abs(x)\n", "y2 = -1 * y1\n", "plt.plot(x, y1, 'r-', x, y2, 'r-', linewidth=2)\n", "plt.plot([0,0], [-1.5,1.5], 'k-', [-1.5,1.5], [0,0], 'k-')\n", "plt.xlim(-1.5,1.5)\n", "plt.ylim(-1.5,1.5) \n", "plt.axis(\"off\")\n", "plt.title(r\"$L_1$\", fontsize=18)\n", "\n", "plt.subplot(142)\n", "y1 = np.sqrt(1 - x*x)\n", "y2 = -1 * y1\n", "plt.plot(x, y1, 'r-', x, y2, 'r-', linewidth=2)\n", "plt.plot([0,0], [-1.5,1.5], 'k-', [-1.5,1.5], [0,0], 'k-')\n", "plt.xlim(-1.5,1.5)\n", "plt.ylim(-1.5,1.5)\n", "plt.axis(\"off\")\n", "plt.title(r\"$L_2$\", fontsize=18)\n", "\n", "plt.subplot(143)\n", "y1 = (1 - np.abs(x**5))**(0.2)\n", "y2 = -1*y1\n", "plt.plot(x, y1, 'r-', x, y2, 'r-', linewidth=2)\n", "plt.plot([0,0], [-1.5,1.5], 'k-', [-1.5,1.5], [0,0], 'k-')\n", "plt.xlim(-1.5,1.5)\n", "plt.ylim(-1.5,1.5)\n", "plt.axis(\"off\")\n", "plt.title(r\"$L_5$\", fontsize=18)\n", "\n", "plt.subplot(144)\n", "y1 = (1 - np.abs(x**100))**(0.01)\n", "y2 = -1*y1\n", "plt.plot(x, y1, 'r-', x, y2, 'r-', linewidth=2)\n", "plt.plot([0,0], [-1.5,1.5], 'k-', [-1.5,1.5], [0,0], 'k-')\n", "plt.xlim(-1.5,1.5)\n", "plt.ylim(-1.5,1.5)\n", "plt.axis(\"off\")\n", "plt.title(r\"$L_\\infty$\", fontsize=18)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For Figure 10.3, preparing data\n", "#### The source of the data set https://www.statcrunch.com/app/index.php?dataid=1406047\n", "#### Reference: http://scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html#example-neighbors-plot-classification-py" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "path = \"/home/yeseul/practice-notebook/weight.xls\"\n", "csv_data = pd.ExcelFile(path).parse('Sheet1')\n", "female = csv_data[(csv_data['Gender'] == 0) & (csv_data['Age'] >=360) & (csv_data['Age'] <=480)] #Age is by the number of months. 20~40\n", "male = csv_data[(csv_data['Gender'] == 1) & (csv_data['Age'] >=360) & (csv_data['Age'] <= 480)]\n", "\n", "#Data\n", "x = np.append(female['Weight'], male['Weight'])\n", "y = np.append(female['Height'], male['Height'])\n", "X = np.vstack((x,y)).T\n", "h = .2 # step size in the mesh\n", "\n", "#Make labels\n", "a = np.empty(len(female))\n", "a.fill(0)\n", "b = np.empty(len(male))\n", "b.fill(1)\n", "Y = np.append(a, b)\n", "\n", "#Fit the data\n", "k = 1\n", "c=neighbors.KNeighborsClassifier(k, weights='uniform')\n", "c.fit(X, Y)\n", "\n", "# Plot the decision boundary. For that, we will assign a color to each\n", "# point in the mesh [x_min, m_max]x[y_min, y_max].\n", "x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n", "y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n", "xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n", " np.arange(y_min, y_max, h))\n", "Z = c.predict(np.c_[xx.ravel(), yy.ravel()])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.3 Color space by the color of its nearest neighbor" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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cOBwTATAYJlC9+mmGDfuR06d3Mn58DyyWI2jZdS4AxVHogJUVaEkkFhEQ8AW5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AJ8iR/JQnS9Gk5nHapV28P3zz3B2rg46rlc1HY68depw8gbbuC1u+9mScWKzHI4+B41S0zQdZKq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\nGC5CH5uNJcAbIiQ4HLTJheJO+9hYljscvCXCEqCP0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create color maps\n", "cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])\n", "cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])\n", "\n", "# Put the result into a color plot\n", "Z = Z.reshape(xx.shape)\n", "plt.figure(figsize=(5,5))\n", "plt.pcolormesh(xx, yy, Z, cmap=cmap_light)\n", "\n", "# Plot also the training points\n", "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=cmap_bold)\n", "plt.xlim(xx.min(), xx.max())\n", "plt.ylim(yy.min(), yy.max())\n", "\n", "#Labels\n", "plt.xlabel('Weight(kg)')\n", "plt.ylabel('Height(cm)')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.4 Color space by the color of its nearest neighbor\n", "From figure 10.3, figure 10.4 is just a simple modification away, which is to change the value of k.\n", "The left figure has k = 3. The right figure has k = 10." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.5 Left - Voronoi diagram\n", "Reference : http://scipy.github.io/devdocs/generated/scipy.spatial.Voronoi.html\n", "http://scipy.github.io/devdocs/generated/scipy.spatial.voronoi_plot_2d.html" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ccOzYMURHR+PLly8wNTXFyJEjK2x03qpVK4k3YC4L+l/5pq+vL86ePYshQ4aw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['figure.figsize'] = 6,6\n", "\n", "#generate 50 uniform points\n", "x = np.random.rand(50,2) #2d array with 50 points\n", "#find the voronoi\n", "vor = Voronoi(x)\n", "voronoi_plot_2d(vor, show_vertices=False)\n", "plt.xlim(0,1)\n", "plt.ylim(0,1)\n", "\n", "#color the points black\n", "plt.plot(x[:,0], x[:, 1], 'ko')\n", "\n", "#Hide the x and y axis.\n", "plt.gca().axes.get_xaxis().set_ticks([])\n", "plt.gca().axes.get_yaxis().set_ticks([])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.11 - K-means\n", "#### The source of the data set https://www.statcrunch.com/app/index.php?dataid=1406047\n", "You can look at figure 9.17, which is another version of this figure but using logistic regression." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 69.02926136 161.4375 ]\n", " [ 97.65482456 172.71929825]]\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Ztgzee09737KQaN/XFpcOlVzbWU4Ud29Tl+q7+xw69S6OSW9eO1hE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\nFzBd0uAczCv0t7v9DyW7Zsr2ns9hvcuBTwKoSbLrCeYI/ZL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,4))\n", "female = csv_data[(csv_data['Gender'] == 0) & (csv_data['Age'] >=800) & (csv_data['Age'] <=900)] #Age is by the number of months. 20~40\n", "male = csv_data[(csv_data['Gender'] == 1) & (csv_data['Age'] >=800) & (csv_data['Age'] <= 900)]\n", "\n", "plt.scatter(female['Weight'], female['Height'], c='red', s=10, lw=0)\n", "plt.scatter(male['Weight'], male['Height'], c='blue', s=10, lw=0)\n", "plt.xlabel(\"Weight (kg)\")\n", "plt.ylabel(\"Height (cm)\")\n", "\n", "y = np.append(female[\"Height\"], male[\"Height\"])\n", "x = np.append(female[\"Weight\"], male[\"Weight\"])\n", "\n", "z = [[i,j] for i,j in zip(x,y)]\n", "algo = KMeans(n_clusters=2)\n", "algo.fit(z)\n", "label = algo.labels_\n", "centers = algo.cluster_centers_\n", "print centers\n", "plt.plot(centers[:,0], centers[:,1], 'y*', markersize=10)\n", "\n", "#Find the perpendicular bisector\n", "midpoint = [(centers[0][0]+centers[1][0])/2.0 , (centers[0][1] + centers[1][1])/2.0]\n", "lineslope = (centers[0][1]-centers[1][1])/(centers[0][0]-centers[1][0])\n", "perslope = -1/lineslope\n", "perx = [60,100]\n", "pery = perslope*(perx - midpoint[0]) + midpoint[1]\n", "plt.plot(perx, pery, 'k-')\n", "\n", "#Draw the convex hull instead.\n", "division1 = [i for i,c in zip(z, label) if c == 1]\n", "division1= np.array(division1)\n", "division2 = [i for i,c in zip(z, label) if c == 0]\n", "division2 = np.array(division2)\n", "hull1 = ConvexHull(division1)\n", "hull2 = ConvexHull(division2)\n", "\n", "# to make the line come back to the first point, I appended the first vertice to it at last.\n", "plt.plot(np.append(division1[hull1.vertices, 0], division1[hull1.vertices[0],0]), \\\n", " np.append(division1[hull1.vertices,1], division1[hull1.vertices[0],1]),'b-', linewidth=1.5)\n", "plt.plot(np.append(division2[hull2.vertices, 0], division2[hull2.vertices[0],0]), \\\n", " np.append(division2[hull2.vertices,1], division2[hull2.vertices[0],1]),'r-', linewidth=1.5)\n", "plt.xlim(20,160)\n", "plt.ylim(140,200)\n", "plt.title(\"K-Means Clustering\", fontsize=16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For Figure 10.12" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#Data set\n", "size = 20\n", "x1 = np.random.sample([size]) +2\n", "noise = np.random.normal(2,0.3, size)\n", "y1 = [10]*size + noise\n", "\n", "x2 = np.random.sample([size]) +5\n", "noise = np.random.normal(1,0.3, size)\n", "y2 = [8]*size + noise\n", "\n", "x3 = np.random.sample([size]) +5\n", "noise = np.random.normal(1,0.3, size)\n", "y3 = [14]*size + noise\n", "\n", "x4 = np.random.sample([size]) +7\n", "noise = np.random.normal(1,0.3, size)\n", "y4 = [11]*size + noise\n", "\n", "size=100\n", "x5 = np.random.sample([size])*4 + 9\n", "noise = np.random.normal(1,0.1, size)\n", "y5 = [5.9]*size + noise\n", "\n", "x6 = np.random.sample([size])*4 + 9\n", "noise = np.random.normal(1,0.1, size)\n", "y6 = [4]*size + noise\n", "\n", "x7 = np.random.sample([size])*4 + 9\n", "noise = np.random.normal(1,0.1, size)\n", "y7 = [2.1]*size + noise\n", "\n", "x8 = np.linspace(-2,2,30)\n", "f1 = [np.sqrt(4 - i*i) for i in x8]\n", "f1 = np.array(f1)\n", "f2 = -1 * f1\n", "\n", "x8 = np.append(x8, x8) +14\n", "y8 = np.append(f1, f2) + 14\n", "\n", "x = np.append(x8,y8)\n", "y8 = np.append(y8,x8)\n", "x8 = x\n", "\n", "x9 = np.random.sample([size]) +13.5\n", "noise = np.random.normal(1,0.3, size)\n", "y9 = [13]*size + noise\n", "\n", "xlst = [x1, x2, x3, x4, x5, x6, x7, x8, x9]\n", "ylst = [y1, y2, y3, y4, y5, y6, y7, y8, y9]\n", "x = []\n", "y = []\n", "for i in xlst:\n", " x = np.append(x, i)\n", "for j in ylst:\n", " y = np.append(y, j)\n", " \n", "X = [[i,j] for i,j in zip(x, y)]\n", "X = np.array(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.12" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(1, 18)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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qnF7X2P0bOk3aLlIqZWbY5aNGzXR02q4nAf24JudSSuUAr2utJ4X52yXAZVrr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\nN27mBz94gPb2IcDnwEkMGvQ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1SYwe/RWrV9/JuHFjWbBgKVu2NAIuzj47E6U6WbPGv8cK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\n5wcXQkIuDzfJe855z83vwnmmRMQ22fKrbTB8Cqw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "plt.plot(x, y, 'bo')\n", "plt.xlim(1,18)\n", "plt.ylim(1,18)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For Figure 10.14, I made these functions." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def initialize_centroids(points, k):\n", " centroids = random.sample(points, k)\n", " centroids = np.array(centroids)\n", " return centroids\n", "\n", "# Define the function to find the closest centroid for each point.\n", "def closest_centroid(points, centroids):\n", " closest = []\n", " for i in range(0,len(points)):\n", " k = []\n", " for j in range(0, len(centroids)):\n", " k.append(np.sqrt((points[i,0]-centroids[j,0])**2 + (points[i,1]-centroids[j,1])**2))\n", " closest.append(np.argmin(k))\n", " return closest\n", "\n", "# Define a function for finding the average points of the points assigned to each centroid.\n", "def average_points(points, centroids, cluster):\n", " result=[]\n", " for i in range(0, len(centroids)):\n", " pointsByCluster = []\n", " for j in range(0,len(cluster)):\n", " if cluster[j] == i:\n", " pointsByCluster.append(points[j])\n", " pointsByCluster=np.array(pointsByCluster)\n", " result.append([sum(pointsByCluster[:,0])/len(pointsByCluster), \\\n", " sum(pointsByCluster[:,1])/len(pointsByCluster)])\n", " return result\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.14 - Initialization for k-means clustering animation\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [], "source": [ "# Initialize k number of centroids\n", "k = 5\n", "random.seed(7)\n", "centroids = initialize_centroids(X,k)\n", "#Nearest points to the centroid.\n", "nearest = closest_centroid(X, centroids)\n", "\n", "centroids = np.array(average_points(X, centroids, nearest ))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.14 - The iterations of K-means" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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77limHZpGw+4GzA1mwiaEoY9Sbmjg61oLbYcsA4YEqN5MQ9Ip55TnXZrXsZiw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6bDJi7lUlJxbITySaWrS+l0mYMD6iqtK/SSP/yr/3O7vf++0gpTXq7MTnGy+4ofqNpv3YrYvK9t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\nmQjjAACQiTAOAACZ/ANol3ffhvHGZgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['figure.figsize'] = 13,7\n", "fig, ax = plt.subplots(2, 4)\n", "plt.subplots_adjust(wspace=0, hspace=0) #Adjust the whitespace between subplots\n", "\n", "k=3\n", "random.seed(4)\n", "colors=[\"red\", \"m\", \"c\"]\n", "textx = 7\n", "texty = 17\n", "\n", "#Just the dots\n", "ax[0,0].scatter(X[:, 0], X[:, 1], color='orange', edgecolor=\"\")\n", "#Add the centroids\n", "ax[0,0].scatter(X[:, 0], X[:, 1], color='orange', edgecolor=\"\")\n", "centroids = initialize_centroids(X,k)\n", "ax[0,0].scatter(centroids[:, 0], centroids[:, 1], color='black', marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[0,0].axes.get_xaxis().set_visible(False)\n", "ax[0,0].axes.get_yaxis().set_visible(False)\n", "ax[0,0].text(textx,texty, \"Iteration 0\", fontsize=14)\n", "\n", "#Classify by the nearest centroid\n", "#Nearest points to the centroid.\n", "nearest = closest_centroid(X, centroids)\n", "ax[0,1].scatter(X[:,0], X[:,1], c=[colors[i] for i in nearest], edgecolor=\"\")\n", "ax[0,1].scatter(centroids[:,0], centroids[:,1], color='black',marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[0,1].axes.get_xaxis().set_visible(False)\n", "ax[0,1].axes.get_yaxis().set_visible(False)\n", "ax[0,1].text(textx,texty, \"Iteration 1\", fontsize=14)\n", "\n", "\n", "#Now move the centroids to the average points classified to.\n", "centroids = np.array(average_points(X, centroids, nearest ))\n", "#Classify by the nearest centroid again.\n", "nearest = closest_centroid(X, centroids)\n", "ax[0,2].scatter(X[:,0], X[:,1], c=[colors[i] for i in nearest], edgecolor=\"\")\n", "ax[0,2].scatter(centroids[:,0], centroids[:,1], color='black', marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[0,2].axes.get_xaxis().set_visible(False)\n", "ax[0,2].axes.get_yaxis().set_visible(False)\n", "ax[0,2].text(textx,texty, \"Iteration 2\", fontsize=14)\n", "\n", "\n", "#Now move the centroids to the average points classified to.\n", "centroids = np.array(average_points(X, centroids, nearest ))\n", "#Classify by the nearest centroid again.\n", "nearest = closest_centroid(X, centroids)\n", "ax[0,3].scatter(X[:,0], X[:,1], c=[colors[i] for i in nearest], edgecolor=\"\")\n", "ax[0,3].scatter(centroids[:,0], centroids[:,1], color='black', marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[0,3].axes.get_xaxis().set_visible(False)\n", "ax[0,3].axes.get_yaxis().set_visible(False)\n", "ax[0,3].text(textx,texty, \"Iteration 3\", fontsize=14)\n", "\n", "#Now move the centroids to the average points classified to.\n", "centroids = np.array(average_points(X, centroids, nearest ))\n", "#Classify by the nearest centroid again.\n", "nearest = closest_centroid(X, centroids)\n", "ax[1,0].scatter(X[:,0], X[:,1], c=[colors[i] for i in nearest], edgecolor=\"\")\n", "ax[1,0].scatter(centroids[:,0], centroids[:,1], color='black', marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[1,0].axes.get_xaxis().set_visible(False)\n", "ax[1,0].axes.get_yaxis().set_visible(False)\n", "ax[1,0].text(textx,texty, \"Iteration 4\", fontsize=14)\n", "\n", "#Now move the centroids to the average points classified to.\n", "centroids = np.array(average_points(X, centroids, nearest ))\n", "#Classify by the nearest centroid again.\n", "nearest = closest_centroid(X, centroids)\n", "ax[1,1].scatter(X[:,0], X[:,1], c=[colors[i] for i in nearest], edgecolor=\"\")\n", "ax[1,1].scatter(centroids[:,0], centroids[:,1], color='black', marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[1,1].axes.get_xaxis().set_visible(False)\n", "ax[1,1].axes.get_yaxis().set_visible(False)\n", "ax[1,1].text(textx,texty, \"Iteration 5\", fontsize=14)\n", "\n", "#Now move the centroids to the average points classified to.\n", "centroids = np.array(average_points(X, centroids, nearest ))\n", "#Classify by the nearest centroid again.\n", "nearest = closest_centroid(X, centroids)\n", "ax[1,2].scatter(X[:,0], X[:,1], c=[colors[i] for i in nearest], edgecolor=\"\")\n", "ax[1,2].scatter(centroids[:,0], centroids[:,1], color='black', marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[1,2].axes.get_xaxis().set_visible(False)\n", "ax[1,2].axes.get_yaxis().set_visible(False)\n", "ax[1,2].text(textx,texty, \"Iteration 6\", fontsize=14)\n", "\n", "#Now move the centroids to the average points classified to.\n", "centroids = np.array(average_points(X, centroids, nearest ))\n", "#Classify by the nearest centroid again.\n", "nearest = closest_centroid(X, centroids)\n", "ax[1,3].scatter(X[:,0], X[:,1], c=[colors[i] for i in nearest], edgecolor=\"\")\n", "ax[1,3].scatter(centroids[:,0], centroids[:,1], color='black', marker=\"*\", s=150, edgecolors=\"\")\n", "#Hide the x and y axis.\n", "ax[1,3].axes.get_xaxis().set_visible(False)\n", "ax[1,3].axes.get_yaxis().set_visible(False)\n", "ax[1,3].text(textx,texty, \"Iteration 7\", fontsize=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.15" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "error is 17798.4144566 for k = 1\n", "error is 6655.84355085 for k = 2\n", "error is 2308.04327114 for k = 3\n", "error is 1765.94810745 for k = 4\n", "error is 1452.48465421 for k = 5\n", "error is 1217.58548075 for k = 6\n", "error is 1028.63139929 for k = 7\n", "error is 910.669085502 for k = 8\n", "error is 761.659065899 for k = 9\n" ] }, { "data": { "image/png": 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Joa3cj/4ezOMc47wFFxbSomUOs/XuiyHWLMmAMZIQVNLs2fvZvfvf+afnzt1g\n5kzDU/us7bff9A/gev/9HSxbVrnFjIx59tk17NunO3dXoYDdu0dZ5J6irKKcnJsj6P/3waotKWHj\nhAloNYZrUVjTgDlzcPXx0dlemJXFV3fdZZF7pl+8yI999I99affSS3gHS7Esa9j8xhtl1qeI37Tp\n5jLLVYQPPrSno959P/Ct0WmIlTWLmRSh+8pKhYqBDLLIPW9n84Tg1KlUzp61r/XHr1zJ4u23/9DZ\nfvly5Ra5sJTu3SNp0kR/nYChQ5ezapV51zWfMGEDc+boX3J2zJjWeHnZV+2B/Bs3SNy/nxI7Ww53\n9dNPo76tsl9ucrLONlsbOHeu3u3Jx47xTUf9D+TKunH+PF9ERelNilw8POj9ySdmvZ+laTUakg4d\nIjvReOGcquTStm2cWLpUZ3vW5cs2iKZ8femHCy4627Vo+ZwZpFWyOmF55vIVyVzXu+8+7jfrvQyx\nWUKQl1dMnz4/0rjxLKKjv+C++xZTVGR8KVRrSkzM5s8/L5KRUcD+/Yls2RLP9u2XmDv3gM7qfQBD\nhugWXbG1gwefQaXS39V0//1LmTJlq1nuc++9C/n00z1690VE+DFrVn+z3MdaDnz9NdNDQ5nbpg0z\nwsO5urdq9f6UFBeTsGMH6RcukHb2LAk7d3Ju/XquHzvG33oeuNH9++NiQilfa2o6dCiNBw/Wu+/K\n7t18FhmJxgy9Guc2bmRmVFS53dKj9u1DacKqi1VFxqVLfNm0KV/HxDAjPJzNEyfaOiQdqadPc3n3\nbvLT07myZw/nN24k6dAhdn38sU5SpnR2JnqA4Xn51qZEyWjG6N2nQcP/MZ1zlVz2+FYllPApH3MZ\n/QlRE5rRTE/BJEux2qDC1atPM23aTgoLSxg0qCEbNpxn+/ay60HPmzeAp56qGmVDP/lkFxMnbtZb\ndjcgwJ20tLIjlPv2bcC6dSOsFV6F7N59mY4d55e7PyzMhyNHnsXfv+IlMQ8dSqJLl2/1JkgAKpUT\nSUnjK3VtY8w1cCs7MZHNEyeSuH8/ddq3x6t2bXZ+9FGZB1do27Y8/ddfd3wvc0g9fZoFd9+t91uV\nk6urTo+G0tWVCdeu4e5fNReUmhEWVv4Sx0olA+bOJaacMQeGlBQV8cPdd5OwbVu5x/T6+GM6TZhQ\n4WsbY85BhXv+7/848t13uPn7E9W/P/tnzyb9fNl32c8cOkTtlpado24KrVbLqsce4+iCBXr3u/n7\nU5CeXmb6yH8hAAAgAElEQVRbl8mT6fHuu9YIr8J2sJ2NrC93f10ieIwncMb4qp23O8B+fmFluft9\n8WU8r1X4usbYfJbBwYNJtGkzF43G8LVeeaU9n35qfH67pV2/nkNY2Ay9A+P0UamcOHBgNE2bWras\n5J1YuPAoI0eW3/gAWrQIZOnSwTRsaHw1rV9/PcOYMb8afE3i5KTgxInniY62zOpx5nrozmvXzmgP\ngIunJ2/mVI1Bo8uGDOHE8uUmH9/x1Ve5e9o0C0Z0Z4rz8pgeFkbBjfLfzbr5+9Nl8mQ6vvyy0esV\nZmWx7KGHOL9xIxjoYYgZPZoBc+ZUKmZjzNU2D82fz+qnnjJ63AMLF5Zb9Mmazm/axI+9deuglMc7\nNJQXTp/G1dPTglHdmdWsYj/7DB7TgCiGMkxvYaPb7WQHf/IHBZT/Cs8Nd8bzKirMXyTLUEJQ8bSm\ngnJyihg1ao3RZAD0L91rCxcuZJicDAC8+GK7Kp0MAIwY0QI3N2cGD15W7jFHjybTqNGX1KrlQefO\n4XTtWhdfX1fOnr1BixaBnDuXwbZtl9i9+zI5OYbXqHd2VnDq1PPUr1+1l5LdN3u2Sa8DvIKqTrnl\ntDNnTD7WOzSUXh9+aMFo7pyLhwcvJyTwWd265JdTwrggPZ1Nr7zCltdfJ7hVK+p260ZQTAxpp0/j\nWasWSmdnErZvJ2H7djIvXTJ6z7Yvvki/CpZDtrbMy5fZ8sYbJh1bs3FjC0djmoq0TYB+X3xRpZMB\nuFma2Aln/mJ3ucec4yzv81988aMuEdQlHA1acsklgACukcRFLpBEkk6Ng9u54854XsMV64+5snhC\nEBf3HQcPJpl07MaN53nppfYWjsi4mJhgAgM9SE7OM+l4S3SHW8KDDzZh/foR3HffYgoLyx+vkZKS\nx8qVp1i58lSl7lO7tic7dz5JvXo1KhuqVZxYuZLfnnvOpGPT4+PJTEjAN7ziC5mYW9S993L96FGT\njnVydUWhtPnYYaNcPT15+fJlvuvenUQDCZqmuJire/dWfkyHQkGf6dNNKm1sSyVFRcxu3pzCzEyT\njj+5YgXBrVpZOCrjGvTpg0KpNHlGS1VPBv7Rn3upgT/r0K3tcqtMMjjKYb2FhUwRSihPMkrvgEZr\nsOiTIi0tj/37TUsGAJKSqkaXrKurE3PnDjTpWKUSHn64mYUjMp8+fRpw48ZrREVZ5sO6f/8okpIm\nVPlkAGDj+PEVOt7QAjzW1O3tt/GqXdukY1s9/bSFozEfF3d3Rv31F10mTarw6oamUPn68vyJE1U+\nGQA49csvJicDgN5VG22hRoMGtB1nWuEzz6AgIrp3t2xAZtSBTozlJVQmvBaojK504xmes1kyABZO\nCOLj040fdIucnCKKi6vGTIPvvz9i0nFaLUYX+alqPDxcOXNmLH/88RgBAeZp3E2b1uTUqedZu9b2\n7zFNVVCRD/gqVEntwpYt5CYnm3SsT1iY3VXM6zF1Kq+lpRHV3zwzU5QuLgz85hsmZmRQ08JVEM0l\n+fjxCh1fmFU1pjwX5+dzbp3h1QFvPRY7a5u1qMUkJjOIB1CY6eMzmoa8wVv0wvSxF5Zi0YSgomMC\nzp27wXffVa6rxZzOnk1jxQrT5uhrteDu/h5xcd9z9WrV+KU0VffuEaSmvs60ab2oXbviXXdKpYL6\n9f1ZvXoYx48/T8OG+mseVFW1Y2NNP1irZe3o0ZYLpgL0Td0qzy+PPsr00FCO/fSThaMyL3d/f4av\nXcuzR44QHBuL0qXi35pUfn60GjWKN3NzaVWJWQq2FNZBd5EdQ47/9BNJB/XXALGmU6tWkXb6tEnH\nFmVl8b6nJysffbTK1cgwJoZYJvM2MbQ2aSDh7ZQoCSaE5xjLSB7Fnarx2tniswwaNPic8+dN7yl4\n5plYvvrq3ju65506fjyZ5s31l5A0ZMCAaFavftgCEVlHYaGaxYuPs3LlSY4eTebq1ewytSHc3Z2p\nW9eX2NgQRoxoTt++DWxag/xOR3L/vXw5y4cMqcgNeacKVPv7pmNHruwuf4CTPkpnZ168cMGkhX+q\nqqRDhzg4bx5Xdu3ixoULFN3Spa5wdsYrKIiajRvToE8fWj31lE2nWd5p29RqNEx1c0NTbHjw7q3u\n/fprYkfZthro4e+/55fHH6/wed2nTKHb22+bPyArySefA+znLGdIJZUcstHy7/9/V1ypQQBhhBNL\na0IIsVmsNptlkJSUrfe1gUrlhJubM5mZusudduli+0FbzZoF0rVrXbZtMz5a+Va311WwNyqVM489\n1pLHHrP9fGZrOPTNN3q3+9atq3eket0uhpcttZY2zz1X4YRAo1Zzedcumg4daqGoLC+4VSv6z5pl\n6zCsIn7zZr3JgMrPj6LsbLQlt71aVSgI79zZStGVr9GgQfweElLhCoqXDNSKsAfuuNOZLkaXNq7q\nLJoQ7NiRoPcVUa9e9Xjrra4MGbKMK1dudrOrVE688EJbhg+3XlUmQ9aufZhZs/Zx6NA1QEtIiDcP\nPtiYDh3C2LnzMj//fJLPPy9bqCY2Vmqh25OregoNKZ2deXzrVjaOH8/JFStKt4e2b8/A+eUXd7Km\nFiNH4h4QwImlSynMzkbl40Od9u1pOmwYxTk5nPrlF/58911yr1379ySFguCYqlH0Sxh34fff9W7v\nOmkSnkFB/Pb88xRlZwM3azT0+vBDalWBqYduvr48tWcPe7/4goz4eJSurvhHRtJs+HACoqI4t24d\nB7/5hjOrV5c5L7gir++ExVj0lcGZM2k0avSFTlLg5KQgJeVVfHxUxMenExLijaurEy4u9lE+tKio\nhLCwGSQn55Zu8/Bw4eDB0Xb3Ht2e3Wm37PdxcVzculVn+92ffELH8ePJTkxE6eyMq7c3Lu5V4x2f\nKTa9/jq7bitE1HnSJHpOnWqjiKqfO22bxxYtYoWeQkM1oqIYe+YMxXl5ZCcm4l2nDs52MrUUIO3s\nWWY1alRmDIxv3bo8e+QIbr5Vow6No7PZ8sfR0QH8979xevdpteDkpCQqKgBPT1e7SQbg5oJMtyYD\ncDNJkGTAvvSbOVPvinv/PKy8Q0LwDAy0q2QA0Fuqt0b9+jaIRFRW06FDibpXdyzVP23TxcODGg0a\n4OLmZjfJAEDCjh06A2K9ateWZKCKsHhLmjSpK88+W7Y76JFH7qJGDft6yN6qfn1/fH3LlpSU1wX2\nJ7BZMx7/4w+cXP+tCOYeEECLkSNtGNWdq63n1YC8LrAvSicnhq9ZQ2i7dmW220MNBUNC9LwakNcF\nVYdV1jLQaLQsWnSMHTsSaN06hMcea4mzs/1ktfqsXHmSUaPWkJaWT/36/vz881Duusu0YjHCPMxV\nLz75+HEOffstLu7uxIwahV/dumaIznbyUlNZ8sADJGzfjrObG13eeouukybZOqxqxVxtsyg3l4Nz\n55J25gxR/fsTbabaDLa0/f332fbf/6IuKCC8c2eGrliBZy3j66cI87D54kaOqrBQTWJiNhERfjad\nflddmXNFOUeUefkybr6+qPS8FhGWJW3TsMKsLAoyM/ENC7N1KNWOJATCIclDV1RV0jZFVWWzQYVC\nCCGEsA+SEAghhBBCEgIhhBBCSEIghBBCCCQhEEIIIQSSEAghhBACSQiEEEIIgSQEQgghhEASAiGE\nEEIgCYEQQgghkIRACCGEEEhCIIQQQgiqaUJw/vwNjh9PtnUYQujIzi5k796r5OYW2ToUIXRcP3qU\njIsXbR2GsJBqlRCUlGh4+OGfadBgJs2bz6ZTp2/IzCywdVhCALBy5UlCQqbTrt08QkI+Zd26s7YO\nSQgA8tLSmNu2LV/ddRf/FxnJqscfR6vR2DosYWYOu/zx4cPXyMkpIjY2mGXLTnDpUgb5+Wo++GBH\nmeMee+wuvvtukI2iFHfCXpeYTU3N4+DBJGJigrlwIZ3ffjtLZKQ/Y8asJS9PXXqcl5crGRmv4+RU\nrfJ2h2CvbVOr0XB51y5cvbzwDQ/n6MKFqPPzufLXX5xasaLMsffOnUvs00/bKFJRWYaWP3a4hECt\n1vDAA0tYs+YMAB4eLuTlFZd7vErlRFbWG7i6OlkrRGEm9vjQXbLkOI89torCwhKcnRWUlGgx9CPM\nnz+QJ55oZb0AhVnYY9vMTUnhhx49SD5+HABnd3fU+fnlHu9fvz7jzp2zVnjCTAwlBA731WPVqlOl\nyQBgMBkAKCws4dy5G5YOSwjUag3jxq2nsLDkf383nAzAzZ4uIaxh9/TppckAYDAZAMi6csXSIQkr\nc7iEoKIf7iqVE/Xr+1soGiH+lZVVSHJyboXOqV+/hoWiEaKs9Ap+2/cODbVQJMJWHC4h6N8/CoXe\nzhD9iopKyMmREd3C8mrUcCc2NrhC50jbFNYSPWBAhY4vKZK26WgcLiHYuTOhQsc7OSlwcZHxA8Ly\nzpxJIyUlr0LneHi4WCgaIf5VUlREwo4dxg+8haunp4WiEbbibOsAzGnmzL8YN259hc7p06c+Pj4q\nC0UkxE3XruXQvv080tNNn+bq6qpk5MgWFoxKiJvWjB7Nke+/r9A5MaNHWygaYSsO1UMwZ86BCh2v\nUMC8eQMtFI0Q/1q27O8KJQMAr7/eiZo1PSwUkRA3FeXmcmzhwgqdo/L1pcPLL1soImErDpUQVLR7\nNTjYm1q1pNtLWF5luv67d4+0QCRClKV0dsbJ1bVC54R16oSiIoO1hF1wqITgzTe7oFSa3kgTE7P5\n44+LlgtIiP8ZOrQpUVEVmzEwe/Y+C0UjxL+cVSo6TJhQoXPOrVtHXmqqhSIStuJQCcGgQY04dOgZ\nAgLcbR2KEGV4e6vYv380DzzQyORz7KyujbBjcVOmMHTlyoqdJD0EDsehEgKAFi2CaNBA95uYSuWE\nSlV2NkF0dABxcRHWCUxUez4+Kvr3j9a7r2nTWmX+rlTCuHHtrBGWEABE9e2Lq5eXznbf8HCdbc2G\nDcMjIMAaYQkrcriEAOCdd7rh4vLvj+bu7sySJYPZv380AwZE06RJTcaObcu+faOkTrywqoceakrz\n5oFltg0Z0oTdu5/irbe60KxZLXr0iGTPnqfp2rWujaIU1ZGzmxtd3nqrzDbP2rV5eM0aRm7cSHiX\nLgS2aEGvjz7i/h9+sFGUwpIcbi2Df8THp7Nu3VlCQrwZMKAhzs7ywe9o7LFePEBBgZpVq06RlVXA\nvfc2JCTE29YhCTOz17YJcHXfPq7s2UNQ8+ZEdO9u63CEmVWrxY1E9WHPD13h2KRtiqqqWi1uJIQQ\nQoiKk4RACCGEEJIQCCGEEEISAiGEEEIgCYEQQgghkIRACCGEEEhCIIQQQggkIbCqa9dyKCxU2zoM\nIXTk5BRx40a+rcMQQodGoyUxMRuNRuo6WJokBFZw+XIm7drNIzj4U0JCprNgwRFbhwTAX39d4fff\nL6BWa2wdirChiRM3U7PmNGrWnMaQIcsoKLB90pqUlM3atWe4di3H1qEIG9q16zL1639OaOh0GjT4\nnN27L9s6JNRqDb//foG9e6/aOhSzk0qFVjB48FJ+/vlk6d8VCvj22/vIyiokL0/N2LFtcXJScOVK\nFhMnbub33y8SFVWDkSNbMHx4M2rU8NC5plqt4caNPI4dS+bUqVSKikpo164OkZF+DB26jB07LhMc\n7MXy5UPp2DGMhIRMvvxyH8nJuXh4uLBu3Tni49MBaNSoJlu3PkZQkO7CJlWZVIO7cxs3nqdPnx/L\nbOvZM5IXX2zH7t1XGDy4CTExwSQlZbNq1Sk+/HAnGo2WwYOb8MgjLYiJCdZ73ezsQi5cyODIkWtc\nuZJF/fr+3HNPNJ9+upOPPtqJWq3luefa8NlnfSkp0fDtt4fZtesyrq5OXLqUwaZN8ZSUaHFxUfLt\nt/cxYkQLa/xzmI20zTun0WiJippZ+pwC8PR0YeXKoezfn0RgoCdPPNGK3Nwizp1LY+zY9Zw8mUq7\ndqE88kgLHnigMSqVs851i4pKSE3N48CBRM6evYGbmzNxcRHk5hbz8MPLOXcunebNA/n11+GEhfly\n4EAi3357mIICNQoFrFp1mtTUPAD69m3A6tXDcHFx0rlPVSWli20sPHwGly9nGTzGzc2JgoISvfuc\nnRV06xaBv787TZrUpLCwhOnTd1NcrPvN3s3NWecbXni4DwkJhu//+uud+PDDXkZ+kqpFHrp3burU\nbUye/IfBY1QqJwoL9bdNuLlSY5MmtXBzc6JPnwa88cYWve3d09OZ3NyybdPPT0V+vtrg9WvV8iAx\ncbxdrUcibfPOpaTkEhj4icFj/lmBubx/ah8fV7p2rYtK5Uz37nXZvj2BpUtPlHut268TFOTJ9eu5\nBmNYunQwQ4Y0NXhMVWIoIdBNn4TZRUcHGE0IyksGANRqLVu2XDDpXvq6e40lAwAXLmSYdH3hWMr7\nhn8rQx/WAH//ncLff6cAsGDBsXKPuz0ZAMjIKDR6/5SUPHJyivDzczN6rHAcNWt6ULu2J9eulf+B\nbCznysoqYu3aswBlemlNvZaxZAAc69lpPym3nYqPTzf5w9yWOnQItXUIwgbeeGOLrUMwKjDQU5KB\namjp0r8NJgNVRf/+UbYOwWwkIbCwDz/cYesQTNKnTwNbhyCsLC0tj6NHr9s6DKPq1/e3dQjCBv7z\nn622DsEkTZrUsnUIZiMJgYVVhRHbxigU0LBhTVuHIazMzc0+3hiOHGlfAwqFeRQVVf3ZTz4+KhQK\nva/j7ZIkBBb28cd32zoEo7RaOHgwydZhCCvz9HQlLMzH1mEYdeiQtM3qaMqU7rYOwaicnEKKigyP\nsbEnkhBYWFCQFzNn9tW7z8vLhdBQ20/1UyggIMDd1mEIGzh+/Dm8vV11tjs5KQgP96kSI/tr1fK0\ndQjCBkaObMFDD+kfvR8Q4E7NmrrTsa2tRg2PKvE7Yi6O85NUYS+80I5z58YSGxuMSuVEjRrufP55\nX7Kz3+TixZdp3Nh4d727uzMrVgzls8/68OSTLUun2/j6qvD3V3Frr1Xr1sHUrFn+B7yvb9njR4+O\nJTJS3tNWRz4+KlJTX+PFF9vh4+OKSuVEv34NyMiYyKVLL/PBBz1Nus7EiZ2YObMf06b1Kk0ulcqb\nSYXylqdMUJAnbdqEGLyWl5dL6X/XqePD88+3qfgPJhzC4sWD2br1MSIi/HB1dSI83IeNG0eSmvoa\nBw+OxtdXpXPO7T349ev7s2TJYGbO7EePHpGl24OCPPHw+Ld+gLOzgq5dw3FzK7+mwK3PVYUC3nuv\nB0ql47wykDoEVUBKSi6ffbaHLVsu4OKi5K67ghg9ujWzZu1lzZozNGhQg08+6U3btv/OBLhwIZ2E\nhEzat69TWnwjK6uQ4uISAgI8UKs1/PjjEXbvvkLv3vXZvz+R33+/SMuWQUyZEkdeXjGbN8fTqFFN\nunata6sf/Y7IXG/rWLToGD/8cITU1DzCw30ZNqwZRUUaPvxwB7m5RTzzTCyvv9659Pj8/GL++usq\n9ev7ExbmC0BJiYakpBxCQrxRKhUcPnyN+fMPEhzsTd26fnz77WGUSgUvvdSOuLhIVq8+TVFRCffd\n1xBvb92HflUnbdM6Tp9OZfr03Rw8mISPj4qOHcN58MFGvPPOn/z11xU6dgzj88/7UafOv6/Gjhy5\nRkGBmrZtQ0vf/6ek5OLm5oy3t4rMzAK+/voAFy9mMGBANMuWneDvv1O4++56TJrUlWPHrnPwYBKd\nO4fTtGmgrX70SpPCRMIhyUNXVFXSNkVVZSghkFcGQgghhJCEQAghhBCSEAghhBACSQiEEEIIgSQE\nQgghhEASAiGEEEIgCYEQQgghkIRACCGEEEhCYFVarZbff7/Ad98d5tq1nNLtSUnZXL6cabZ7zJ69\nj379FvLCC79x5UqWWa4rHF9CQibz5x9i586E0m35+cWcPJlCcbF5FnA5eDCJkSNXMGjQYtauPWOW\nawrHV1RUwsqVJ1m8+Di5uUWl2+Pj00lJyTXLPXJzi3jnnT/o3XsB77zzR5n7VBdSqdCKhgxZxvLl\nJwDw8HBh3brhfPPNYRYsOIJWCz16RBAdHUBWVhGPPtqCPn0aADcfyhMmbGTLlgu0a1eHadN6ERR0\nc1EkjUbL6tWnOXLkGvff34i1a88yadLvpff08HDhiy/68sQTMSQn55KcnEtUVA2mTPmT1atPU79+\nDd57rwfNmtltCU5bh+EQfv31DPffv4Ti4ptLzj77bCz33BPF44//wo0b+dSu7clDDzXjypUsYmKC\neeml9nh43FxzYMWKE7z33nZcXZ15551u9O3boPS658/fYOHCY0RH16B16xBatpxDbm5x6f6BA6NZ\nsOABPDxc+PvvZCIi/Ni9+woffLCDnJwiRo2K4dlnW1v3H8MMpG2aT3Z2IZ06zefYsWQAwsJ8+O23\nEYwZ8ys7diTg7Kxk8OAmqFROuLgoGTu2HS1aBAFw9WoWY8eu4+TJFO6/vzHvvNOttNR7QYGahQuP\nkpqaz/DhzXjppQ2sWHGy9L4hId4sXPgA3btHcPFiBiUlGry9VUycuJndu6/QoUMdPvqol90tviWl\ni6uAvXuv0q7dvAqds2bNw9x7bzT16v0fFy5klG53dVVy6tQLeHq6EBPzNVevZpfuUyoVaDQV+38W\nFOTJxYsv4ebmXKHzbE0euubTqtUcDh++ZvLxAwZEs3r1w8yevY/nnvutzL7x4zvwySe9ef75X/ny\ny/2l211clKUJR0UsWTKYoUP1r3pXVUnbNB99bcwQd3dnjh0bQ716/ri7v0dh4b+9W0FBHly8+DKH\nDyfRs+cC8vKKDVxJl0Jxc7n4f/ToEcmWLY9W6Bq2JglBFTBv3kFGjVpToXPc3Jzx8VGRnKzbJebh\n4UxJiYbCwoo/YPXZtOkRevWqZ5ZrWYs8dM2jsFBN7dqfkJFRWKHzQkO9yySjt2rSJIATJ9LMER5D\nhjRh6dIhZrmWtUjbNJ8xY9by1VcHKnSOr6+KoqIS8vPVOvvq1fMjPj5Dz1mVc+PGa/j728/y8YYS\nAvv6SminevT4nj/+uFjh8woK1BQU6DZogLw8/dsrKzzc16zXE/Zh8eLjPPLIStTqiieW5SUDgNmS\nAcDueq6EeeTnF9O48SwuXar4+KrMzPKTW3MmAy4uSry8XM12PVuTQYUWtnjx8UolA9ZWt64kBNXR\n00+vrlQyYE1VPT5hGc8+u7ZSyYA1KRTg4uJk6zDMRhICC9uw4ZytQzDKyUnhUI1amKaoqKTMAL+q\nqlOnMFuHIGzgwIEkW4dglL0NKDRGEgILs4fBUK+/3gmlUu8rJeHAXF2d8PFR2ToMg3x8XBk9OtbW\nYQgb6NEj0tYhGDV//kBbh2BWkhBYWL9+UQwa1NDWYQDQoUMdIiP9ymz773/jeO+9njaKSNjaqlUP\nVYlk0NvblYceaorillAaNQogLe116b2qpj79tDf16vnbOgwUChgypDHe3v+OFXBxUbBu3XB6925g\n4Ez7I7MMrGTp0uNMmLCRGzcKiIz0o0GDGuzadYWUlFxUKiVFRdrS6YI1a3rwww+DmDz5dw4cKDsV\nrEOHUG7cKCAoyIv27UPp3z+aRo1qMmHCRhYsOFrm2JdeakejRjVRKCA2NoTY2BDg5rzeEydSaNo0\n0K4HxMhIbvPIzCzg3nt/4vDhJDw9VXTqFMbp02mcPXuDoqISPDxcykzPmjo1jvx8Ne+9t73MdZo0\nqYVSqUCpVBATU5suXcJ54IHGbNoUzyOPrCwz/Ss2NphnnomlpERDrVqe9O8fXTp48OjR63h5uVaJ\nD4PKkrZpPlOmbOWLL/ZRWKimadNA/PxU7N59hczMQry8XMjNLS6dCtiiRRAfftiTJ59cXab4m6ur\nEzExtcnIKKB+/Rq0aRPC4MFNcHFx4qmnVrNjR0KZe3788d14ebni6upEjx6RRETc/CJ1/XoOly9n\n0bJlbZyd7fP7tEw7rMJycopQqZxwclKyYcM5srIKueeeKLy9VaSl5TFo0BJ27EjA1dWJCRM6lPtt\nvri4hKefXsPChUdRKhWMGhXDzJn3VIlvf5YiD13LUqs15OcX4+2t4uzZNHbtukxsbEhpEauPPtrB\nf/7zJwUFalq3DmH16mEEB3vrvdaKFSd59tm1pKTk0bx5IMuXDyU6OsCaP45VSdu0vMzMAry9VRQW\nqvn117O4uTnTp099XFycOH48mUGDFnP+fDq+vipmzbqHESNa6L1OSkougwcvY9u2S3h7u/Leez0Y\nO7adlX8a65GEwM5dvJiBj4+KGjWMz3VNT89HqVTg6+tmhchsSx66tpeZWUBaWr5J3+aLi0tISckj\nJER/0uBIpG3ankaj5fz5G4SG+pRW1TTk+vUcfHxUuLsbP9aeSUIgHJI8dEVVJW1TVFWGEgL7fAki\nhBBCCLOShEAIIYQQkhAIIYQQQhICIYQQQiAJgRBCCCGQhEAIIYQQSEIghBBCCCQhsIqSEg3Tpu2k\nY8dvGDlyBWfP3vla8cXFJRw6lERmZoHB47RaLenp+Xd8P+G4duxIYMCARcTFfc/ChUeNn2CC+Ph0\nzp27YfS4nJwiiopKjB4nqqfMzAJefnk97drN48UX15nlWZaVVcihQ0lG251arSErq/CO72dPpDCR\nFfznP1uZMuXP0r+HhHjzxBMtOXr0OsnJuVy6lEmTJrWYPr03Xl6ubNlygWbNAunY8eayr+np+Xz4\n4Q7OnElFo1GQmVnAgQOJ5OQUo1RC69YhjBnTBhcXJfn5avr2bUCdOj7s2nWZRx9dyfnz6URG+rFs\n2RBOn05j6tRt5OYWM3p0DG++2QWFwj7LG0vxlzsXH59O06ZfUlCgLt02YUIHLl/OIjk5l4SETBQK\nBWPHtmXUqBjWrDlDSYmGgQMb4ul5cx2MRYuO8fPPJygp0VJUpObkyVQuXLi5jn1AgDvPP9+G5s0D\nuXGjgKioGsTFRZKXV8wTT/zC8uUncHNz5uWX2/P00zGMHbuOPXuu0KFDHb744h7Cw31t8u9yp6Rt\nmnI0ruwAACAASURBVMeAAYtYu/ZM6d+7dAmnVavanD2bxrVruSQmZhMXF8Fnn/Xl4sUMjhy5Trdu\ndWnYsCYAZ8+m8cknu7h+PQeNBpKTczl4MIniYg0uLkr69WvAsGHNKCoqwclJyYAB0fj6uvHDD0cY\nP34jqal5tG0bytq1D/PVV/uZO/cg3t4qJk/uyrBhzWz0r3JnpFKhDWm1Wvz9PyIzs+KZZtu2IQwb\n1oxXXtlYofNcXJS0bh3C4cPXyM9XGzz2rbe68N//9qhwbFWBPHTv3HPP/crs2fsrfJ63tytTp8bx\n3/9uIzW1Yt/aGjYMoKiohAsXMgweFxrqzZUrr1Q4tqpA2uadu3o1izp1Zph0rEIBt/5zDx7cmBo1\n3Pn664MVuqePj4qGDQPYvz8RY//7NmwYSe/e9St0/apAEgIb+uSTnbz66mZbh2FQfPw4IiPtb2U5\neejemezsQnx9PzT64LOlRx5pwQ8/3G/rMCpM2uad6937BzZtumDrMMqlUjmRm/smTk729eZdShfb\n0LRpu2wdglGvvVa1ExZhGUuW/F2lkwG4+TpCVE+bN1fdZACgsLCExYuP2zoMs5KEwMLU6qo/YOri\nRcNdt8Ix2cOAKbW6imcswmKqerIKcPJkqq1DMCtJCCzs4Yeb2zoEo+Li6to6BGEDo0fH2joEozw9\nHXspWlG+pk1r2ToEozp3Drd1CGYlCYGFzZrVH39/N1uHUS4nJ3jllY62DkPYgJeXK6+91snWYRj0\n+uudbR2CsJHt25/AyanqzoAKCHCzy0GFhkhCYAVvvtlFZ5uHh3O5xzdqVJPAQI8y226dGWjOWYJ+\nfu7Uru1lvgsKu/Lqqx1xdXUqs02hAKVSfyPz8nKlXbvQcq+n7wF+J+21efPAyp8s7Jq/vztDhjTR\n2e7uXv6zs02bENzcyrbnf9qyuWdXt2oVXO7vib2ShMAKRo+OJTY2uPTvrVsHc/36q/z44/2ljVep\nVPDUU60oKnqLkyefJyHhZZ56qhU1a3rQsmVt1q0bQX7+JLTadzh48Bnc3P79pahVy4O9e59m1qx7\neOWV9gQFeaJQQLt2odx7bzQdO9bhww97MGVKN1xcyv4vd7QuL1ExNWt68N//xpU+2Dw8nFm/fiTX\nro2nSZN/u2wjIvy4fPklsrPfYM+ep1m06EEaNgwgMNCTCRM6kJf3Jmr1ZNTqt+nWrewrqBkz+rBk\nyWA++KAnHTrUAW7W4nj44Wa0bRvCY4+1YO7ce3U+/J2dlbRpE2LhfwFRlf3nP90JDv73C8uIEc3J\ny5vExImdSj/gVSonPvusDxrN2+zdO4rz58dxzz0N8PNzIy4ugqNHn6WgYBIazTv8+GPZGSsxMcHs\n2zeKzz/vy+OP34WHhzMqlRN9+tSjZ88I4uIi+Oqre3j66VY6sXXt6nivWmXaoZVoNFp27EhAobj5\nIfxPMaCMjAKOHbtO8+ZB+PmZ/mrhxIkUvvvuMG5uzowaFUNY2L8FXDQaLcXFJahUupn0ihUneeGF\n30hKyqFjxzAWL36wzLn2RKZ2mU98fDonTqTQsWMYNWq4AzdraBw4kISXlyuNGtU0+Vp5ecV8881B\nzpxJo3//aPr2bVBmf0GBukxC+4/k5FyGD/+ZLVsuULOmB59+2ptHH73rzn4wG5G2aT4FBWq2br1I\ncLAXd91Vu3T71atZXLyYQZs2oTq9XIZs3XqRFStOUreuL6NGxeLjoyrdp1Zr0Gq1uLjoXu+DD7bz\n/vs7yMsrZvDgJnz33X24u9vfGBepQyDKKCm5WZLT39/d1qHcEXnoOqbMzAI8PV1xdrbfDkxpm46p\nsFBNUVEJ3t4q4wdXUZIQCIckD11RVUnbFFWVFCYSQgghhEGSEAghhBBCEgIhhBBCSEIghBBCCKD8\nCg//ozB3NQchzEjap6iqpG0Ke2M0IZCRsqKqkpHcoqqStimqKkOJqrwyEEIIIYQkBEIIIYSQhEAI\nIYQQSEIghBBCCCQhEEIIIQSSEAghhBACSQiEEEIIgSQEQgghhEASAiGEEEIgCYFZxcXFMW7cOFuH\nIYQOaZuiqpK2WXVIQuBAnnnmGZRKJdOnT7d1KELwxBNPoFQqy/zp2LGjrcMSAoAzZ87w4IMP4u/v\nj6enJ61bt+b06dO2DsumjK5lIOzD8uXL2bdvH6GhobYORYhSd999Nz/++GNpXX9XV1cbRyQEXLx4\nkc6dO/P444/z9ttv4+vry6lTp/Dy8rJ1aDYlPQQWtGXLFvz9/fn6668tep9Lly7x8ssvs2jRIpyd\nJccTxlmrbapUKmrVqkVgYCCBgYH4+flZ9H7C/lmjbU6aNIk+ffowbdo07rrrLiIiIujbt2+1/0Il\nCYGFLF++nAceeIB58+YxevToco9r1qwZ3t7e5f5p3ry5wfuUlJQwfPhwJk+eTMOGDc39YwgHZK22\nCbBjxw6CgoJo2LAho0ePJiUlxZw/inAw1mibWq2WNWvW0KRJE/r160dgYCBt27Zl6dKllviR7Ip8\nnbSAuXPn8tprr7FixQp69uxp8Nh169ZRXFxc7n4XFxeD57/99tsEBgYa/OUR4h/WbJv9+vXjwQcf\nJDIykosXLzJp0iR69uzJgQMHjJ4rqh9rtc3k5GRycnJ4//33mTp1Kh999BFbtmxhxIgReHt7069f\nv0r/DHZPq9WW++fmbmGq7t27a+vUqaN1dXXV7tmzx+L3++OPP7ShoaHa1NTU0m0RERHaTz/91OL3\nrgqkfZrO2m1Tn8TERK2Li4t25cqVNrm/NUnbNJ2122ZiYqJWoVBoR44cWWb78OHDtffcc4/F729r\n/2ubej/zpYfAzFq2bMmxY8eYN28e7dq1M3p8s2bNuHTpUrn7IyIi+H/27js8yipt4PBvWnolhBRI\nJXRCEUITRKqgSFNEAUEFBQVsa8V1V90PKyqCDRDFgkqVJiBFOkiTXgMBEkqAkN6nfX8MApN5MyWZ\nluHce+Va563PkJN3njn10KFDkvs2bdpEZmYmkZGRN7ZptVpeeeUVpk6dSnp6us3xl5dr2bEjg+XL\nT3LwYCY7d16gpERDcLA3XbrE0qJFJAMHNiY5uQ4KhWhxqkmcWTalREVFUa9ePVJTU60+51Z6PZzJ\nhSXH4e9M2HIOMgtBqYDkcGhTF3rEQ69ECPSu0i0EF3Fm2axduzZKpZImTZoYbW/SpAnz5s2zLfBb\nFBSUsXbtadavP8PevZc4dOgKGo2WyMgAunSJ4447ohg4sDEJCSHIZLIq38eRZPrrvX8ld8pkenP7\nBWPdunUjOTmZF198ka5du3LPPfdY7BiTkZFhseorJiZGcl9WVhZXrlwx2ta7d2+GDRvGk08+SYMG\nDayKu7CwjHfe2cyiRUdJS8u16hyFQkbz5nUYObIlzz/fHrnc+cmBTCZDlE/rOLtsSsnKyqJu3brM\nnj2bESNGWH3er4fh6z2w8yKUaqw7J9If+iTBf++C+FCrb2U3omxazxVl88477yQpKYnvv//+xraR\nI0eSnZ3NihUrrI49LS2H//1vE6tXnyIzs8iqc3x8lLRrF83TT6fw8MPNrb6XvVwvm5IZiUgI7Oif\ngj1t2jTS0tLo1q0bffr0YcaMGU6LISEhgYkTJ/Liiy9aPLaoqJxRo5awaNGxat1TLpfx5ptdePPN\nrk6tNRAPXes5u2wWFRXx1ltv8cADDxAVFcWZM2eYNGkSFy5c4OjRo/j7+1u8xm9HYdgS65OAyrSK\ngNXDIcKJI8pE2bSeK56bS5cuZejQoUyfPp3u3bvz559/MmHCBJYuXUqfPn0snn/5ciF9+vzE/v2X\nqxWHr6+SuXMHM2hQE8sH24m5hEDU+drRrdVAiYmJbNiwgdWrVzNu3DiXxGDOpEnrCQ5+v9rJAIBO\np+fttzcTFPQ+8+Ydrvb1BPtzdtlUKBQcOnSIgQMH0qhRIx5//HGaNGnC9u3bLSYDuy9C5McweGH1\nkwGA/Zch8hO4/xfQic9ot+OK5+aAAQOYOXMmU6ZMoUWLFnzxxRf8+OOPFpMBnU7P/ff/TGTkx9VO\nBgBKSjQMHjyfyMgp7N59sdrXq67bo4ZAr4eSH6F8LSibg98EkFv+huKJiovVdOnyLX//nemwezz+\neCu+/XaAw67/D4/5FnbtMBz5GvQ6aDYWard0dUQuM3MPjFsJjvqthvvBnjEQ6+DpEDylbKqLi9n9\n5ZdcPnCA+G7daPX4427b/u1o587lkpIyi6tXix1yfZkMZsy4jyefbOuQ69+8z+3eZFDwHyj8383X\nXj0hbK3r4nGRq1eLSEj4jKKiytve/hEY6EVMTCBFRWoKC8sJC/NDr4eMjDxKS7UWz69fP5QTJyY4\ntAnBIx66uSdhXmvQXH/IKHxgyB4Ia+bauFxg8Hz47bjl41RyiA6EABVcLgIvBdTyhUuFkF1iOZmQ\ny2DrY9DR+u4PNvOIsgn8fN99pK5ceeP1na++Ss/333dhRK6xY0c6nTvPQWdFFVNYmC9RUQFkZ5dQ\nXq4lIiKAwsIyLl4sRK3WWTx/0KDGLF481B5hSxIJQWYI6POMt9XaBN53uSYeF8jMLCAh4TOzH+ZK\npZzRo1vxv/91Jzy88hqUkyezmDhxFWvXpmGueMTFBZOaOhGVSlGd0CvlEQ/dzc/CoenG2+L7w31L\nXROPi/T/BZZbGHzQtDZ8c7/5D/JiNXy5C/672fDflZEBa0dAj8QqhWuRJ5TN7NOnmZ6UZLRNrlLx\nWm4uKj8/F0XlfOvXp9Gr149mn3X+/ireeutunnkmBT+/yudA2LEjgzFjlnH0aJbZe95/fwOWLRtW\n1ZDNun0TAs0ZyJ8IZb+b7lM0hjrVbz+vCYqKyomImFJpzYBcDrNn9+exx1rbdF29Xs+ECSv58ss9\nlR7TuHEYx45NsOm61qrRD11NKRz+Era/CnqJhvLB2yDq9lgIaNQS+OFg5fvvioXfh0GAjcsg/JUB\nPX6qPDGQAYfGQbM6tl3XGjW6bAIX9+xh8YgRXJNY7KfVY48x4LvvXBCV8x05coXk5K8qTQb8/JT8\n+eco2revZ9N1CwvLue++n9m8ufKhk6NGtWDOnEE2Xdcat2dCUDIfch8BzFTR1D4KKuf17nSVJk0+\n5/jxa5L76tcPYefOJwkLq3rGf+zYVdq1m0VhofSTd+TIFnz/vcMKtt2v63Cl12BRJ0NzQWVaPg+d\nP3VeTC7y4wEYWUlliFwGi4fAgMZVv75GC/f/CqtPS+/3VULOK+Bt5xlZamzZBNZPmsTW996rdL/S\n15c3ih3Tju5Oyso0hIZ+QEmJdM/WPn2SWLHikWo1iy5depzBg+dX2hTxww8DefRR+/Ypuj1HGRS8\nhtlkAEDu+StbjR27vNJkoG/fJE6deq5ayQBAkybhXL36CnFxQZL7f/jhIIsX3x61MVY5Mst8MgBQ\nIv078yRpOTCqkmTAVwlpE6uXDIBh0qJVw+HtrtL7SzSQMqt69/AkRVeusP2jj1wdhltISZlZaTLw\nzjt3s2rV8Gr3kRowoDFpac/i6yudkY4atYQzZ3KqdQ9beG5CoLNiSEjhdMvH1GB5eaXMnPm35L7B\ng5uwcuVwu93Lx0fJmTPPExcXLLl/5Mjf7HavGq/EirKZscYw6sCDDZwn3QHQRwEZz0OcHUcC/Kcr\nTL1Het+hq7C6apMnepzia9fQacyP9dSUlHB6zRonReQaq1alcuiQ9EJcU6few5tvVpJhVkFcXAjp\n6S/g42Pa10qvhwEDfrXbvSzx3ITAx4oOGcUfgfqI42NxkXbtpL/6tGoVwaJFD9n9fjKZjNTUiQQE\nmHaqKSpS8+STy+x+zxopyYoexCWXYY1jOhW5g58OwqErpttlwMkJUM1KK0nPtYdnU6T3DZoPWs/O\nv6wS3qQJtRtbrpb5ZcAA1B7abKDV6hg0SHoK42efbcdzz3Ww+z1r1/bjxIkJSI3oPHToCnPnmulk\nY0eemxAEfWLdcUWfOzYOF9mxI4OTJ7NNtnt7K9i7d6zD7qtSKdi7V3rlxW++2YdGI566RHawbq6B\nM5470mD8KuntX90LMdKVTHbxWV+Il7h+qRZevv1GIkvqOWWKxWO0paVGwxE9yUsvraGszHQ0Vnx8\nMJ995riVEGNjQ/jyy3sl940f75x/a89NCNQ7rTtOEeXYOFzkjTf+lNy+evVw5PKqTyySmVnIzp3n\nUasrH77YsGFtnn5aenKN6dOt/L14urI8y8eoPLOPy64LkF9mur1pbRhbjTlZ1FrDtS8VWLj/GENN\nREXfHaj6vT3J1cPWzTbqFRjo4EhcY84c04Igk8GuXU9W67qnTmWzf7/5CeHGjUuhadNwk+15eWXs\n3n2hWve3hucmBHIrVjSR1QI/x31bdpUrVwrZsOGsyfbo6ADuvjvB7Ll//32JceNWMGHCSo4eNW5D\ne//9rcTEfEqHDrNJTJzG4cMSdb7XffnlfSgUpo/dyhKV245PLcvHdJjs+DhcYEQl3UlWPGL+vPwy\neHeL4fwfK9SgHr0K9adD+9kQ+xlM3lL5dcL9YUAj0+25pfC7hb6etwPfUMvPzoiWLanfq5cTonGu\nFStOkptbarJ9wIBGZudmAfj995OMGrWEN95Yz+XLhTe263R6RoxYTIMG02ndegbt2s0iO7uk0uss\nXy79hzBixGIr30XVee6wQ4DsgVBWSbWr8g7DbIVyKx7MNcyQIQtYuPCoyfbDh5+mmZlB1/v3Z9Kh\nwzc3qst8fZXs2DGa3bsvcvFiAW+9tdFoPO4999Rn9erKV62bPn0nzz672mT73LmDGTYs2YZ3JK0m\nD+3izDJYNRj0EjUtMiU8sA0i2jk/LgcrKocAiYnu+tYHS31c75oDW25Z0fuNztA9wbD2wZLj8Nct\nX6DkMjg1ARIq+WxTa8HnXdO1DRJCIO1Zq96KWTW5bJYVFPBN+/ZkHZMeGXTHU0/Rd9o0lN6et8Z0\nYuJnnDljvOKrXC6jtPQNsxOs/fTTQR599GamGxMTxMaNo1i+/CSnT+cwffouo+MnTerM5Mk9Kr3e\nvffOZdWqUybbCwtfx9/fxgk5KjA37NDOo2/dgC4bch6G8o2AGuQNQFexC7EX1FpnXS1CDbR1q+lk\nF0FBXmaTAYBvv91n1HZWUqKhY8fZlQ69qViDUNHEie0lE4Jffz1sl4SgRtr/Kex+G8rzwKcOaIoM\nP7dK+a9HJgNQ+dTE71X+bATg8BXjZADg3a0weav08To9nLhWeUKgUsAdkbDnkvH29DzDudVoVaux\nso4fZ/6DD5J1/DjIZIQmJZFzyvhDKTgujvuduHqrM+l0etLTTZvy2rSJtDjb6pdf7jZ6nZGRT5Mm\nX1BeLt1n6tgx8zMVvvdeD8mE4LffjjFihOPWOvG8JoOchwyLGHF9khxdKnj1BkU8EACqFAjbBgrP\nTAZ0Or3k4huDB1uegEmqX0BlyQBAz57mmx8AGjQwrYHZt89xCyu5tbSlsO1FQzIAUHq9yaVuN1AF\ngV8EdJoCKf92XYwO9otE87SPAlpGmj/PR+Kri7nv3/4q6GRhrYL/Sowc0+oh1fOngDChVav5rksX\nrh45gl6rRa/RkHPqFI0GDsS/Th28AgNp0K8fT2zb5upQHebEiSy0WtNS9V+pglJBYWG5ybbKkgEw\n1K6a07JlpOQwxF+k/oDsyLNqCPTFUC7RRq09C3XOOD0cV9i2LV2yUE+dan5ZzzNncpg9e59N9yoo\nsLxI0ocf9jIZwnP+fD7l5Vq8vByzxoHbOr3QdJumCNr/D6LudH48LrBHYoXXh61Yx2ncCtvuo9EZ\nmieCzNRq92sIvgooqZAHLzwGb3Sx7X413YWdOynOMv3W6hMUxEuXq7/Mb00gNXmar6+S++6T6HBy\ni9WrUzkkNYbWjIIC0wSioocfbm7SwXFPxSotO/OwGgIfkIWZbla2Bu0VyB0NV1tA3tOGpgUPtHOn\naU/U4GBvgoN9zJ7Xu/ePVq3EdatFi46itTB4u0ePBMmxtcePm29u8EiBsabbZEoIbQyHv4YF7WBp\nLzi/wfmxOUGpBq5J9KV64g7z5y0/AevP2navMi3MN+1GY6KFRM3Elsqnl/dYQfXqIfWHGtGqFZcP\nHeLXgQOZ0bo1m955x+LERTWV1LoCLVpEWDyvf3/bJw76+uvdFo95/HHTtWWuXSumtNRx//6elRDI\n5BD8GUZvS14Xgj+C3Aeh5FvQHILiryH3UZeF6Ug7dmSYbEtKstxxMi3N9ukx9XrIyjI/OUlgoLdk\nJ5itW03j9HgtnoPA+JuvZXLo8jmcWw2bnoYru+H8OljRF/LSXBamo1wqMFTJV9TaQnPBV3urdr+/\nrfgy1VliTRqJ6Ts8Xkh8PB3/9S+jbfU6dqTlyJH80KMHJ5YuJXP/fjb+979seucdF0XpWKmppr/4\nzp0tr5Ft6xcpgAsXLIyNBe64w3RIvFar55KlcbXV4FkJAYDvMKiTDsHfQ631EHEe8ILyCuOQylaB\nrkjyEjVZRka+ybbGjSVqTSoIDKxaz9Xz503vV1FkpOl4+rNncyWO9HB+dWD4Sei3Enp8D6NzIHks\nnF5gfJy2zCMnJToh0TbvrbC8imFH2xaSuyGv8pFdNyRLfAG86nmPBav0/ugjnj58mP6zZzPu4EFG\nb99uaEq4alybd3TBgkquULNdlfjFJ0sVEDsoLdVaHIUSEOCFl5fpR/QJqT8kO/G8hABAURf8RoJ3\nd8NreRDIKkyiIa8NMvPV6DXR8eOm7YCWmgsAPvigamOKpXrlmjIt+Fu3pkscdxtQqCCuLzQeCd7X\nF4Pyr2t6XEAVPwXd2GGJViJrRua93hkkprSw6C+J/goV1ZeoPKtklfDbQp1mzWj9xBNEJBtGAQXV\nMy2HUts8gdTy8NbUrg4aZL6PQWWs+TIl5cgR2/or2MIzE4KKZL4Q+B435ydTQOCHIPO8Tm1SnVX+\ntqLu9OLFqlVD/VhxhhgJmZmmmbcjC3WN0/oV4wSgbndIGOi6eBxkmcSQQzMdsW+4XCjd1GDxPCu+\n6R+QGPBSM2cPcIyIFi1oPXr0jdfeQUF0+9//XBiR40glp5ZmFgQoLq5am/62bZa/FEmNVFi69ESV\n7mcNzxplYI7/ePDuA+o9oOoAyjhXR+QQcrnMZG3tAEt1ssD69VUbhZGebrnqX6UyzTu9vT0vGauy\noDhDU0L6GvAOhuiukh28aroQiYoqa97laQeu/lrb/ORzAtD/m29oO24cuWfPktCjh1UzGXqK2lYU\nkKpOKWxNs6lMZpqohIb6Vul+1rh9EgIAZX3DjwerU8efzMxCo23Nm5ufkAio8qJDXl6Wi1BkZAA5\nOcbTgbZv75nVjlWm9IXEAa6OwqEGN4blFeYI87biCSQxrYZVrEk2akusqnh7VJvaJrptW6LbVmOh\niRpALgddhcdgeLjlD9/i4qq1MVkz7NrbW0FpqfG42EGDLK9GWVWi7HsYqTavM2csf8W6666q1Zh0\n7x5v8ZiiItNmDKketIJnk2qv12gt9yNoYTmflWRNsnFMol+DFV1uBA8k1dfq6FHzMwoCdOgg0QfI\nCi2kxrzeQq/XS35Rq1/fcTU0IiHwMI0amY4oOH7ccq/UJk1qV+l+UVGWVzy7LNGYKzWDoeDZEiWe\nYxq95V79dYPMTzBUmWArzpGaKCnKMxeZFCyQepbt2WO5OaB+fcujuKSkpESb3X/1ahEajWm2nCj1\nh2QnIiHwMG3bmhYya9qqqjolZt265hOCjIw8ybXF7747vkr3E2qu6ECQGEXFOgvdV1adkl4u2RJr\nPtj/knjeN65abizUcFLDs6Umeqvot8oW6LBAqTT/8btunelcJF5ecqKjHbfstEgIPEz37qbrC5SV\naTl61Hyv/sBA27+C+fgo6N/ffHvW3LmmoxBUKjnR0UE230+o2WQyiAk23f61hYmHAlRVu99bFqag\nV2tBYi4a+ldtFJlQw0k9y06ezJZc4+VW1nTarqhBg1oWVy38WuIPIzY2GJkDOxyLhMDDNGwYJrko\nxpgxy82e9/LLnVDYONj7558fQG5hWbgPP9xusq1Bg1oWzxM8U1eJripb0833I+iZaFiZ0BZtomCA\nhb5XU3aYLn8M0Mez+x0Llegj8YvX6fR8/PEOs+f95z932XQfmQzWrRtp9hi9Xi85V0vXrvE23ctW\nIiHwQFESdaV7pBpLb9GhQz12735S8lwpdesGMmiQ+RUU8/PLTEYXALRpY77tTPBcwyVWvdYDi0zX\nlblBIYftT8CDlhfsvOG97paPmSlRM+ElhwjRh+C2FBERIDkz4IwZ5quwRo++g19/fQB/f+uqsnr3\nrk9srERV2S0WLToqmSQPG9bcqntUlUgIPNCoUa1MtqnVOqZP32n2vNato7h48V8cPz6ew4ef5qmn\n2lTaXjVpkuXl4EaN+k1y+8svd7J4ruCZ7o6XHg748lrz53krYcEQuPoSHBoHM+6FtpHS12oVaahV\nMOf4VTgrMclmBzEa9rbWoYPp2gVnz+ZaXIxt6NDm5OW9xoED49i5czQPPtiEIImesEqlnDfftFyj\n8NJLa0y2yWRw992Wl5yvDpm5+ZRlMpne0nzLgvvR6fT4+k6mvNy47cswpvXfNl2rtFTDtGk72bo1\nndJSDbVr+/HAA0144IGmZs/LzS0hNPRDk+3x8cGcOfO8TTFURiaTWZwPXHA/g+bBEonJ1pY8ZLma\nv6I/z8B3++FKsWFdhDZRMLEd1LIwfLzR59KLGKU/J93PwVaibNZMGRl5xMZONdnesGEtTpyYaNO1\nLl8u5NNP/+Lgwcvo9Xrq1QviiSda07Gj+QWTliw5xqBB8022DxzYiN9+e9imGKRcL5uSbbYiIfBQ\no0cv4dtvD5hsf+21zrz3Xg+H379Vq684cMC0I+PatY/S09LXNyuJh27NdKkAoj813R6ggvzXHD9J\n48pUuO8X0+31Q+DUs/a5hyibNVdS0jROS0yP+fvvw7j33gYOvbderycw8D3JdRUuXfqX5EJxQaB7\nFwAAIABJREFUtjKXEIgmg+oong1XkuByPSiY7OpojEyZco/k9vff31qlpY5t8c03eyWTAV9fpd2S\nAcGC3FRY2gu+CYXf74cC91luOioQGkgMpS5Uw8B5jr13mQYkvnwB8K4V/Q6E6tPrdKyfNImPo6L4\nvHFjDv/6q6tDMjJ5snRBGDRoHmVlVVu3wFoDBvwqmQw0bFjLLsmAJSIhqKry7ZA3BrSnQXcBCv8N\nJXNdHdUNoaG+jBzZQnJf8+ZfUlhYhYHdVjh06DJPPrlCct9333n21LxuZeUgOL8OynLh7ApYN8LV\nERlZOUy6/X/ZSZi5x3H3Tf4ayiVGkSWFwkOO7a8lXLfriy/Y+t57FGZmcu3ECRYPH87Vo0ddHdYN\nQ4c2l5wNsLxcS3LyVw6774wZe1i+/KTJdpnMUDvhDCIhqAq9FvImmG4vXeX8WMz47ruBkosIlZRo\nSEycZtLHoLouXMjnjjtmSO5r1CiMoUPFE9cpjn8POUeMt13cDGorlv9zkqQwGCEx4gBg7EpDtb69\ndflOet4BgPWP2v9+gqmSnBw2vf220Ta9TsepP/5wUUTS/vxTelhgamo2d931nd3v9/vvJxk37nfJ\nfY8+2oKkpKrNhmgr1yYEJQvh2l1wrRuUmh8n71ZKfgbNPtPtShvGRTmBXC5jwYIHJfddvVpMnTof\nkZlZtWWPK9qy5RxxcVMlp9qUy2WV/oG5q1xyWMQCvuJz1vAHaqq2gInTaUpg6wum2wPjQCmxko8L\nfTug8umF7/sFPt9ln/todZD8FWytpNXkuXYQG2KfezmDHj3fcZmHOMF40jhKFVd/coFNb79NyTXT\nqdTDm7jXszM2NoTnnmsvuW/LlnSSk79Eq63agnAVff75Lvr1k+jUAgQHezN7tvNqVp3XqVBXBKWL\ngHLwGQwlSyB/9C0HyCHsL/BKsc/9qktz3NDDSX0E5MGgywJ9AchrgTwK1FuMj5dHQvhxw7FuZsKE\n3/niC+l6WIVCxjff3M9jj7Wu8vVfeukPPv74r0r3z58/hCFDzI9KqAp7dtw6x1kucIF44gkimBl8\nRR43p3xuSwr9GWiXe1WbTgO734HTC0HhBTotFF9ft71OCqRL1FT1WwlxfZ0bpxXO5EDSdKjs0dor\nAVYNN8xFUBXbM6DPXCgwXV8LgJZ1YP+4ql3bHHuWzSzUrCOPIBR0J4hPuMhP3Fx0JwgFa2hKkJss\nXpu2fj2b33mHwsuXUQUEUHjpEpqSEkITEykvKuLaceOpfut16sQTW7c6dAa+qmrZ8msOHrwsuS8o\nyIvVq0dYHDVQGa1WR9++P7F2rfTc3XI5nDr1LAkJ9l27wPWjDHS5kNUetP+0j3gBEn+h/i9DkOlQ\nNafTa+BqEmjPWX9OyE/gO9xxMVVT+/az2LWr8smJGjeuzU8/DbJp0qD5848wfvwKsrJMJx/6x0sv\ndeSjj3rbFKu17PXQXc9aNrHx5nWRocf4uj74MIk3q30vu9j9Duz6r/XHR94JD2x1XDzVtOwEDDDT\nmdBbAf/uAv+2YUK4SwUwaglU8qwFDEMTM18EleVVaG1mr7KZSgkjSKUAQ/OeFzLKMb3ux8TTF8ct\nemOt3HPn+LxRI7RlVvZRkskYf/QotRs7bknf6lCrtURGfkx2dkmlx/Tqlcj33w+0aqG3f/zf/23i\n//5vi+Q6L/9YuvRh+jtgHm3XjzIonHpLMgCSyQCA3DntJBap/7YtGfAeAD7O6fRRVTt3PkmbNpUv\nOXz8eBZt284iPPxDPvhgq+SSyXq9ngMHMnnppT/w85vM0KELzSYDEyakOCwZsJciCtnMJqNtFZMB\nAG+qsNyeo5xebP2xXiHQw/5tnvbUvxHMNVP5UqaFNzeC8n8wbJFhqmOp7i9ZxTBnv2GOgehPzScD\noT5weqJjkgF7+oQLN5IBQDIZAAh3k9qB1JUrrU8GgB7vvuu2yQCASqXg9OlnCQmpfE3stWvTiI7+\nhEaNpjNnzj6yskybcMrLtWzdms6wYYtQKt/hzTc3mk0G5s4d5JBkwBLHl6LCT6HobcvHAWhN5252\nCUU9DLmSlW1EqpaOHzxtB3v2PEWPHt/z559nKz0mK6uE115bz2uvrQcMb0uvv/n/1nJkzYC95JHH\n53wmmQBUVEIJatSoqOJKO/YUGAfXTOeYkKTwhhDHjp22h2EtDLMRPrSw8r86rR5+OWL4AcMohX9+\nc7f+tyWxQZA6EbzcPBl4gTQ2YV0fn4tu0sclJE5isQozwpvavynR3kJCfLh8+SUaNJhGenp+pced\nPJnN448vA4yfl7Y8O+VyQxOrpYnfHMWxNQT6Mih4yfrjy7ZYPsYZFNHg+5T1x6s6OC4WO1u/fhRf\nf32f1cf/U5CtLdAKhYx9+8a6fTIAsJTfKMO6bzPllJNJpoMjslL7/4Hcylw+sqNjY7GjB5pC9isQ\namVljL6S/zZnVAs497z7JwMnKeYPJOZWrsQuKxMHR0vq04fI1tb1R5IpFES3bevgiOzDy0vBuXMv\nMGqU9FDuim59Xlr77AwN9SYn51WXJQPg6IRAk4rV37IBZJVXyzidV2ekR0pXpAQf9+usZc7YsW1J\nS5souf53dXTvHk929iu0amXj0nQukoFtNVK13KCNFgDfOuBTx7pjW9mQkLuBYB/IegWeaAX2XBAz\n3Bf+GA5z3KRfqCXrbEgGwNCx0B3I5HJiu1he5wQgKDaWwOiatdDZnDmD+OOP4YSHW5gb2wZyuYzR\no1uRlfUqQUGu/Qx0r3kINHug3IGzklhLlwf5Y7Hue4cGckdBifSwEXeVkFCLY8cmsGHDSOrUqd5w\ntMaNw0hPf57160e5vEDbwgfb/qj/ZL2DIrHRX5Og2PzqlTesfxx2/geKTWeOdFdyGczuD8WvQ88E\n69Lyyvip4PO+cOVl6F2DljWubWNr7mKyyMOxs+hZ4/zOneyaNs2qY/POnmXZk09ybvNmB0dlX717\nJ3Hlyit8/nlf/Pyq3oQok0HPnokUF0/im28GuMWS8I4dZaDXQ2Y4YDrutFJ+z0LwZ1W/pz2U74Rr\nVWgGCHwXAl63fzxOkJVVzCef7GDx4mOcPp0tOZ/AP3x8lDRrFs6IES0YO7YNvr6uaVevbk/uHWxj\nFSutPl6Jkv9gZX8YR/q1JVw7aNs5wQ3gkcOGYYo1jE4PC47AjL9hz8XKhxCCIXmoGwh9k+CVToYJ\nkFyhumUzBw2dOWR1UwjAe8QyANd2zN71xResmiAxaZs5MhnDV64kqU8fxwTlYKdOXeODD7axevVp\nLlzIN9tEEBCgol27uowd25YHH2zqkiTA3CgDB3cq1F7/sYHcDaplVckgCwF9ruVjb1X0RY1NCGrX\n9uPdd3vw7rs90Gp1XL5cxP79maxcmcqBA5n06JFA167xtGoVSUiIj1uOGbZVAYU2He9rY42Cw0R3\nsT0hyEuFjHUQf69jYnIguQyGNjf8ABSVw6HLsOsC/HYCogJgSDNoUQdig91/5IA1Sm1par3OHeYh\niLOyucCIXs+er7+usQlBUlIYs2b1BwzDFNPT8zhwIJOFC49y6VIhgwY1pl27uiQnR+Dv794JuWNL\nUPl6QOJD1asbqNpC0UfG2+X1wG+sQ0OyiswPQudD3jjQpsE/Q85UbQ1DDItngO4KVOzII3OjoWnV\noFDIiY4OJDo60OGre7nSIUx76suR8zDDWcR8kw6H3enprNDMaz8ZCi/A2WUgU4JODUGJkDAQ8tLg\nwnrQloGuQofJGlg7IMXfCzrEGH6erTn9eW2yjGzJ2oExhHOcUrZWePa0xp8uBDknODMiWrTg3i++\nYMN//kNpTg5ypRKlry+xnTsTlZLC3q+/prygAHWR8TTaCi/PKJsqlYL69WtRv34tBg92/xEUFTm2\nyaBsDWRLrLonqwMR56FsNZStBX254cPWd4h7zfSn1wNl0p0ds++FsgozwgXPAD8bRicI1VLdatlP\nmEIupvMtDOURoolmH/vIJ48QQmhMUyJxs86S2jKQq0BWoStQ2m+w6gGM+sCEt4Ehu0yPFRyiumVz\nJplM5ZLJ9k4E8iWJLCeHwxShQk4b/OlOCKpq9bawL71Oh1atRult/CVJXVLCF02akHfu5jwvcqWS\nxzZtIqZTJ2eHeVty3UyFei1ktQGNxJjpOumgqNqUjy6nSYOrFXooyQIg0j2G/twuqvvQ3clf/I7p\nGhpduZse9KpOaK61tJdhpcNb9fwRGrnXioeerLpl8wpq7ucoBRWaDsJQsoVKVoWqAY4sWMDChx4y\n2lavQwdG79jhoohuP66bqVCmgLDNIK/wwa9oaGgeqKlkKkz6Psvca+EYwbL2dKAjpt9KEqhB3dGl\nyCU6eaocv5a6YD91UPELDfGq8JxpT83+PUo1DfiEukG/MQFwxrBDeRCE/QleXQy3U6VA6IIaMbNf\npRQx4POI8Tb/V10Ti1At99CXO+mCF1744cc99CWRRFeHVT2t/mU8cVFYMsTVvM6Et7tEfPmK+iTi\ngwLoRjCTqMFfpIAGfftSJ/lmDYdcqaTjiy+6MCLhVs5b7dDT6DVQugDUB8G7B3i7SYez24g9V5Tz\nONcOwan54BcJjUaCl/ULrwjVJ8pm5coKCjjwww8UZmbSbMgQIlpYN/ufYB+uX+1QEBxAPHQFdyXK\npuCuXL/aoSAIgiAIbk0kBIIgCIIgiIRAEARBEASREAiCIAiCgEgIBEEQBEFAJASCIAiCICASAkEQ\nBEEQEAmBIAiCIAiIhEAQBEEQBERCIAiCIAgCIiEQBEEQBAGREAiCIAiCgEgIBEEQBEEAlJYP8TBl\na6DwQ9AXg99Y8Bvl6ogEAYAiiljHGi5wnhhi6UlvfPF1dViCAMACsljENQJQ8CQRtEcsqe1pbo/l\nj/VloMsF3TXISgZ0N/eF/AK+D7ssNKHqPGWJ2QIK8MWX75hNBuk3tscQy5OMdWFkQlV5StksQosG\nPVvI5xXO3diuAJbThHh8XBecUCXmlj/2zISgdCkUTgZ9ISiSoXwN6HNBFmDYdit5JERcck2cQrXU\nxIduAfmsZhUZpBNBJLnkcplMvPGmjDKT48fyNHWp54JIheqoiWUT4AeuMJ9r+CMnHCVbKECLHgUy\n1Bi/nw4E8C0NXBSpUFXmEgLPazJQH4acBwCt4bXm2M19FZMBAF0maM6CMt4JwQm3u/nM4xxnAcgl\n98Z2qWQA4DCHRUIgOMVysnmfC5L7dJgmNwcpdnRIgpN5XqfCshXcSAasIgOZqPYSHK+EkhvJgLW8\nUDkmGEGoYD15Nh3v64EfH7c7z/uNKhJtPMEL5KEOCUUQbuWFF3742XSOr43HC0JVxeBl0/EBKBwU\nieAqnpcQePUCvG04oczQ2VAQHEyBgiiibDqnmCIHRSMIxjoRiGTDciWKbKqJFWoCz0oI1Afgan2o\npD1WkjwBFNEOC0kQAHTo+IW5nOa0Tec1oJGDIhKEm/4gh6c4LdFToHLtCHBYPIJreFZCUPAq6HNs\nOydoimNiEYRbHOcYxzhq0zkx1/8nCI6kRc9kztva84qXqeuokAQX8ayEQHPKtuPlceA72DGxCMIt\nssm2+Zw+3OuASATBWDE6stDYdE5Pgomwsc+B4P48KyHwud+243XnQHPSMbEIwi0a0hCZTS20cJQj\nDopGEG4KREEb/G065y8KKb91gjfBI3hWQhD4LvhNxKZOhepDDgtHEP5RhwiG8gjBhFh9ziXEhFmC\nc3xMAj0JtjplLUDLVdQOjUlwPs9KCGS+EDzNhk6CSvDq4tCQBOEfTWlGCu0k9ykl5ghLErPACU5S\nBxX/I1ayU6HUTBhRqIgWTQYex7MSgn/4DDHd5v0g+L0I/4ydlQVDyEJQ1HFqaMLtrQlNkVf4s/PC\ni0E8iP/1alsZMpJpQUc6uSJE4TYVjJL2EiMHniGKu25ZyCgKFV9R3+YmMMH9eeZaBno1FL4DJfNB\n5gV+48DvaZDJQV8K6EAmJnyp6WrqfPGppLKZDeSTTz1iuZf78McfPXpKKRUrHHqAmlo2s1HzKZf4\niwJqoWQCUXQhCDDMO6BChpeHfo+8Xdx+ixsJt4Wa+tAVPJ8om4K7MpcQiFRPEARBEASREAiCIAiC\nIBICQRAEQRAQCYEgCIIgCIiEQBAEQRAEREIgCIIgCAIiIRAEQRAEAZEQCIIgCIKASAicZnYODEiH\nFzMh07aVRgXBoQ4evMwTTyzloYcWsGbNaVeHIwg3lZfAqsnwRT9Y9a7hteAwYqZCJ/ggC167cvN1\ntBJS64OfwvTYg6WwqhCaeEO/AJBXYbrwJfnwRyEk+8ATIeBzPe1LK4d8HcSqYEE+fJUNRXp4KgRe\nrl219+ZKYja46svIyKNp0y8pLCwHQCaDH38cxPDhLUyOzc8v49dfD6NWa3nooWaEh9u2ZC7A6dPZ\nzJ69D51OzxNPtKZhwzAACgvLOXz4Cg0bhnHkyFU++WQHu3ZdoFOnGKZOvYe6dYOq90adTJRNO5n1\nEPy94ObrpLvgxY2GglrR8fVwbjc06AqJHW2/l6YcdnwHGfuhUXdoc8uaOOcPgpef4WfL17D7F/AO\ngL7/hjsesP1eLiSmLnaxhqcgtdx4mz9QBMiAeCX08oeNxXDylhVFZUC4Au4PgMdDDdU5iV5QqIN3\nrsKmIsjWQqHesC9BBQ28YFXRzWvUlsO0SHgvCw5ViOFWP0TDo9avzOsWxEO3+qZM2c7LL6812iaT\ngUolp7xch4+PkkceaUZ6ej6bNp1Do9HdOM7XV0m7dtEMH96CDh1i0Ol0NG0azhdf7Oa77/aRkZFP\nQUE5er0eb28lQ4Y04YcfDnLrr+zTT+9h796LLFhwlLIyLTIZVPyVdu4cy5Ytjzvyn8HuRNm0g5I8\n+Fct0OuMt/sGG/bJZBDXHiIawNE1UHD55jEyOdSKhTuGQtuHQV0MdVvAxUOw8v/g/D7DNdQlIFNA\nXAqU5ELmsZvXiE2Bdo/Auo8h94J0jDI5vHEA6ja3//t3EJEQuFhKGuwpdXUU5g0Jgvn1XB2FbcRD\nt/pmzdrLU0+tsNv1pD7Q7SE7+xVCQ2vOok+ibNpBeYmh6rK82NWRmDfwfbjnVVdHYTWxloELlekg\nQ235OFeLkWi+EDxfRkaeXa/niM/AwEAvAgO97X9hwb0VZoG2Bjw8w5NcHYHdiITAwb7OgctaV0dh\nWZ9Ay8cInqW0VMO77251dRgWRUUFoFSKR9Vt5+exNSMhSL7f1RHYjfgrc7ANRZaPcQed/VwdgeBs\neXmlaLXuX619//2NXB2C4ArnD7g6AssUXqDycnUUdiMSAgcbFezqCKxztQbUYgj2FRERgErl/o8A\nX1+lq0MQXCGpi6sjsMzL3zHtZC7i/k+DGm5QMNRXuToKy8TcCLenb78d4OoQLLp4scDVIQiu8PhP\noHLzjqSleTWjWcNKIiFwgtQkeKRCG32MElbGQEYDsDZfaOwFTb0g1MJvzdapC5K8oI2PjScJHmHE\niBasWPGI0bdwhULGf/7TlYsXX2TQoMZWXScoyJumTWvfmFfAHKkh5OYMHVpzhnQJdqRQwgeXIeYO\n4+0JHeCVv2DiH1ZeSAb1WkJkU1Ba6Jwqs/EjsdUgUHpOk4EYduhEWj1sLAI/OXS8pc3+1zyYmAlZ\n16vtA2TQwx82FBsmEgJ4KQw+ijD89xUNfJYNZ8thYKBhroK9pXBNC8EKeCQYsjUw7AKcLjfMTXBF\na2gWCJDD5xGQqr45AdI74Yb5DWoaMbTLvlJTr3H8eBZdu8YTFGR4cF68WMCwYYvYtOkcYEgWWrSI\nQC6XsXfvJQAaNgxj8+bHiIgIAGDu3IP8/nsqDRuGMXBgI/buvUh6ej4ajY677oqjW7cExoxZxsKF\nRwkM9CI6Ooj9+zMBGDy4CaNGtWDatF2Ul2sZPz6lRiYEomzaWVkRnNwItRMgqunN7SvehjXvg/r6\nuO6A2tDgbjiwBHQakCth5HfQfoRh/6VjsPFz0JRC+0ehJN8w90BxDoTGGI47uhYWPGvYFp0Ml44Y\nhj4GR8PIb+HvhZC+1zBJ0v3vgG+NnDRLzEPgznR6KNGDr+zm7IT5WthUbPgG36Sao67K9XC0zNB8\nEeghQwzFQ9d5iorK8fZWGvX23749g6Kicrp1S6j2KIC0tBzkchnx8TVsdqxKiLLpRFo16LSGDn7y\n6+Uw57zhQzsuBUKiq3f9kny4dsaQiChqQPuvBSIhEDySeOgK7kqUTcFdiYmJBEEQBEEwSyQEgiAI\ngiCIhEAQBEEQBJEQCIIgCIKASAgEQRAEQUAkBIIgCIIgIBICQRAEQRAQCYFHKs3N5dhvv3H54EFX\nhyIIRvR6PZs3n2PVqlTKy8WKWoJ7KeciuayhnIuuDsUlxDJiTnRi+XL+eOEF8jMyaPLAA/SbMYNL\nf//NX598gra8nLbPPENIfDwl2dnE3nkncuXNX09OWhpnN20islUrolq3rvQeGdu3M7dvX8ry8wFo\nPmwYD8yda3Jc9qlTpK5aRWhiIg369kUmF7nh7azo6lWWjxlD6sqVhDVqxL2ff05EixZseucdLu3d\nS+xdd5Hy9NNcPXqUiBYtCIiMvHFuSYmalStTkctl3HtvA7y9pR8r5eVa7rnnJzZuPAtAVFQA27Y9\nQUJCqNFxJSVqFi8+RlGRmsGDm1C7tlib+3b36VJ4byGUqeGZvvDuSJi7Eeb8CbUC4NUHDPu8lNC2\ngfG5RRyilFQCaY8XdSu9xzUWkc5bgBaQE80LRDDa5LgiDlDEAfxpiT8t7fk2XU7MVOgkRVeu8Gls\nLNqyshvb/CMiKMrKAq3pN6VaSUmM2rCBoHr12PLuu/z5xhs39jUaNIiHFy8GYMenn7LprbcoLywk\nODYWnU5Hfnq6yfW8a9UiND4edDpkCgWZ+/ah1xkWSmj64IMMWbDAzu/Y8cRscPaz8OGHOTJv3s0N\ncjnB8fHkpaXd2CRTKNBrtchVKu778kvuGDOGy5cLSUqaRmGhYcW3wEAVJ09OJDIykGPHrvLgg/M5\nceIa3t4K2rSJZssW07KpUslo0CAMLy8Fvr5KTpy4Rna2YW76sDBfduwYTYMGlhdNcieibNrPnweg\nx5vG2+pHwunMm6/lMsP07wA9WsKKN8HHC7ZnvcMPa2tRXu5Nvx5L6FjvAaJ4Aj0aMniHbJahR4MP\njSnjNHrKqEhOOCrCkSNHRyllnLqxL4oXiORJR7xthxFTF7uBY7/9xvzBg206J+bOO0ns1YtNb71l\nsi+xVy+8g4I4tmiRXeIbu38/kS1rVrYrHrr281F4OMVZWVYfr/D2psub/2XERwWczzNeaEOplDN7\n9v2MGbMctVpX7dieeaYtX3xxX7Wv40yibNrPv3+CyfNtO2doZ4gIu8qc9SryCw3rY/h4FzPnw2F0\nTuhCPlso5WS1Y5PjRzLbkFPNxWacyFxCIJoMnODE8uWsHD/e5vMytm0jY9s2yX1pa9dWNywjpTk5\ndr2eUDOUFRYyb9Agiq9ds+k8bVkZG/89iWImQoWHoUajY9So37BXF6WsrGK7XEeoeaYshs+W2X7e\nvK0A4UbbSsv8WPTHQzQc9392iQ1ARwl6yqn4N1BTiYTAwXLPnuXXAQPAzb8txHTq5OoQBBf4pn17\nso4erfL5eiS/aGDP/srVXUlRqJm+/xNenmPfa+p19i5LShQE2vmariP+0hxs2wcfuH0yAIjqzduQ\nTqOpVjIA0IG/jF77UFKt60kJD/e3+zUF91eVmgFz5HItD/adZ/lAm3jWd2rPejduyP+W3tjuKqxR\nI5TenlHlJVhPJpcjk8tvdC6tivbsIpQcUmlACDlsoJsdIzT417862v2agvsLsXMe+Mzwz2iYcMKu\n1wyjZvVtsUTUEDjYna+8gtLX19VhGMhMq3d9atXiqb17XRCM4GoyuZzkESOqfZ2GpHIfK8miNnpk\nyNHYITqDH34YQExMsN2uJ9QcU8dQaYOUrRrXP8ITQ76pxhVMPyp9aUIMb1fjmu5HjDJwgtL8fL5K\nTjYaDihXKtFpKn9wxnXtSvrWreglhiT+Q+HlRUB0NFFt2pC2Zg3lBQVG+wOiowFQ+fkR16ULPd59\nF7lSybrXXyfn7FmaDBpE27FjkSsU1XyHriF6ctvH6hdeYOfUqTdey1UqdGp1pceHN2tGcVYWRZcv\nG23XyVXodVqyCWWNsh85/ol07dmIAwcuc+qUcadVf38VISE+KBRy4uKCef31zvTpk8TMmXtZuPAo\nSUm1eO21zsTFhdj3zTqJKJv2cTQd2r8EhYZRqMhkhiRBV8k/rUIO7RrCjuMV9+j586dOhATlGa6D\nF97UR0kIRexBj3F5VxIB6FEQQDA9iGI8pZwjk6/QUUxtHiKE7vZ8q04jhh26iezTp7l28iQJ3bsj\nk8u5sHMnF3btwi88nPLCQv6eNQuFlxcp48fT8tFHObtpEz/26nXj4RzWsCFjdu1Cp9HgW6sWslu+\n8eekpTErJYWS7GwAAqKiGPv330YTyHga8dC1H01ZGWlr11InOZmQuDhyzpzhzIYNlObkEHXHHWz7\n8EPyzp4loWdP7n7rLXyCg5mVkkLm/v2Aobbh4aVLqdexI14BASZNUEOHLmT+/CM3Xs+Y0Y+nnmrj\n1PfoTKJs2tfuk1BcDnc1g6JS2HIUDp+DhnVh5wlYuhPqhsGkIXB3MkxbDs/Nunn+gPaw+I0S9GiQ\nE4DslrqHfLZymmfges2WHy1oyFxk1MwvSpaIhKAGu3zwIId//RW/2rVp9fjj+IaGVnpswcWLHJw7\nF7lSSYsRI/APD6/0WE8gHrquVVZQwP45cyi4cIGmDz5IdNu2lR6r1epYtOgYR45c4Z57kujUKcaJ\nkTqfKJuut24//LEPmsbA8K7gpar82BJSyWMdKuoQyn3I8XFeoE4mEgLBI4mHruCuRNkU3JW5hEB0\nKhQEQRAEQSQEgiAIgiCIhEAQBEEQBERCIAiCIAgCIiEQBEEQBAGREAiCIAiCgEgIBEH3UVU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ivNXBOPq2zcBt37m3YWrKhTO3j8/9u77/ioqvTx458p6YVUCCRAaNKLoCJVmoCiIgKKrg1FV7+y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\nkXDepozN1HAREdxLPJHnfIs3Y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['figure.figsize'] =9,9\n", "fig, ax = plt.subplots(3, 3)\n", "plt.subplots_adjust(wspace=0, hspace=0) #Adjust the whitespace between subplots\n", "np.random.seed(10)\n", "\n", "for i in range(0,3):\n", " for j in range(0,3):\n", " result = KMeans(n_clusters= (3*i+j+1))\n", " yprediction = result.fit_predict(X)\n", " inertia = result.inertia_\n", " print 'error is ', inertia, 'for k = ', 3*i+j+1\n", " ax[i, j].scatter(X[:, 0], X[:, 1], c=yprediction, edgecolor='', s = 27)\n", " title = 'k = ' + str(3*i+j+1)\n", " ax[i, j].text(8, 16, title, fontsize=14)\n", " #Hide the x and y axis.\n", " ax[i,j].axes.get_xaxis().set_visible(False)\n", " ax[i,j].axes.get_yaxis().set_visible(False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For Figure 10.16, I made the following functions" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Define the function to find the closest centroid for each point and the sum of squared distance to it.\n", "def sum_of_sqrd_dist(points, centroids):\n", " distance = []\n", " closest = []\n", " for i in range(0,len(points)):\n", " k = []\n", " for j in range(0, len(centroids)):\n", " #a**2 + b**2 = c**2\n", " k.append((points[i,0]-centroids[j,0])**2 + (points[i,1]-centroids[j,1])**2)\n", " distance.append(min(k))\n", " return sum(distance)\n", "\n", "#random numbers for centroids.\n", "def initialize_centroids_random(k):\n", " rlist = []\n", " for i in range(k):\n", " rlist.append([random.uniform(0,18), random.uniform(0,18)])\n", " centroids = np.array(rlist)\n", " return centroids" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data points for Figure 10.16" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[17798.414456595608, 6655.8435508510593, 2308.0432711423555, 1765.9481074495247, 1457.8125262414303, 1217.5432896329351, 1028.6076645397698, 884.5593404560808, 754.09541750218216, 643.51508469249256, 530.49615495335513, 425.29192689185589]\n", "[54946.823262070189, 38776.407749241669, 20921.0679286983, 16186.727994916715, 12763.196228658773, 10438.591360566073, 9403.0783908174199, 7210.167802727693, 7341.8742586562857, 6283.9382072103117, 5279.9025421874285, 4467.2007327154952]\n" ] } ], "source": [ "#This is for calculation of MSE (or to be correct the Absolute Error)\n", "errorlist = []\n", "for i in range(1,13):\n", " result = KMeans(n_clusters=i)\n", " yprediction = result.fit_predict(X)\n", " errorlist.append(result.inertia_)\n", "print errorlist\n", "\n", "#For calculating sum of squared distance to random centers.\n", "#And the mean of 5 different ones.\n", "random_errorlist = []\n", "num_runs = 30\n", "for i in range(1,13):\n", " value = 0\n", " for j in range(num_runs):\n", " centroids = initialize_centroids_random(i)\n", " sum_dist = sum_of_sqrd_dist(X, centroids)\n", " value += sum_dist\n", " random_errorlist.append(value/float(num_runs))\n", "print random_errorlist" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.16 - Error Curve" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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0gEe429uq+lc3AcwA6gIrgIGqekxEqgNvAR2BPUA/t4McEXkUZzTWMeBeVf3S\nLe8NvOh+/muq+kwRsVSu5zzyO/98OHwYVq2yVQaNMSVSrll1RWQ+hSz+pKqXF3J40Kr0yWPCBLjj\nDli8GDp39joaY0wIKG/y6OTzsgZwHXBcVR/2X4iBV+mTx8GD0KgRJCbCxIleR2OMCQF+X89DRJaq\n6vnljqwCVfrkATBoEHzwgbPKYFSU19EYY4JceSdGrOezNRCRXkCM36M0gTdkCPz8M7z7rteRGGNC\nXEmardJx+jwEOA6kA0+o6jeBD89/rOaBs8rg734Hp54K34TUfz5jjAeKq3mc9CFBVY33f0jGEzmr\nDI4YAevWOYnEGGPKoMiah4j8sbgTVfWDgEQUIFbzcO3YAU2awP33w7PPeh2NMSaIlanDXESKm4pV\nVfVWfwRXUSx5+OjbFxYtgsxMZ7laY4wphN9HW4UiSx4+PvsMrr7aGXl17bVeR2OMCVLlfc4jBkgC\nLnWLFuB0mB/wa5QBZsnDx/Hj0KwZnHuuk0iMMaYQ5V1J8HXgZ5zFmG7AmdvKVhcKZVWrOs98zJoF\nW4ucR9IYY4pUkuTRQlWTVHWTuyUDZwQ6MBNgt94K2dkwaZLXkRhjQlBJksdhEbkk54WIXAwcDlxI\npkK0bAkJCfD6604SMcaYUihJ8rgTeFlENotIBs6a4XcENixTIYYMgU2bYMECryMxxoSYEo+2clcC\nRFUPBjSiALEO80IcPuxMlnjVVbbWhzGmgPLObXWvmzh+Bv4uIstFxNYzDQc1a8KAAfDee7Bvn9fR\nGGNCSEmarW51axs9gfrATUChCy6ZEHTbbXDkCEyb5nUkxpgQUpLkkVNluRJ4U1XX+JSZUHfuudCh\nA7z2mteRGGNCSEmSx39E5Euc5DFbROoANjwnnAwZAitWwPLlXkdijAkRJXnCPALoAGxS1f0iUh9o\nrKqrKiJAf7EO82Ls2+d0nA8ZAi+/7HU0xpggUe65rdwZdi/BWdfjG1X90L8hBp4lj5NITISZM51V\nBmvW9DoaY0wQKO9oq3/iPNfxPbAaGCoi9udpuBkyBA4ccCZLNMaYkyhJs9U6oG3On+1uM9ZaVQ2p\nlYSs5nES2dnOU+dxcTB/vtfRGGOCQHknRvwRaObzuimw0R+BmSASEeHUPlJTIS3N62iMMUGuyOQh\nIp+KyCdAHeAHEUkVkfnAD26ZCTeDBjlJ5PXXvY7EGBPkiltJ8LJizlNV/TowIQWGNVuV0B/+ACtX\nQkaGM3WM9GiLAAAeTklEQVS7MabSKlOzlaouKGwDTgA3BipY47EhQ2DbNvjiC68jMcYEsZIO1e0I\nDACuB9KB91X1pQDH5ldW8yiho0fJaNSISbVqkd2yJRGNGzMoJYW4+HivIzPGVLDiah5FtkuISGug\nv7vtBt7GSTZdAxKlCQoZW7cy7sQJkjMzicrMJAtIWryYe+bMsQRijMlV3GirdcDlwFWqeomqjsNp\nsioxEWkiIvNEZI2IfC8iw93yuiLypYisF5HZ7jrpOeeMFZGNIrJSRDr4lN8iIhvcc272KT9XRFa5\n771QmvhMQZNGjiT5wAGi3NdRQHJaGpNGjvQyLGNMkCkuefwR2A7MF5FXRaQbpZ8Q8Thwv6q2Ay4E\nhonI74BHgK9UtQ0wD3gUQESuwFn2thUwFHjFLa8LjAJ+D3QGknwSznhgiKq2BlqLSK9Sxmh8ZG/d\nmps4ckQB2du2eRGOMSZIFddh/pGq9gN+B8wH7gNOE5HxJV3PQ1V3qOpKd/8QzjDfJkAfYLJ72GT3\nNe7PN93jlwAxItIQ6AV8qaoHVHU/8CXQW0ROB+qo6jL3/DeBviW7dVOYiMaNycpXlgVEHDxoy9Ua\nY3Kd9CFBVc1S1WmqejXOF/8KYERpLyQizXEmWFwMNFTVne7n7wAauoc1Brb4nJbpluUv3+pTnlnI\n8aaMBqWkkNSiRW4CyQKSatZk0H/+A927O0N4jTGVXqkG8qvqPmCiu5WYiNQG3gPuVdVDIpJ/2FNR\nw6D8um7I6NGjc/cTEhJISEjw58eHhbj4eO6ZM4fnRo4ke9s2ImJjueeJJ4ibNw/+/Gdo3x5eeAEG\nDwaxZV2MCSepqamkpqaW6NgSr2FeViJSFfgMmKWqL7plPwAJqrrTbXqar6ptReQVd/9t97h1wGVA\nV/f4O9zyV3Ca0hbknOuW9wMuU9U7C4nDhuqWV3q6kzQWLHDWPX/1VTj9dK+jMsYESHnntiqv13Em\nUnzRp+wTYJC7Pwj42Kf8ZgARuQDY7zZvzQZ6iEiM23neA5jtNnkdEJHzRUTccz/GBEZ8PMybB3//\nO8yZA2ed5ax/boypdAJa8xCRi4GvcaZzV3d7DFgKvIMzyWIGcIPbEY6IvAT0xmluH6yqy93yQcDj\n7mc8qapvuuWdgElADeBzVb23iFis5uFPP/wAN98M330HAwbASy9B3bpeR2WM8aNyLwYVDix5BMCx\nY/D005CSAqed5qyD3ru311EZY/zE62YrE64iI2HUKFi8GE45Ba64Au64Aw4d8joyY0yAWfLwg/T0\ndAYOHEjXrl0ZOHAg6enpXodUsTp1gv/8Bx58ECZOhHPOgW++8ToqY0wAWbNVOaWnp9OjRw/SfBZQ\natGiBXPmzCG+Ms4FtXChsy5IerqTTJ54AmrU8DoqY0wZWLNVAI0cOTJP4gBIS0tjZGWdC6pLF/jv\nf+H22+Fvf4PzzoPly72OyhjjZ5Y8ymnr1q2Flm+rzHNB1a4Nr7wCs2bBvn3QubPTqX78uNeRGWP8\nxJJHOTVuXPhsKLGxsRUcSRDq3Ru+/x5uuMHpWL/oIli3zuuojDF+YMmjnFJSUmjRokWeMhHh3nsL\nfdyk8qlXD6ZOhXffhU2boGNHZ3oTm2TRmJBmHeZ+kJ6ezsiRI9m2bRtRUVHMmjWLfv36MWXKlIBc\nL2Tt2OH0hXz6KSQkkPHEE0yaMIHsrVttxUJjgpA9JEjFPiQ4atQoUlJSmDNnDt27d6+Qa4YMVZg0\niYy772bc4cMkqxKFO3tvixa2YqExQcSSBxWbPH799Vfat2+PiLBq1Spq2FDVApL79uXBjz/Os/BU\nFvBcYiJJVmMzJijYUN0KVqNGDcaPH8/GjRt5+umnvQ4nKGX7LHWbIwrI/u9/rT/EmBBgySNAunfv\nTmJiIs888wzr16/3OpygU+SKhatXQ4cOTge7JRFjgpYljwB6/vnnqVWrFnfccQeVpXmwpApdsfCM\nMxj097/D0aPO8N6zz4a334YTJ7wM1RhTCOvzCLCJEycydOhQJk+ezM0331zh1w9mGenpTPJZsTB3\ntNWJE07NIyUF1q6Ftm3hL3+BG2+EKlW8DtuYSsM6zPEueWRnZ9OlSxc2bNjAunXrqF+/foXHELKy\ns+H99535sVavhtatnSTSvz9ULdUKysaYMrAOcw9FRETwyiuvsH//fh5++GGvwwktERFw/fXOXFnv\nvedMsHjzzU5NZNIkZz0RY4wnLHlUgPbt23P//ffz+uuvs3DhQq/DCT0REXDddbBiBXz4IdSp46yl\n/rvfOQtQWRIxpsJZs1UFycrKol27dtSqVYuVK1dSrVo1z2IJearw2WdOc9Z330FcHDz2mDMVvP1e\njfEba7YKAlFRUbz88sv88MMPPPfcc16HE9pE4OqrYelSmDkTGjaEoUOhZUsYPx6OHPE6QmPCntU8\nKtif/vQnZs6cyerVqwtMqGjKSBW+/BKSk2HRImjcGB55BG67jYzt250RXTZ/ljGlZqOtCJ7ksXXr\nVtq2bctFF13ErFmzECn0v4spC1WYO9dJIt98Q8appzIuO5vkPXts/ixjysCarYJI48aNefLJJ5k9\nezbvvPOO1+GEFxHo3h2+/hrmzWOSSG7iAGf6k+S0NCZV1lUejfEjSx4eGDZsGJ06deK+++5j//79\nXocTfkSga1eyzzyz8Pmzli2DnTu9iMyYsGHJwwNVqlRhwoQJ/O9//+Pxxx/3OpywVeT8WRs2QGws\nXH65s1zu//7nRXjGhDRLHh7p1KkTd999N+PHj2fp0qVehxOWCp0/q0ULBs2aBY8/Dtu2wZ13QqNG\nTnPXxImwa5eXIRsTMqzD3EMHDx6kbdu2nHbaaSxbtoyqNuWG3xU5fxY4Hezff+/Mo/X227BxozN3\n1uWXOxMzXnst2HQyphKz0VYEZ/IAeP/99/nTn/7E888/z/333+91OJWXKqxaBe+84ySStDQnkXTv\n7iSSvn2d9diNqUQseRC8yUNVufrqq0lNTWXt2rU0a9bM65CMKqxc6SSSd96BTZuciRh79HASSZ8+\nULeu11EaE3CeJQ8ReQ24Ctipqme7ZXWBt4E4YDNwg6oecN8bC1yB0zw9SFVXuuW3AI8DCvxVVd90\ny88FJgE1gM9V9b5iYgnK5AGwefNmzjzzTHr27MlHH33kdTjGlyosX/5bItm8GSIjoWfP3xJJTMxv\nzWP2MKIJI8UlD1Q1YBtwCdABWOVTNgZ42N0fATzj7l8BzHT3OwOL3f26QBoQA5ySs+++twT4vbv/\nOdCrmFg0mI0ZM0YB/fDDD70OxRQlO1t16VLVBx9UbdZMFVSrVdPNl1+uD5x2mh5yUo0eAn2gRQvd\nvGmT1xEbUy7u92ah36kBb7YSkTjgU/2t5rEOuExVd4rI6cB8VW0rIq+4+2+7x/0AJABd3ePvdMvH\nA6nAAmCeqp7plvfzPa6QODTQ91oex44do1OnTuzbt4+1a9dSp04dr0MyxVF15tZ65x2Sx4/nwcOH\n8zxTkgU8l5BA0muvORM32iJWJgQF2xPmp6nqTgBV3QE0dMsbA1t8jst0y/KXb/Upzyzk+JAUGRnJ\nK6+8QmZmJklJSV6HY05GBDp3huefJ7tz58IfRkxNhRYtoFYtaNfOGb01YoQzjfw33zjPlwTxHzTG\nFCcYxoYW9a+n0k36dNFFF3H77bfz4osvctNNN9GxY0evQzIlkPMwYv6aR0SPHtCvH6xfDxs2ONvn\nnztrtOeIiYE2bZxVEnO2Nm2gVSuIyp+SsL4VEzS8SB47RaShT7NVzuO9W4GmPsc1ccu24jRf+ZbP\nL+b4Io0ePTp3PyEhgYSEhCKP9cozzzzDRx99xNChQ1m0aBFVrLkj6A1KSSFp8WKS09LyTsA4YQLk\n/2I/cQIyMpxE4ptUvv4apkzJe2zjxr8lk9atyYiOZtwTT5D800+/XWfxYpvo0fhNamoqqampJTq2\nIvo8muP0ebR3X48B9qrqGBF5BDhFVR8RkSuBYar6BxG5AHhBVS9wR2d9B5yL08z2HdBJVfeLyGJg\nOLAMmAmMVdUviogjqPs8fE2bNo3ExEReeuklhg0b5nU4pgSKfRixpH75BX78sWBiWb8e9u0jGXiQ\ngjWc5xITScqfeIzxAy+H6k7DqTXUB3YCScBHwLs4tYYMnKG6+93jXwJ64/ybGKyqy93yQfw2VPdJ\n/W2obifyDtW9t5hYQiZ5qCo9e/Zk6dKl/PDDD8TGxnodkvGSKuzZQ1KvXiQvX17g7aSoKJIfesjp\nU2nf3umPMcYP7CFBQit5APz444+cddZZ9OnTh7ffftvrcEwQSB44kAenTi1Y8zj1VJJ273aSzBln\nOEnk2mvhwgud9d+NKaNgG21lSqBly5Y8/vjjvPPOO3zxRaEtcaaSKXKixyVLYPt2mDDB6SMZOxYu\nucSZOXjoUPjii7yd9Mb4gdU8gtiRI0c455xzOHr0KKtXr6ZWrVpeh2Q8VqK+lQMHnFFdH37o/MzK\nckZ1/eEPTo2kd2+oXdubGzAhxZqtCM3kAc7oh65du/Loo4/y1FNPeR2OCTW//gpffeUkkk8+gd27\noXp1Z3qVa6+Fq6+GBg08Cc2GHQc/Sx6EbvIAGDRoEFOnTmXlypW0a9fO63BMqDp+HL791kkkH34I\nP/3k9Ilceulv/SRNndHvgf5iz0hPZ1yPHgWHN9uw46BiyYPQTh67d++mTZs2nHnmmSxYsIAI6wQ1\n5aUKK1Y4SeSDD2DtWqf8vPPIuOwyxr3zDslbtpTui13VSVDHjhW++byX/OijPDh7tg07DnKWPAjt\n5AHw+uuvM2TIEDp37kzNmjVp3LgxKSkpxNtfacYfNmzIrZEkL1lS+PMkdeqQ1KBB0cnhxIkSXy4J\nSC6svHZtkvv0cR6MzNlatXKmeDEVrrjkEQzTk5gSSEhIoEaNGixZsiS3bPHixcyZM8cSiCm/1q2d\nebdGjCD7oouIWrQoz9tRQHbNms4orshIZ6ta9bf9/Ftx70VGEvGPf5C1YEHBKV1q14aFC2Hq1Lzx\nNWsGv/td3qTSpg00aXLS51qsbyUwLHmEiFGjRvHrr7/mKUtLS2PkyJFMsWq+8aOIM84ga9Giwufq\nevNNv1xj0Nlnk1REnwfx8c7T9hs3Ok/Xr18P69Y5P994Aw4d+u2DatUqmFBy5gqrXbvwvhWb0sUv\nrNkqRHTt2rXQOWcSEhKYP39+xQdkwlZFdWaXaUoXVeeZlpyk4rulp+edpbhxY5KPH+fBnTutb6WM\nrM+D0E8eAwcOZGr+qjwQGxvLv//9b+Li4jyIyoQrv8zVVdF+/dWZG8wnoSR9+CHJP/9c4NCkmjVJ\n7tbN6U/x3Zo2tafyfVjyIPSTR3p6Oj169CAtLS23rH79+hw6dIgqVaqQkpLC8OHDqVrVWiKNyVHk\nlC5Nm5JUt66TbH755bc3q1d31mBp1cpp+vJNLLGxxfavhGPfiiUPQj95gJNARo4cybZt24iNjSUl\nJYWIiAiGDRvGzJkz6dixIxMnTuS8887zOlRjgsJJm+BUYds2p39lwwbnZ86WlgZHjvz2YbVqQcuW\nBWsrrVuTkZXFuJ49w+65FUsehEfyKIqq8v777zN8+HB27tzJPffcQ0pKii1lawzlaII7cQIyMwtP\nLJs2Oc+tuJKrVuXB48cL1nCuvJKk6dMhOtrv91URLHkQ3skjx4EDB3j00Ud55ZVXaNy4MS+//DLX\nXHON12EZE36OH3cW9XITS9Kzz5K8teBadLnPs8TEOMONi9piY53hzSVQkc1jljyoHMkjx6JFi7j9\n9ttZvXo1f/zjHxk7diyNG4fs8u7GBL0i+1YuvpikPn2cqWB8t717835ARISzcqRvQomLy/s6JqbC\np3Wx5EHlSh4Ax44d4/nnnyc5OZnIyEieeuop7rzzTlvW1pgAKPWX+qFDsGVLwaSSkeH83LIlT7MY\nANHRJIvw4IEDFTb02JIHlS955EhLS+POO+9kzpw5nH/++UycOJFzzjnH67CMCTt+Hd584gTs3Fkg\nuSRNm0bynj0FDk/q2pXkefPKeQcFWfKg8iYPcDrUp0+fzn333cfevXu5//77SUpKIioq6uQnG2OC\nRpHNY1bzCJzKnDxy7N27lxEjRvCvf/2L5s2bM378eHr37u11WMaYErI+Dw9Y8vjN119/zdChQ1m3\nbh39+vXjH//4B6effrrXYRljSqAin/635IElj/yOHDnCmDFj+Otf/0qtWrUYM2YMt912m60VYozJ\nZckDSx5FWb9+PXfccQepqalccsklTJgwgZo1azJy5Ei2bt1q64YYU4lZ8sCSR3FUlcmTJ/PAAw9w\n4MABoqOj2bdvX+77LVq0sHVDjKmELHlgyaMkdu3aRefOnUlPTy/wXrdu3fjHP/5BgwYNqF+/PtWq\nVSv39XLm6rIajjHByZIHljxKqqh1Q/KLjo6mQYMGJ91OPfVUGjRoQN26dfM8oFjYLMGBqOFYgjKm\n7GwZWlNiRU1j0q1bN+644w52797N7t272bVrV+7+jh07WL16Nbt37+YX3+mtfYgI9erVy00qGRkZ\nZGZm5jkmLS2NgQMHMmLECKKioqhduzZRUVF59mvWrImcZNnRHIUlqEAt3WtJylQ2VvMweZS3RvDL\nL7+wZ8+e3MRS1LZkyRKysrJKHZ+IFJlY8v+cPXs2q1evLvAZl19+OU888QQ1atSgZs2aBbbIyMgS\nJyiouFpUzrUsSZmKYs1WWPIojcLWDfH3F1RRKyNeddVVjB49mkOHDpGVlUVWVlah+yd7P2cri4iI\niCITS82aNQu8t3DhQjZs2FDgczp37sywYcOoXr16qbfChkyHW5KqqERoCbfswj55iEhv4AUgAnhN\nVccUcowljyBSEV+EiYmJTJs2rUB5jx49eOihhzh8+HCB7ddffy20vLhjdu7cyYkTJ/wSc44qVaoU\nSCh79+7l50KWVI2NjeX8888nMjKSyMhIqlWrVq79PXv28Je//IXt27fnXqNJkya8+uqrxMfHExkZ\nSdWqVXPP8d2qVq1aolpbRfZ5hVPCrcjrQJgnDxGJADYA3YBtwDKgn6quy3dc2CSP1NRUEhISvA6j\n3HL+EaxZs4Z27dr5/R9BRX1xFFWL6tu3L3/72984cuSIX7YvvviCXbt2FbhO7dq1iY+P59ixYxw7\ndoyjR48Wuu/vBFeUKlWqFJpYfJPOtm3b2L9/f4FzY2NjOe+886hatWrusTn7Jd18z3njjTdYsmRJ\ngeskJCTw6KOPFnneycpzyiIiIhCRsEyGEP7J4wIgSVWvcF8/Amj+2kc4JY/Ro0czevRor8Pwm0De\nT0U0wXmdpBITE5lSgknxsrOzcxNJcUnmtttuY/ny5QXOb9euHY899hjHjh3j+PHjeT7LdyvJe6mp\nqewpZHbY2rVr07Jly9xjS7JVVFIsStWqVcnOziY7O7vAe1FRUTRq1KjYZFelSpWTJsScY+bOncv6\n9esLXKek/w+UVriPtmoMbPF5nQmc71EsJsjEx8cH5B9V/mvMmTOHkSNH8u2333LxxRcHJEmlpKSw\nePHiAkkqJSWlROdHRETkNoEVp23btoUmjw4dOjBgwIDSBV2EohJhnz59Sv3fS1U5ceJEoQnnrrvu\n4qOPPipwTq9evRg1alTucYWdW5qyKVOmsGXLlgLXqV27Nr///e85ceJEkcnv6NGjuUnwZImysNoa\nwLZt20r1O/MLVQ3pDbgOmOjzeiAwtpDjNFwkJSV5HYJfhdP9BPpeNm3apImJidq1a1dNTEzUTZs2\nBeQaLVq0UCB3a9GihV+vVRHXqMjrJCYm5rlGzpaYmBiS18nhfm8W+t0bLs1Wo1W1t/u6yGYrL+Iz\nxphQpmHc51EFWI/TYb4dWAr0V9UfPA3MGGPCWMj3eajqCRG5G/iS34bqWuIwxpgACvmahzHGmIoX\n9iv/iEhvEVknIhtEZITX8ZSHiDQRkXkiskZEvheR4V7HVF4iEiEiy0XkE69jKS8RiRGRd0XkB/e/\nUWevYyorEfmziKwWkVUiMlVEyj+NcgUSkddEZKeIrPIpqysiX4rIehGZLSIxXsZYUkXcy7Pu/2cr\nReR9EYmu6LjCOnm4DxC+BPQC2gH9ReR33kZVLseB+1W1HXAhMCzE7wfgXmCt10H4yYvA56raFjgH\nCMnmUxGJBe4BzlXVs3Gat/t5G1WpvYHz797XI8BXqtoGmAc8WuFRlU1h9/Il0E5VOwAb8eBewjp5\n4DzvsVFVM1T1GDAD6ONxTGWmqjtUdaW7fwjny6nwaXBDgIg0Aa4E/uV1LOXl/uXXRVXfAFDV46p6\n0OOwyqMKECUiVYFaOLM3hAxV/QbYl6+4DzDZ3Z8M9K3QoMqosHtR1a9UNeepxMVAk4qOK9yTR2EP\nEIbsl60vEWkOdAAKzr0QOv4BPIQzVj3UxQO7ReQNtxluoojU9DqoslDVbcDzwE/AVmC/qn7lbVR+\ncZqq7gTnDzHgNI/j8ZdbgVkVfdFwTx5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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "e = errorlist\n", "\n", "e2 = random_errorlist\n", "\n", "x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]\n", "\n", "plt.rcParams['figure.figsize'] = 6,4\n", "plt.plot(x,e, 'k-', linewidth='1.5', label='K-means')\n", "plt.plot(x,e, 'ko')\n", "plt.plot(x,e2, 'r-', linewidth='1.5', label='Random Clustering')\n", "plt.plot(x,e2, 'ro')\n", "\n", "plt.xlim(0,13)\n", "\n", "plt.xlabel('K (num of clusters)')\n", "plt.ylabel('Absolute Error')\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For Figure 10.18, I made the following functions." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def minDistance(L1, L2):\n", " min = float(\"inf\")\n", " minvalues = []\n", " for i in L1:\n", " for j in L2:\n", " k = np.sqrt((i[0]-j[0])**2 + (i[1]-j[1])**2)\n", " if k <= min:\n", " min = k\n", " minvalues = (i,j)\n", " return minvalues\n", "\n", "def maxDistance(L1, L2):\n", " max = 0\n", " maxvalues = []\n", " for i in L1:\n", " for j in L2:\n", " k = np.sqrt((i[0]-j[0])**2 + (i[1]-j[1])**2)\n", " if k >= max:\n", " max = k\n", " maxvalues = (i,j)\n", " return maxvalues" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.18" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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GQqUBeCQ4TjgASGrwCU9oXTFL0gZW4v4CUBHAnoQzSMYAWCEif8E4Q5FYAyspFwAUFZG8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\nW6Tlk0R0dDRCZs5EdFQU6tvZwadhQ5T18sKZs2cxaNAg9O7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "reds = [[1,2],[2,4],[3,1],[4,4],[6,1]]\n", "reds = np.array(reds)\n", "blues = [[6,7], [7,5], [8,6], [7,10], [10,6]]\n", "blues = np.array(blues)\n", "centroidx = [np.mean(reds[:,0]), np.mean(blues[:,0])]\n", "centroidy = [np.mean(reds[:,1]), np.mean(blues[:,1])]\n", "\n", "plt.figure(figsize=(12,3))\n", "plt.subplot(141)\n", "plt.plot(reds[:,0], reds[:,1], 'ro', blues[:,0], blues[:,1], \"bo\",\\\n", " centroidx[0], centroidy[0], 'rx', centroidx[1],centroidy[1], 'bx')\n", "plt.xlim(0,11)\n", "plt.ylim(-1,11)\n", "d = minDistance(reds, blues)\n", "d = np.array(d)\n", "plt.plot(d[:,0], d[:,1], 'k-')\n", "plt.title(\"Nearest Neighbor\\n(Single Linkage)\")\n", "\n", "plt.subplot(142)\n", "plt.plot(reds[:,0], reds[:,1], 'ro', blues[:,0], blues[:,1], \"bo\",\\\n", " centroidx[0], centroidy[0], 'rx', centroidx[1],centroidy[1], 'bx')\n", "plt.xlim(0,11)\n", "plt.ylim(-1,11)\n", "for i in reds:\n", " for j in blues:\n", " x = [i[0], j[0]]\n", " y = [i[1], j[1]]\n", " plt.plot(x, y, 'k-')\n", "plt.title(\"Average\")\n", "\n", "plt.subplot(143)\n", "plt.plot(reds[:,0], reds[:,1], 'ro', blues[:,0], blues[:,1], \"bo\",\\\n", " centroidx[0], centroidy[0], 'rx', centroidx[1],centroidy[1], 'bx')\n", "plt.xlim(0,11)\n", "plt.ylim(-1,11)\n", "plt.plot(centroidx,centroidy,'k-')\n", "plt.title(\"Centroid\")\n", "\n", "plt.subplot(144)\n", "plt.plot(reds[:,0], reds[:,1], 'ro', blues[:,0], blues[:,1], \"bo\",\\\n", " centroidx[0], centroidy[0], 'rx', centroidx[1],centroidy[1], 'bx')\n", "plt.xlim(0,11)\n", "plt.ylim(-1,11)\n", "d = maxDistance(reds, blues)\n", "d = np.array(d)\n", "plt.plot(d[:,0], d[:,1], 'k-')\n", "plt.title(\"Furthest Neighbor\\n(Complete Linkage)\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.19 Left" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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gNWpQGnJbPaK3t1cePXpUsL2jo8Px+FAoJIZhyPnz52taPgBoBGpQGnJausg0\nTYlGo47HHzp0yPH4fPNdfp5UNBoVwzDk8OHDjveMAgCdMA9KU06rR4g4z3m6cOGCDA8PO642UWzA\nBfOfAOiApY5agG3bcvLkSZmdnZUnT56sbS8WNG7LHuWxBh8Ar7HUUZPL14QuXry4IZxECu8PtV6p\ne0Fxo0IAuiKgmkSpoeduQVPqXlDMgwKgKwKqSZSqCbkFjdOAizzmQQHQGcPMm0SxmlCxoDEMQ2Zm\nZtZqYDdv3pTBwcG15zBAAoCuGCTRJJxG43V1dcmrr74qb775JkEDoGkxiq8FVHrjQgBoBgQUAEBL\nDDMHADQVAgoAoCUCCgCgJQIKAKAlAgoAoCUCCgCgJQIKAKAlAgoAoCUCCgCgJQIKAKAlAgoAoCUC\nCgCgJQIKAKAlAgoAoCUCCgCgJQIKAKAlAgoAoCUCCgCgJQIKAKAlAgoAoCUCCgCgJQIKAKAlAgoA\noCUCCgCgJQIKAKAlAgoAoCUCCijCtm1JJpMSi8UkmUyKbdteFwloGz6llPtOn08V2w+0Mtu2ZXJy\nUrLZ7No20zRlZmZGDMPwsGRAa/H5fKKU8m3eTg0KcJFKpTaEk4hINpuVVCrlUYn00YiaJbVXUIMC\nXMRiMZmbmyvY3tfXJ8eOHZN0Ol2zmpRt25JKpWRpaUmGhoZq+tq1ttWapdN7FZEN206ePCknTpyg\n9tom3GpQopRyfTzdDbQny7KUiLg+TNNUuVxu7fhcLqfi8bjavXu32rFjh+rv71fxeLzgGMuy1Pj4\nuLIsS+VyOZXL5VQ4HN7w2t3d3er06dMqEomoXbt2qUgkojKZTM3e2/pyJBIJFY/H1fj4uIrH4yqR\nSGwo32aJRMLx8+jp6SlZxlwup0zT3PC8cDishoeHN2wLBAKO57Asq2afAfTxTdYUZpDTRkVAAY4X\nU7cLplPI5B/f+ta31oJo8+uZpqmOHj1a9Bz5h9/vV0ePHi0aHqXej2VZ6tChQ64BUE4I79ixo2gZ\nN4fU+jCMRCJlndftEYvFtv4PC+0QUEAV8hfXvr6+ohfMUrWtRCLheswzzzxT1cV6fXg41cw2v49S\nYVsqhMt5nyKitm/frs6dO1dxGFZaFrQOt4DyCwBXhmHI1NSUJJNJmZ6eLtgfCoVERGRpaano6yws\nLMjevXsd93311VdVlS0/YOPkyZPy+uuvy8OHD9f2/fznP5fvf//7srq6Krt27ZL/+q//kk8++aSq\n8ywvL68IOSGhAAAPk0lEQVT9udT7FBF5/Pix/O3f/m1V5ypmeHh4rb8K7YGAAlzMz8/L8ePH5c6d\nOxIIBGRwcFBu3ry5tt80zbUL5q5du4q+1v/+7//K6upqzcuYzWYLwklE5NGjR3Lx4sWanGNxcVGS\nyaSk02kZGhqqyWuu9yd/8idy//59efDgQdHjRkdHGSDRZhjFBziYn5+XiYmJDaHi8/nk8OHDsmPH\nDgmFQmsj7WzblsOHD8utW7caXs6enh65f/9+Q85lmqb89Kc/lVdffVW+/PLLmr1ud3d3yXASeTqq\ncnZ2tmbnhT6YBwVU4Pjx4wU1HqWU/PrXv5Y//vGPa9vyQ669CCcR2VI4BQIBiUajsnv37rKOz2az\ncubMGXnttdeqPqeTcsJJ5P+bU9E+CCjAwZ07d1z3/f73v5fp6WkZGRmRf/iHfyiYzFspv7/xLe2R\nSEQuX74s7733nvzwhz8s+3nZbLYu/UuldHd30//UhggowMGzzz5b8piVlRV59913q3r9SCQi0WhU\nAoFAXfqmitm2bZu89NJLa38/efJk2c+9ceOG/OM//mM9iuVq+/bt8k//9E/0P7UhAgpwcPbsWfH5\nCie2b/bkyRPXfdu2Of/3yg+4+OSTT2RlZcXxmFAoVJcBCSJPy3z+/HmZnJwU27blzJkzZT/3008/\nlU8//bQu5XLz+PFj+clPfsJSR22IgAIcjI2NyVtvvVVWSHV2dm74e1dXlyQSCXn33XfFsiyJRqMS\niUTk4MGDEggEZGVlRRYWFooO+15eXpY//dM/FdM0yy5zIBBw3B6JRCQYDBZszw9TL2foeN6XX34p\nXgycYg3E9kRAAS7+5m/+Rubm5lwv/HmvvvqqWJYlsVhMLMuSxcVFefvtt2VsbEympqbkvffeE9u2\nZf/+/a41Jif37t2TmZkZiUQiRY/r6OiQeDwuFy5cKAg00zRldnbWdQ7W8vJyxTW1F154oWb9Zt3d\n3WUfu34+FtoD86CAIsbGxuTy5cuSSqVkcXFRrly5sqHPyDRNOX36dFn9I5XUVESeNvMZhiGRSESu\nXbtWsN/n88nExIScOXNm7fwzMzOSSqVkeXl5w1B4txDKH7OwsFD2YI99+/bJ6dOn5fjx4/L5559L\nX1+f3LlzR7744gvHMg4MDMjq6qp89tlnBftHRkbENE3JZrNy8+bNtblmTu+XUXxtyGl5CcVSR4Cj\n/JJCsVis4vXwylkmKP9Yv4yR2/MqWfbHbR3AzUslxWKxtcVjo9FowTJFm9fmy3NbQDaRSFT8HkqV\nFa1HWIsP8Fap9fACgYCKRqMFwVerC3Y14Vruc3K5XMGK5MPDwxsCsJL3sJUfAmg+bgHFShJAA+Xv\nhbS8vCw7d+4Un88nd+/e3dAcV+p5pY71SqkyNsN7gDfcVpIgoAAAnmKpIwBAUyGgAABaIqAAAFoi\noAAAWiKgAABaIqAAAFoioAAAWiKgAABaIqAAAFoioAAAWiKgAABaIqAAAFoioAAAWiKgAABaIqAA\nAFoioAAAWiKgAABaIqAAAFoioAAAWiKgAABaIqAAAFoioAAAWiKgAABaIqAAAFoioAAAWiKgAABa\nIqAAVMy2bUkmkxKLxSSZTIpt214XCS3Ip5Ry3+nzqWL7gXZj27akUilZWlqSoaEhSafTYhhGzZ+j\nM9u2ZXJyUrLZ7No20zRlZmamqd8XvOPz+UQp5SvYoZRyfTzdDUAppXK5nDJNU4nI2sM0TZXL5bb0\nnFwupyzLUuPj48qyrKKvV+w8W32NclmWteH95B+RSKRm52/k+4H3vsmawgxy2qgIKKCA24XZsqyq\nn1NN6G2WyWRUIBDY0mvkAyEajapIJKIOHTrkGgzj4+OO72n9o7OzUyUSCcfnlwqfWnwmaC4EFLBF\nbhfmjo4OdfToURWPxwsuum7PicViSqnqQm+9XC6nurq6XGs05VzUnQLBKRjywTIwMFAyoPIPn8+n\nent71cDAgEokEiqTyRScKxwOq0QisfbZxePxLX0maD4EFLBFbmHi9BgeHl67oBe72JYKsGJyuZwa\nGhoqqxxuzy8ncPKB6xZitX50dnZW/ZmgORFQwBZVepEeGhpyrDGYpqkymYyyLEvt3r3b8bmJRKJm\nZXF6rUqe7/f7XWtpjXxQg2pdbgHlFwBlO3DggFy/fl2+/vrrkscuLS3J3/3d38nzzz8v9+7dE5/P\nJ9FoVH784x/LiRMnNoyC20x9M3rWbQTgqVOnij5/vYWFhYJtqVSq7Oevrq7K6upqWcfWSzgclnQ6\n7WkZ0HgMMwdczM/Py/Hjx+XOnTsSCATk8ePHcvPmzS29pmmacuDAATl//nzR46LRqASDQfnlL38p\njx492vD8n/70p/Laa69t2F5Mf3+/fPrppyLyNPBOnTolFy5c8Dx0KjExMSEXL170uhioE7dh5gQU\n4GB+fl4mJibqchHv6OgoWQMLBAKysrLiuK+np0fu379f9vm6urrk0KFD0tvbK7/5zW+2HLJeCAaD\nTVlulIeAAipgGIZcu3bNk3MXC6d2RUC1NreAog8KcHDnzp2Gnq+7u1tGRkbENE25evWqvP/++w09\nv+6i0ajXRYAHWIsPcPDss8829HzPPfecvPXWWzI1NSV79uyp+PnhcFh6e3vrULL6CIVCMjw8XNax\ng4OD8uabb9a5RNARAQU4OHv2rPj9jWtguH79uqRSKRERSafTYppm2c8dGhqSubk5+au/+qu6lC0Q\nCEhXV5ds3769YJ9pmvK9732vrNcZGhqSWCwmlmXJv//7v0smk5F4PC7PPPNM0ef8+te/Zo2/duU0\n9lwxDwpQmUxG9fT0lJyfs3mZIbfH9u3bi+5fPxE1l8upRCJRMP/I7/cXPC8/GbecuU3f+ta31I4d\nOzZs6+rqUufOnVOJRKJgXzgcdpzL1dXVtbaUUS6XU+FwuGg5iy1VlMvlVDweL5igy/JG7UNc5kER\nUEARThdfEVHd3d0qGo0qy7IcL+BOj6NHjxYNM6eJqPnVHmKxmLIsSx09erToc90u9p2dnSoej68F\nyvrXdFq4dv2+cpZj2vy8/ERkp3MU+6wrfQ5aAwEFVCl/0Q8GgyoYDDougrr+4hqPx9Xw8LBjbcCt\nZlRubaHcpZFqebHfynJMQDncAopRfEAJhmGUnFhrGIZMTU2t/T2/AsTy8rKEQqEN94B6++23i+4v\nZmhoyHF7KBQqWp6tKPecQK0xDwpoIl7cLJAbFKLemKgLtIhqa1/Ndk60DwIKAKAlt4BiHhQAQEsE\nFABASwQUAEBLBBQAQEsEFABASwQUAEBLBBQAQEsEFABASwQUAEBLBBQAQEsEFABASwQUAEBLBBQA\nQEsEFABASwQUAEBLBBQAQEsEFABASwQUAEBLBBQAQEsEFABASwQUAEBLBBQAQEsEFABASwQUAEBL\nBBQAQEsEFFCEbduSTCYlFotJMpkU27a9LhLQNnxKKfedPp8qth9oZbZty+TkpGSz2bVtpmnKzMyM\nGIbhYcmqZ9u2pFIpWVpakqGhIUmn0037XtA6fD6fKKV8m7dTgwJcpFKpDeEkIpLNZiWVSpX9GjrV\nwPKBOz09LXNzczI9PS2Tk5N1KVOl71unzwn68HtdAEBXS0tLjtuXl5cLtjnVTESkoAa2sLDgWAOr\npmaTf042m5WbN29KMBiUwcFBUUrJ3bt3pbe3V3w+n3zxxRcyNDQk9+7dcwzcvXv3yq5du+Tw4cPy\n4x//WM6cObNWjpMnT274e7nl2vy+f/7zn8trr70mb775puN7L/dzQptRSrk+nu4G2k8ul1ORSESJ\nSMHDsqyCY03T3HBMV1eXGhwcdHx+JBJRuVxu7fmZTEYFAoENx5imueEYp/JtPmepxzPPPFPR8SKi\n/H5/ReVSSinLslxfr7OzU8Xj8Q2v4Xb85s8ZreubrCnMIKeNioBCGyt18T937tyG44tdkN0e4XBY\nTUxMqN27d7seE4lE1Pj4uLIsqyAU4vF4xees1SMfHLlcTlmWVVDG8fHxkq/R3d2tXnnlFdXf3698\nPp/jMf39/SXDEK2BgALKVCpwenp61i6cuVxO7dq1q+6hsL7mkcvlVGdnp2cBFYvFHEM8X7uqJrDd\nHuFwmJBqA24BxSg+YJNoNCrvv/9+0WMCgYDs2bNH/vu//1sePnzYoJI9HUV44MABOX/+fMPOuVlf\nX5/09fXJtWvXCvZNTEzI4uKi3Lx5s2bnsyxLpqamavZ60I/bKD4CCtjEMAzHi68uBgYG5Pbt214X\no2Gi0ai89957XhcDdcQwc6BMg4ODnp5/27bi/y0fP37coJLooZa1MTQXAgrYxDRNT89/5MiRomV4\n8OCBDA8PN7BEtbFjx46qnuf1DwZ4h4ACNkmn0xIOhz07/+PHj2VmZkZ2797tuP/hw4fi8/kkkUjI\nzp07t3y+UjW2Wqn2PF7/YIB3CChgE8MwZG5uTo4ePerJ+UOhkBiGIT/84Q9dj7l+/boEAgGJx+NV\nnWP79u3S19cnkUhEpqenGxICX331VcXPMU1zbdIz2pDT0D7FMHNAKVV6vlEgEFCZTEZlMhk1NDTk\nOqen2PPX/339RNhS87HchnuvfwwODhZMtt38ME1TZTIZZVmWikajKhKJqP7+fsdjK31/6x89PT2O\n24eGhtTBgwdVT0/P2uPgwYOO87/QmsRlmDkBBRThNum0r6/P8QKanwfU19dX8oK9PhhisZjr65Va\n0SJ/zlgsphKJhIrH4xteL5PJqEgkovr6+lxDopzVMUzTVNFo1PX9FAvC7du3q3Pnzjm+ZiaTcZ1T\nhfZAQAFVqHYZnkqX+ymm2KTYSrkFbiwWczzv5vB0e1+RSGRDLSwYDKpnnnlGdXR0qG9/+9sqk8lU\n/JosddQ+CCigCtWGg9v6fIlEoqpgcbqwV2OrYVDLsMyrJDTRmtwCiom6QAn5VcOXl5clFAqVfQ+l\nap9XT7W4x1Wt31cymZTp6emC7awg0T5YSQKAiOgXnK14Y0hUhoACoC3dQhONRUABALTEWnwAgKZC\nQAEAtERAAQC0REABALREQAEAtERAAQC0REABALREQAEAtERAAQC0REABALREQAEAtERAAQC0REAB\nALREQAEAtERAAQC0REABALREQAEAtERAAQC0REABALREQAEAtERAAQC0REABALREQAEAtERAAQC0\nREABALREQAEAtERAAQC0REABALREQAEAtERAAQC0REABALREQAEAtERAAQC0REABALREQAEAtERA\nAQC0REABALREQAEAtERAAQC05C91gM/na0Q5AADYwKeU8roMAAAUoIkPAKAlAgoAoCUCCgCgJQIK\nAKAlAgoAoKX/A3bjXREB35SKAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(frameon=False, figsize=(6,6))\n", "\n", "plt.plot(X[:,0], X[:,1], 'ko', linewidth=1)\n", "\n", "plt.gca().axes.get_xaxis().set_visible(False)\n", "plt.gca().axes.get_yaxis().set_visible(False)\n", "plt.xlim(1,18)\n", "plt.ylim(1,18)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For Figure 10.19 Right\n", "#### Source: http://www.astroml.org/book_figures/chapter6/fig_great_wall_MST.html" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Get the x, y coordinates of the beginning and end of each line segment\n", "n_neighbors = 9\n", "edge_cutoff = 0.9\n", "cluster_cutoff = 10\n", "model = HierarchicalClustering(n_neighbors=100)\n", "model.fit(X)\n", "T_x, T_y = get_graph_segments(model.X_train_,\n", " model.full_tree_)\n", "T_trunc_x, T_trunc_y = get_graph_segments(model.X_train_,\n", " model.cluster_graph_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.19 Right" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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HiPR0jh/4+OP47XnmhYcf5uwBLVqwxhKNmsjIkeGHAzRvnn+y1Bo1Il8eKVpG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\nAW91tghXbhQGAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "\n", "plt.plot(T_x, T_y, 'r-', linewidth=2)\n", "\n", "plt.gca().axes.get_xaxis().set_visible(False)\n", "plt.gca().axes.get_yaxis().set_visible(False)\n", "plt.xlim(1,18)\n", "plt.ylim(1,18)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.21 Left" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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S7K/kQux/hsE9/WqtaaeHr0da08VOCI6CYpepI6GxUFi6rmnH8dDpOph/pfs5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\nr2Vi8hJZLCef7oTyELGE12C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sTOtq34szrRkHuTngCIL0VNi0yrq4NniYtU9hISz6zDrf\npaPh60+sO9JOaNQYNrnfuSf+pdCVOuX77/dz//2LKCgo4f/9v8GMHn1GlfvPmrWFWbO20Lp1Q559\ndqjHhbDqJCdnk5tbdPIzKF5/Fp550Pq6cTx8thraJFZ/3OEDsGEltO9i3dl2sj6YCg/eVl6OiIQd\nOSd/HvEZha6Ir6z6zlqHYeAQa66tHbIy4ar+sGu7VX7wGbjrb/a8ttSIQlekvsnJhrXfQ+Om0ONs\nf7dGKlDoiojYSHekiYgECIWuiIiNFLoiIjZS6IqI2EihKyJiI4WuiIiNFLoiIjZS6IqI2EihKyJi\nI4WuiIiNFLoiIjZS6IqI2EihKyJiI4WuiIiNFLoiIjZS6IqI2EihKyJiI4WuiIiNFLoiIjZS6IqI\n2EihKyJiI4WuiIiNFLoiIjZS6IqI2EihKyJiI4WuiIiNFLoiIjZS6IqI2EihKyJiI4WuiIiNFLoi\nIjZS6IqI2Ci4uh0Mw7CjHSIipwXDNE1/t0FE5LSh4QURERspdEVEbKTQFRGxkUJXRMRGCl0RERv9\nf7121DmUEJbeAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "algo = KMeans(n_clusters=9)\n", "algo.fit(X)\n", "label = algo.labels_\n", "\n", "plt.scatter(X[:,0], X[:,1], c=label, edgecolor=\"\")\n", "\n", "plt.xlim(1,18)\n", "plt.ylim(1,18)\n", "plt.gca().axes.get_xaxis().set_visible(False)\n", "plt.gca().axes.get_yaxis().set_visible(False)\n", "plt.title(\"K-Means\", fontsize=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Figure 10.21 Right" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LLoXfNsF3SwL30KWlwcDzwBVhP/xy8+bg16nwJFl0DMTEBg5csO8Wtmc3fPTh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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,6))\n", "algo = SpectralClustering(n_clusters=9)\n", "algo.fit(X)\n", "label = algo.labels_\n", "\n", "plt.scatter(X[:,0], X[:,1], c=label, edgecolor=\"\")\n", "\n", "plt.xlim(1,18)\n", "plt.ylim(1,18)\n", "plt.gca().axes.get_xaxis().set_visible(False)\n", "plt.gca().axes.get_yaxis().set_visible(False)\n", "plt.title(\"Spectral Clustering\", fontsize=14)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }