{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 1: Introduction to Clustering\n", "\n", "## Exercise 1.04 - 1.05" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import make_blobs\n", "from sklearn.cluster import KMeans\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import math\n", "\n", "np.random.seed(0)\n", "\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "X, y = make_blobs(n_samples=1500, centers=3, n_features=2, random_state=800)\n", "centroids = [[-6,2],[3,-4],[-5,10]]" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-3.83458347, 6.09210705],\n", " [-4.62571831, 5.54296865],\n", " [-2.87807159, -7.48754592],\n", " ...,\n", " [-3.709726 , -7.77993633],\n", " [-8.44553266, -1.83519866],\n", " [-4.68308431, 6.91780744]])" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:, 0], X[:, 1], c=y,s=50, cmap='tab20b')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "from scipy.spatial.distance import cdist" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-3.09897933, 4.79407445],\n", " [-3.37295914, -7.36901393],\n", " [-3.372895 , 5.10433846],\n", " [-5.90267987, -3.28352194],\n", " [-3.52067739, 7.7841276 ]])" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X[105:110]" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.02775036 10.70202291 5.54216027] Cluster Membership: 0\n", "[ 9.7303528 7.20866583 17.44505393] Cluster Membership: 1\n", "[ 4.06676751 11.11317999 5.15897011] Cluster Membership: 0\n", "[ 5.28441816 8.93146403 13.31415736] Cluster Membership: 0\n", "[ 6.29310516 13.46792103 2.66429839] Cluster Membership: 2\n" ] } ], "source": [ "for x in X[105:110]:\n", " calcs = cdist(x.reshape([1,-1]),centroids).squeeze()\n", " print(calcs, \"Cluster Membership: \", np.argmin(calcs))" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "def k_means(X, K):\n", "#Keep track of history so you can see K-Means in action\n", " centroids_history = []\n", " labels_history = []\n", " rand_index = np.random.choice(X.shape[0], K) \n", " centroids = X[rand_index]\n", " centroids_history.append(centroids)\n", " while True:\n", "# Euclidean distances are calculated for each point relative to centroids, #and then np.argmin returns\n", "# the index location of the minimal distance - which cluster a point is #assigned to\n", " labels = np.argmin(cdist(X, centroids), axis=1)\n", " labels_history.append(labels)\n", "#Take mean of points within clusters to find new centroids:\n", " new_centroids = np.array([X[labels == i].mean(axis=0)\n", " for i in range(K)])\n", " centroids_history.append(new_centroids)\n", " \n", " # If old centroids and new centroids no longer change, K-Means is complete and end. Otherwise continue\n", " if np.all(centroids == new_centroids):\n", " break\n", " centroids = new_centroids\n", " \n", " return centroids, labels, centroids_history, labels_history\n", "\n", "centers, labels, centers_hist, labels_hist = k_means(X, 3)\n" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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jDHxzSylpXduY0GkqLUnr6kYlFCihUGQYIQ5ENmYCadnY4eTLsJbX7NyKfzijQrgVhzVC11JGUmpO7bAXCVBCoTjMEVp0VSPh/hZdkH+kmnaAEgqFgpI5I3AUOeOmQMIQuErdFM1IHEdyuKF8FIrDHs2hM+aSCfh3t0cLCAtB3sQCPGPy+rXB61BECYVCQXQKkltVMKw3ZmUSNfVQKBQ9ooRCoVD0iBIKhULRI0ooFApFjyihUCgUPaKEQqFQ9IgSCoVC0SNKKBQKRY+ogKsBIqXEbNlAYO/b2GYbzpIZeEbPQ3P0nCtBocgWlFAMACklbet/R2D/IrDDgCTc9DHeHc9QOudnGLmjM22iQjEoqKnHAAjVLyVYuwjsEB2FK6QdQppeWtb8Ku39R4JNeHc8T9vGPxPY9y4yEk57n4rDk7SPKIQQ5wMPEC3k9kcp5S/S3edQ4ds9HxnpXigHJJZ/H5ZvL0bumH63b1sBZCSE5ixAiHhN9+99i7aNf4hdaCJq3LRt+gulc+7GyB1DJNiId8dzhOqXAAL3yFPIrboU3ZV827SUEmmHEJqzW3+Kw5u0CoUQQgceBs4BqoFlQoiXpJTr09nvYGObPvw1bxFuXIPmLCBnzFk4io7CDjYnvUdoBnaoBfohFJZ/P63rf4fZvC7WmIFnzNkUHHkdQmhY3j20bfwj2AfqT8hIECIhmlbeTfHxd9C09HvRYzKavcm/51UC+96j7KRforvjt05LO4J3x7/w716AjAQQmoucceeRd8RVCG1oS9sphifpHlGcAGyVUm4HEEI8BXwKyBqhsHzVNC69HWmbsSmGIFj7IZ5Rp2LkTyAS2E+iYpXSNtH76KMIt2zCt+tlQnUfxrcpTQLVrxBuWkPZyffh2/MK2FaCFiR2sJ6WVT9HWv6D2rCQppf2LU9QdMzNcXe1rL2XUMNHMT8LyEgA3+6FmG3bKT7+DpXhSZF2H8UYYE+Xn6tjx7KG5tW/Qlq+mEgASLBDBGsX4SycDIm+cTUHrrJZKYf5XYkEG2n44Baalv2AUN0HJCsXHvHvxb/nVay27SSvhCOJ+PcmacMmWPtB3BGzfWecSBy4NIzZugmzZWOvPoPi0CbdI4pEX0VxT7AQ4ibgJoDKyso0m9M3LO8eIoE6Eo4YIiECtYsRRi4y3PUl03AUHknh9G90HokE6gm3bkLoHkDi3fYUVvtOEAZ6/gQibduA3tXZ9O54Bml2L5bba6SFbQXRjGgK+1DDyiSjk+hnDNYvw1k8rf/9KQ4J0i0U1cC4Lj+PBWq6XiClfBR4FGD27NkZKnEdj5SSUMNKvNuf7v5N2wWrbWv3g0JHdxUSCdbjb1hNcP9/sHy7QRhRf0HX9qRJpG1z32wz2/t0fQIDaVp+O6VzfobQYwVxhEgyiFFTDkWUdAvFMmCyEGICsBe4CvhsmvscENHYiN8SrF2cZEWjpwZMgvsXEdz/IdD1mzpB4duMILG81fhr/k3uuPNxlc/Gu/2ZTqdnHJoT94iTht5ExbAjrUIhpbSEEN8AXiO6PPpnKeW6dPY5UMJNa/ovEnEkHs4PC6SFd9vTeEadhtW2Hc1ZgB1siL9GOHCWHI1tBWhe/SvscCvO4mnkjLug174XxaFD2uMopJQLgYXp7mew8Fe/MQgiMfyRZht171zT8VOCCywkGq1r7un8fZhtW/DvXkjJrDtxFE4aOmMVGUdF1RyEbbZm2oQhRJJshQUkZsOyeNG0TWQkQPPq/0PKYeFOUgwRh4RQmG3bCexfTLhl84AfYGfx9MRLnopO7HAL4ZZNmTZDMYRk9aawSLCR5o9+SsS/H4QGSDRnEcXH/aDfodOeMefh2/7s4Bp6qCEjhJvX4io+MtOWKIaIrB1RSBmhafmPsLx7ohuxIgFkJEgkUEvjsh/2289gB2tB0wfZ2kMPq21Hpk1QDCFZKxThxtXY4Ta6RyhKsMPdIhB73W7zerB7F/x0WCOH8aqOYtDJWqEw27ZHNz0lQEaChFu39KtdobvUiKInhBNn2fGZtkIxhGStUGjOAtCciU8KA81Z1K923SNOAuXRT4FAc3hoiExn2bKt7N/fkmmDFENA1joz3SNPoW3TY4lPCkHO6NNT3i8jYYK17xOsW4LQHLgrPoGr7Hh0dyk5lRfh3/Vi7215azd5j61Drw8QKffgvXY6wbOG176VwUICf3+7gpcW/RGHQycctpg5cwJ33XkVBQWeTJunSBPZO6Jw5FF41Ndio4qOj6GB5iR/8hfRPSOS3muH22j44BbaNv4hlqVqMa1r76Npxf8ibZO8iZ+OraL0jPut3RTc/xFGXQAhwagLUHD/R7jf2j3wDzkMEUguPG4LZjiM1xskHLZYuXIbX/3aI5im8lscqmTtiALAU3EajoIJ+HYvxPLuwsipIKfyIhz5ExJeL6WNtHy0bvg9kWB93P4GGQlitm7Gt2s+eRMuw1kyg3DjRz3akPfYOrRQvPNTC0XIe2zdITOq2Fnr4ul3Slm3MweHIZk7vY0pYwNs3JMDgGXZ7NhZxwUX3s3Xv34Bl116YtK2bNtm/fpqWtv8TJlcQXl54VB9DMUAyGqhADByx1I47aaU10gp8e+ej3fHs0jTR9JcDnYY384XyBl/MdIK9Kp/vT7xdcmOZxsbdnu464mxhE2BjO0mfXV5EYly2fgDYR58aAHhsMklF88hJ8cVd37tx7v54Y/+gc8bRGgC04xw6twj+dEPP43LpYLchjNZO/XoC+1b/oZ365OxLdrJEr5EkZaXhv98BbO1dwlbIuWJ5+XJjmcTUsLDL44iZGqdIgFgRTRMK/EW9FDI4oEHF3L+BT/h69/8Azt31gGwf38LN9/yZ+rr2/AHwvh8IcJhi0WLN3LXT54Zks+j6D+HvFDY4Tb8exYi7d4HYNnh3nvyvddOx3bFL6faLh3vtdN73cZwpa7FQUNbskFn6lwVVsRm1aod3Pjl37FvXzPP/Ot9LKt7fEo4bLH4/Y3U1qrVk+FM1k09IsFGLN8eNGcxRl5lj/kcw83rEMJApikfRIcf4lBb9ZASfAEt4RSjL20EgyaP/+0dNm+uwTQTB7I5HDqbNtcwcmT/lrQV6SdrhMK2/LSuvZ9Q0xqE5kDaEXR3GcUz/gcjb1zyG4cg7XzwrMqsFYbGNoNgGNr9OlPHRUddC5YW8ex/Smn369gDDCmJRGwWLd7I5MkVSa+RErW0OszJGqFoXnUPZssmkGY0IzYQ8dfQuOyHlJ/626Ql/JwlxyATZW86zLFtuOWR8exvciKIxkdUjggxdUyAt1YVETK7CqxkIGnxdF3j8ktPZPWqnQSC3VMLut0Ojj1mfL/bV6SfrPBRmO27MFs3gzx4+iCRdphAzdtJ79WMHPInXY3QXEmvORyJ2NDc5sC0NMKWhmlpbKtx88ry4oNEAgYiEg5D55yzj2Xu3CM59bRpeDwHomkNQ8fjcfKTu65G07LiUTxsyYoRhdm2haQPqx0m3LSW3PGXJL0/d/wn0d3ltG97mohvT9LrDifCloY/1F0QBjshjaZrXH3VaQghuPOOK1m0eCPPPvchzc1eZs6o4jNXzmX06JJB7VMx+GSFUGhGLkJoSXIxCTRn8qCdYP0KfNufwfLtRXMW4Bl7AYG9b4M89NPdJSMUFixYUoQthybL9vYdtZSU5CGE4LRTp3HaqSr9f7aRFeM9V9nxJEvZJjQnnjFnJTzn2/kiLWvuxWzbgoz4iQT2E9j7RoIpzKFLogHCR9ty+Oe7Zd1PAIOdoj8UMnnhxSWD2qZi6MkKoRC6i4Lp3wTNRZzJugv36Hk4i7pnWrLNdtq3PdmlwlcMadFT0NWhwrJNHtr93f/EK7fmDWjZs680N/m6HZNSsmlzDe9/sIl9+5PXcFUMD7Ji6gHgGXkSRk4Fvl0vYbZtRXdFd3m6kuRFCDWsBKHTt3oaHf7/7EdKeGNlMWt3mHz2zAbczgOf66p5DSzbmIc3qBOx06sYTqfBccfF773Zvr2W225/gob6dnRdI2xaHH/8RO668yry8txptUfRP7JiRNGBI388RUd/k/JTHqBk1h24y2clDbiSETNpqTwAoXsQuhs0Z+zfHvKPTL1nJNvYVeti/pJiXl1WRNgS+IMCf1Aj121z0rQ2PK4IAxVGt9vBf11xMqWleQnPOxx63CaxtrYAX/36o1RXNxIIhvH6ojtQV6zYxne/9/iAbFGkj6wZUfQVO9yaPF2b5iJ/6vUYuRVY7TvRnIW4ymYhdCehuiWEm1YNrbFpIGQKWnwGIHj8zRG88H4JR1f5idiCtTty8IcGJ4uXbUumTx/Hy/OXdzvndBo8cN91lJbmdx5bsHAFZtjq5jsxzQgbNu5ly5Z9KYOzFJnhkBQKaVv4UiSeEULDM2ouQnd282/kT72GpqUbk6bZyxbcTsmoYpM99dH4kTa/wfvrC2Jnez+KECJ5wi+nw2De6dO599cvEQp1n+LpukZtXStHHXUgcvajj7YTTHBtR18bNlZnlVDs3FnHipXbcbkcnDr3SIqKEgf+ZTuHpFBYvurEtTQ7MDwIPXEaPUdeJSWzf0Lbxj9itm4hWx2fUsJXLt7Pjx+vJGKDjC2F6rogN9dDKGQSCvWcaCZVWMXEI0Zy7jkzWPx+4p22gUCYF19axhnzju48VlSUixCJ4zU0TZCfnx2h3OGwxe0//AfLV0QLVWuaxq/ufZEbbzibz332Eynvra5u5K+Pv8OHSzbjdBpceMFxfObKU4e1fyarfBS9JlbjIxlaDwV+HAUTKT3hZ5TP+yuO4unJc3MOU6wIPPjCKH76j7FYEdEpEkLAxRfN5p9P3co3vnYBbrcDTeufM9PlcvC9/7kU00otpD5f/Mjsk5fMweVK/P0kJZxy8tR+2dOVNWt28cM7/sH1NzzMPf/3Ajt31Q24zYO5/4H5LF++lVDIIhSyCATChMMWD//2Vc48+8c8/NtXCCYIV9+0uYZrrn2IV15dSWNjO/v2NfO3J97l2ut+Q3v78M1hckgKhZE7FmEkGQIKB+5RqRW/A92RQ8nxPyK36lKEIzrP1lzF5FRdimfsBeg5Y2IrKxnEyOPg2IcXFpfwwfr8hH6ILVv3UVDg4YorTmbh/Nu54fqzcTi6X2cYGlOmjMbt7i6qQkB5eQFTpozm6OnjMMOJR29Op8HJJ02JO3b00ZVccvHsuHZ1XcPlcnDHj67sUwKbLVv2cdfdz/DFLz3I9297go8+2s6f/vwmN3/nz/z73x+zYeNe5i9YzrXXPcw7737c63ZTEQqZvPLKSuYvWE4onHhEFgya/OPJ/3DdDQ9321r/s58/SyAQxu6y2y4cjlBX38oTf39vUGxMB2I41ZCcPXu2XL68u1OsPwTrV9Cy5ldgd1F1oaM5iyg7+V40R37ym5MgpYxbZZGRME0r78Jq33HApyEcQxTQpVE0607cJdOxTR9tGx+NJgoWGjfdO4b61sQvnMOh89y/vhvnYPzzn9/i8SfexbZtLMsmJ8fJiPJCfvPQDTz+t3d56eVlhEIWUkrcLgcOp8HvHr6JiRNHAnD3T//FW2+vjfNTCAF5eW6e/Md3KCmOXxGRUrJ02Vb++cz71Ne1csQRo7jg/OM47rgJOBy9mw2/9vpH/OKeFzBNC9uWCBH1mViRCJFI92fa7XYw/6UfxGXdampqJxSyGDGiEF3v+TvzwyWb+eGPnsS2bYLB3v2Nc3JcXPulM/mvK06ivT3AFZ/+ZdLt9mWl+bz04m29anewEUKskFLOTnr+UBUKgHDzBtq3/h2zdUs00/ao08ifdFXKkO++ImWEUMNKgvveQ9oRXCNPJli3lHDd+90v1tzRuqZWO9HBXJdhuzAQQkfzjMJRNIXgvve6B4vF0HPHUTTjuzhyR8cdt60AttnGRZc/Qnt7Ymesx+PksT99g8rK+MjMmpom3nxrDT5fkJkzJnDiiZM7N2qtW7eHl15eRlOTl+OPn8jFF82K8yVYVoQHHlzAy/OX43DoWJbNuHGl/O+PP8OECSOT/u4aG9v5xf89z9KlW9B1DU0IPv3pU7jh+rNTvrjt7QE+eekvEjpQk9GxTPv1r53P9u21/Pye59mxoxZd13C7nXzly+fyyUvmJL2/pqaJz37+fsJJRhGpcCqNgQUAABS1SURBVLkMJk2q4PYfXMF11z+cVGTy89289sodfW5/MMiYUAgh7gRuBOpjh34gpVyY6p7BFopMIaUk1PAR3u1PEfHvQxj55I6/GEfBETStuDN+lAOAQHOVUDzjuwRq38e/59UuIiEADfeoU3DkT8A14gSMnNSrAv9961/4cMnmhI7I3FwXC+ff3utv7r7g8wXZtauegsIcxo4pTXltMBjms5+7n/qGNiKRqGCeU7eOr+55l5HBNsT4SvjpT+Fzn+t27/wFK7jv/pcJBLr7AFLhcGh43C5CYaubyLjdDr7x9QuZNWsiDkOnoqK4c/RYX9/G57/4wIB8CG63k1v/+5M89JuFtLb6u50XQnDySVM495wZ+ANhZs6ooqoqeSb5waYnoUj3qsd9UspfpbmPYYcQAnf58bjL46NGWz5+IEkQmMQ2vViB/fj3vHKQkEggQqh+GYVHfTVayawHrr/uLFZ+tCPhy/DFz5+eFpEAyM11xy2FpuK111fT0uqLE4nvb1uIp+P3s2sX3BQLgDtILNrbAwnT6vWEadqYZuKXPRg0uffXL+J2O7Ftm7KyAr71zQt57731LFi4ss99dW8/zPz5y/nSNWfwyKOvdxtVaJrggw838/4H0Srxui6YNWsS9/z888Mi8fAh6cwcrljeapIttwqhE6j5d4poUhENS+8FRx01jrvvupqiolxycpzk5rpwuRxcfdWpfP7zqQsjDRXvvbc+7mX5yu53DohEB34/3H57t3unTRuDYQy+E1nK6JJuKGSxd28T3/v+E4MiEh2sWr2TBx9aiBACh0PH5TIwDJ2cHCeRiB23ZByJSJYu3cLPfvHsoPU/ENI9oviGEOKLwHLgv6WUh/XuHyN3NFb7DhIt3UoZQdrJN6xJaWOb7b3ua+7cI3n5xdvYtGkvoZDJ1KljuqXPHwitrX7avQFGjijs1wjF6Yy/Z2SoLfGFu3fT2NhOU5OXiopi8vLczDi2irFjStm2bT/2QfMrl8voVXxIppBSdpsypRodvfXWWqZOGUMoZDJ+fDmGrmFZNsccO55gIMyTTy1i9ZqdFBXlcsVlJzFv3vS0JAEakFAIId4ERiU4dTvwO+AnRN+KnwD3AtclaOMm4CaAysrszDvZW3IrLyFYtzSBj0LDyKnAVT4rGuSVxInpKJjUp/50Xev1VKC31NQ08dOfPcvH63ZjGDpCCD579al86Zoz+vSAXnDBcSxdtqXzpal1FVCRQCwa84r51GW/QNoSSTR+Y3xlGVu27kvY7nAWif5g25JHHn29c6VECHA6HUSsSOfXTcf0bcOGvbz19pq0ZAwbUGtSyrOllEcn+O9FKWWtlDIipbSBPwAnJGnjUSnlbCnl7PLy8oGYM+xxFE4if/IXoisfWlSjhe5GcxVTPPP75Iw+E6El0G5h4Mgfj6Ng4hBbHE9rq58bbvotq9fsxDQjBAJh/P4QT/z9PR76zSt9amvuKUcybdrYzu3uv6+cR+Cgzx7QDB4cdSp2TCQgGseweUtikThU6bqcKmX0d2BFbCKx/zoIBsN8uGQLixb3riZNX0jb1EMIUSGl7PiLXgYMTsRLlpNbeSHuEScS2PcfbLMVZ+EUXOVzOgWiZM7dtKz6RXRTGxpSWjgLp1I049bMGg688OKSbsFCEHUEPv/CEr50zRkUFub0qq36+jbOOftYVq3aiZQ2b4yI1kH5yu53GBlqo9ZVwO8r53UeV/SOQCDMHT9+ijmzJ3HeeTOYd/rRg+LPSefy6N+AmUSnHjuBL3cRjoQcKsujA0VKidW2jUioGSNvbI/LoUPFDTf+lvUbqhOey811cecdn2Hu3O5JhLri8wW5486nWbFiG4au4e/jEqei9wgBxcV5PPybGxlfmXq0nrHlUSnlF9LV9qGOEAJH4SQyvygWT0/LdAc7KBPxvdueYO3aXZhmBCUR6UVKaGry8q1v/4nn/vXdXkWfJkMtjyp6zcUH7dE4mBkzqlLev237ftat2500hFmRHny+EEuXbhlQG0ooFL3m7LOOYeKEkd1GDi6Xg/+59VM9jig2bNjbYwlIxeBjmha79zQMqI1DMh+FIj04HAYP/+ZGnv7nYl54YSleb5ApU0dz/bVnctxxPa/I5Od7Ui7bpUqSo+g/DofBqAHWdVVCoegTLpeDL35hHl/8wrw+33vSiZOTnjMMDSmJW+5TDA6maVE1YWD7RtTUQ5E2Nm2u4amnF/H8C0toaGjD5XLw4zuuxO2KT5jjdBpKJNKIZUW48abfUb23sd9tHNLbzBWZIRgM893v/42P1+4mYttomoaUkmu/dAbXfPEMdu6s48mnFrFhQzUlpXnU1rawa9fA5tCK1AghmHf6dH5692eTnc/o7lHFYciv7n2JNWt2dcndEF3l+Ovj7zBpUgVzTzmS275/Ofv2N3PTl39PU5M3c8YeJkgpWbR4Q7/vV1MPxaDi8wV58601CRO8BIMmf/3rO50//+iOJ2lu9g56YeTDDSGimbRyc10pK8AdvEO1LyihUAwqtbWtKUOG91RHpxg1NU3R3Z+2EomBIiXcftvlLJx/OxMnJtqjGWXGjKp+L08roVAMKqWl+Zhm8h2c5WXR2iINDe0Yhpr5DhannHIkDofBt791UcIIWpfLwde/en6/21dCoRhUCgtzmDNnEobR/dFyu6PJcwDGjitNKSiK3lNUlNMpDrNnHcE9v/g8lZVlOBw6hqFzxBGjuP/X1w4o5YCSdMWgc/ttV/CVrz1CQ0M7gUAYIQQul8EZ847m/POPA6CkOI9TTp7K4vc3KcEYILfcfEnczyfMmcxT//gOzc1eNE3r9Y7eVKjlUUVasKwI7/1nPUuWbMHjcXLuuTM5atrYuGt8/hDf/e7jbNhY3emr6E+W68MVw9C46cZzGTWqCMPQmDN7Erm5/as2dlin61cMfxYt2sBvfvsK1dWNGLpGxJYq8KoHCgtzuPsnV7No0Qaef2FpbJoniERsvnzTOVz1mVP73KaKo1AMW5597sNY6b1okt2wrXaVJqIjvN3h0Bk7tpSHHriBl+cv48WXlhEOW4S77Nd/9A9vUFFRwumfOGpwbRjU1hSKXhIIhONEQpGYadPGcMlFs2lrD3LM0eOYOXMCti154u/vJfzdBYMmf/zTm0ooFIcGK1duH1AilcOFyspyLr30xLhjra3elAK7e3d90nP9Rf2lFBnBitipCs4rYlTv6b6RKzfXnTLCMi+vfw7NVKgRhSIjzJxRhdmPal+HG5Mnx+dLXb+hmmf+9T4ejxPLCnTL3+F0Glz6qYQJ7weEEgpFRsjPd/Pp/zqZZ5/7UPkpkiCE4POf+0Tnz395/N88/td3CIWthCMKj8dJVdWIfuUK6QklFIohIxy2eOwvb/Pccx/S7g1SWprHCXMmsWr1Lvz+IJZlo2kibv9HR3V0IUi4L0TXNWbNOoL2Nj+bNtccMntHhIDvf+8yKiqKeemlpTz6hzdoavYluVZwwpxJXHTRLOadPj0t5RaVUCiGBNu2ueU7j7F+/R5CsaCqxkYvS5dt5fzzjuOGG87G0DVWr9lFS7MXry9ES4uXkpJ8Tj5pKvf88nnWr6+OS3hz7ZfO4LJLTyQ3141lRXjsL2/zzL8+wO8PZbVguFwOnn3mVkpK8nn0D2/w1NOLUo66PG4H5547k7PPOjZtNimhUAwJy5ZvY+OmvZ0i0UEwaLLwlZV84fOnU1JRzGmnTkt4/8MP3cj27bVs3lJDYUHHfpID35yGoXPjDedww/VnEwya+HxBvnDNg7S2+tP6udLBUdPGUlKST2urn388+Z8eo1VNK0Jra+LRxmChhEIxJPz73x93K87bgRCC99/fyBVXnJyyjYkTRzJx4siU1wgh8HicCAHt7YF+25tOUiURFkJw0klTAFi2fCuGofcoFIahM3XK6ME2Mw61PKoYElJvFZCDulJqmhZ3/PjpYTv9qKws589/+hpV47tX75JS8ufH3uaVV1fSm8wRuq4xalQRM2dOGHxDu6CEQjEknH76dDweZ8JzUtL5LToY/ObhV1i2fGAFb9LJ/v0tTKgaydVXn4bT2d3xGAqZ/Pq+lzn22CqsFEvIDofOlCmjefD+69NeL0UJhWJIOPGEyQmLB7ndDs45+1jGjikdlH5CIZOX5y8nFOr/LtTCQk+c03SwESJa6m/BwhWEw8mFYNeuOj732dO6VWfTdY0RIwp55Pdf4U9/+Bqlpflps7UDJRSKIUHXNR568Houu/QEPB4nmiYoLMzhumvP4rbvXz5o/dQ3tKX8dhWClCIghOCsM4/F4Uif+862JUVFuZg9OSnNCDdcfza33HwxI0cWIURUWC/91An8/YmbOXLqmLTZeDDKmakYMtxuJ9/+1sV88xsXYpoRnE5j0IfMxUW5KYfrY8aUcvdPPssNNz6MZXXfzu5yGZx7zkwmTBjJ/Q/MT7jlPcfjpLAwh8Ymb0JH48GxIF1xOHTmzYtOw04/fTrbt9d2WwmCaD6PY44ZjxCCSy6ewyUXz8GyIui6lpGyjGpEoRhyNE3D5XKk5YHPzXVzyilHJgw6crsdXHXlXKZMruDyy07sNqR3uRzMnnUExxxTyRWXn8SdP76SsliOT4AxY0r43cM38uYbd/LMP29l5MiibhvbdF2jrKyAB+6/jpKSvLis2B6Pk/HjR3Drdz4FwIUXHI8nx9lthON2O7jqM6d227NhGHrGarcOKHGNEOLTwJ3ANOAEKeXyLuduA64nWtThW1LK13pqTyWuUQwGra1+bvrK72loaIul4gOXy8mJJ07m7ruuRtejBYnmL1jO4397l9raVoqLcrnyylP4zJVzu4lMOGxhGFq3uqmNje384Id/Z/PmGgwjGkE6oWoEP//Z5xgZq/W5fkM1b8XKF5x88lROPGEy7767jt898hr79jWjCUFBYQ5tbX50XcflMrjmC/O46qpTh1QU0prhSggxDbCBR4BbO4RCCHEU8CRwAjAaeBOYIqVMuQtICYVisDBNi3ffW8/ixRtxuR2cd+5MZg4gXX0q9uxpYO/eJkZVFFE1PnWNzxdfWsr9DywgFDoQaalpgoKCHB68/zqqqkakJQS7J9Ka4UpKuSHWycGnPgU8JaUMATuEEFuJisYHA+lPoegtDofB2Wcd2+uw5t27G3ji7+/y0aod5Od5uPyyEzn//ON69dKOG1fGuHFlPV5nmha/efiVOJGAqHPT7w/xzrvruGFSRZK7M0u6fBRjgD1dfq6OHVMohh2rVu/gS9c9xMJXVrJ3bxMbN+3l1/e/zM3feSylY7SvbNpUkzQiMxy2eOvttYPW12DTo1AIId4UQnyc4L9PpbotwbGEvyIhxE1CiOVCiOX19YOfmUehSIWUkh/f+TTBoBm3UhEMmqxfv4fX31g9aH31NO3JjJuyd/Q49ZBSnt2PdquBrtVGxgI1Sdp/FHgUoj6KfvSlUPSbTZtq8HqDCc8FgybPv7CECy84flD6mjp1NHqSGA6n0+Dcc2cMSj/pIF1Tj5eAq4QQLiHEBGAysDRNfSkU/cbnD6YMwEomIv3BMHRuvvnibiX/dD1apOfyy1JvisskA3JmCiEuAx4CyoEFQohVUsrzpJTrhBD/BNYDFvD1nlY8FIpMMHnSaEwz8aNpGBqzZx0xqP1dcP7xFOTn8PtHXmP7jtpOp+vXvnoeBQWeQe1rMFEFgBSHPff++iXmL1jRbTXC43HyxOPfpqKiOC392rbdLTYjU6gCQApFD3z7WxehaYIXX1qGw6Fj25Li4jz+98efSZtIAMNGJHqDGlEoFDG83iDbtu0nL8/NxIkjMxYunQnUiEKh6CV5eW5mzKjKtBnDkuwZ+ygUioyhhEKhUPTIsPJRCCHqgV0HHS4DGjJgTjKUPalR9qRmuNozXkrZPYlnjGElFIkQQixP5WQZapQ9qVH2pCZb7VFTD4VC0SNKKBQKRY9kg1A8mmkDDkLZkxplT2qy0p5h76NQKBSZJxtGFAqFIsMMS6EQQnxaCLFOCGELIWZ3OX6OEGKFEGJt7P9nZtKe2LnbhBBbhRCbhBDnDYU9CeybKYT4UAixKpYE6IRM2HGQTd+M/U7WCSH+L9P2AAghbhVCSCFEz3nr0mvHL4UQG4UQa4QQzwshijJkx/mxv9FWIcT3U14spRx2/xHN6j0VeAeY3eX4ccDo2L+PBvZm2J6jgNWAC5gAbAP0DPy+XgcuiP37QuCdDP/9ziCaUNkV+3nEMHimxgGvEY3TKcuwLecCRuzf9wD3ZMAGPfa8TgScsef4qGTXD8sRhZRyg5RyU4LjH0kpOzJlrQPcQghXpuyhSxJhKeUOoCOJ8FAjgY4CFIUkySY2hHwV+IWMJldGSlmXYXsA7gO+S5KUjEOJlPJ1KWVH1Z8PiWaAG2pOALZKKbdLKcPAU0Sf54QMS6HoJVcAH3U8jBliuCQRvhn4pRBiD/Ar4LYM2NCVKcBpQoglQoh3hRBzMmmMEOKTREefg5cAc/C4DnglA/326dnN2O5RIcSbwKgEp26XUr7Yw73TiQ7Zzs2wPb1OIjxQUtkHnAXcIqV8VghxJfAnoD+5TgfLHgMoBk4C5gD/FEJMlLExbwbs+QGD+KwM1J6O50kIcTvRDHB/H0rbYvTp2c2YUMj+Je1FCDEWeB74opRyW4bt6XUS4YGSyj4hxOPAt2M/PgP8MR029MGerwLPxYRhqRDCJrqnIG1p1pPZI4Q4hqj/aHUsv8RYYKUQ4gQp5f6htqeLXdcAFwNnpVNAU9CnZzerph4x7/AC4DYp5eJM28PwSSJcA5we+/eZwJYM2NCVF2J2IISYQtRZlpGNUFLKtVLKEVLKKillFdEX5Ph0ikRPCCHOB74HfFJK6c+QGcuAyUKICUIIJ3AV0ec5MZn0/qbwyF5G9A8aAmqB12LHfwj4gFVd/ku7Rz2ZPbFztxP1Hm8itvKQgd/XqcAKop7rJcCsDP/9nMATwMfASuDMTD9TXWzbSeZXPbYS9Q90PMO/z5AdFwKbY8/v7amuVZGZCoWiR7Jq6qFQKDKDEgqFQtEjSigUCkWPKKFQKBQ9ooRCoVD0iBIKhULRI0ooFApFjyihUCgUPfL/GDyG3enC4TYAAAAASUVORK5CYII=\n", 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k6722hE5TaUm61rYpoUAJhSLDCHEgsjETSMvBiSSfhrX8Zt9S/CMZFcKtOKIRupYyklJza0e8SIASCsURjtCisxoJ17fogsKj1bADlFAoFJQtrMRV4o4bAglD4Cn3UjI3cRzJkYbyUSiOeDSXzqRLpxHY0xMtICwEBdOL8E0qGNECr8MRJRQKBdEhSH5NUVYvzMokauihUCgGRQmFQqEYFCUUCoViUJRQKBSKQVFCoVAoBkUJhUKhGBQlFAqFYlCUUCgUikFRAVeHiJQSs3Mjwb2v4pjduMvm4pt4Fppr8FwJCkWuoITiEJBS0r3htwT3LQMnAkgi7e/j3/ko5Qt/hJE/MdMmKhSjghp6HALhlhWEmpaBE2Z/4QrphJGmn851d6f9+naoHf/OJ+je9GeCja8j7Ujar6k4Mkl7j0IIcQHwC6KF3P4opbwz3dccK3r3LEHaAwvlgMQKNGL17sXInzTi9h0riLTDaO4ihIjX9MDeV+je9IfYgSaiwUv35r9QvvAHGPmTsENt+Hc+TrjlHUDgHX8a+TWXo3uSL5uWUiKdMEJzD7ie4sgmrUIhhNCBe4FzgXpgpRDiaSnlhnRed7RxzF4CDa8QaVuH5i4ib9JiXCXH4oQ6kp4jNAMn3AkjEAorsI+uDb/F7Fgfa8zAN+kcio7+HEJoWP46ujf9EZwD9SekHQI7TPvqH1B60m20r/hmdJuMZm8K1D1PsPENKk75Cbo3fum0dGz8O/9JYM+zSDuI0DzkTTmfghnXILSxLW2nyE7S3aNYBGyTUu4AEEI8DHwYyBmhsHrraVtxK9IxY0MMQajpbXwTzsAonIYd3EeiYpXSMdGH6aOIdG6md/czhJvfjm9TmgTrnyPSvo6KU39Ob91z4FgJWpA4oRY63/0x0goc1IaFNP30bH2QkuNvijur872fEm5dE/OzgLSD9O5Zitm9g9KTblMZnhRp91FMAur6fa6PbcsZOtbejbR6YyIBIMEJE2pahrt4FiR642ouPBXzU3bz+2OH2mh962baV36bcPNbJCsXbgf2Eqh7Hqt7B8kr4UjswN4kbTiEmt6K22L27IoTiQOHRjC7NmN2bhrSd1Ac3qS7R5HoVRR3BwshbgRuBKiurk6zOcPD8tdhB5tJ2GOwwwSbliOMfGSk/0Om4So+muI5X+7bYgdbiHRtRug+QOLf/jBWzy4QBnrhNOzu7cDQ6mz6dz6KNAcWyx0y0sKxQmhGNIV9uHV1kt5J9DuGWlbiLj1m5NdTHBakWyjqgSn9Pk8GGvofIKW8D7gPYMGCBRkqcR2PlJJw62r8Ox4Z+Kbth9W9beBGoaN7irFDLQRa1xLa92+s3j0gjKi/oH970sTu3jI828yeYR2fwEDaa2+lfOGPEHqsII4QSToxasihiJJuoVgJzBJCTAP2AtcAH0vzNQ+JaGzEbwg1LU8yozFYAyahfcsI7Xsb6P+mTlD4NiNILH89gYZ/kT/lAjzjFuDf8Wif0zMOzY238pSxN1GRdaRVKKSUlhDiy8ALRKdH/yylXJ/Oax4qkfZ1IxeJOBJ357MCaeHf/gi+CR/A6t6B5i7CCbXGHyNcuMuOw7GCdKy9GyfShbv0GPKmXDhk34vi8CHtcRRSyqXA0nRfZ7QI1L80CiKR/Uizm+bXPr3/U4IDLCQaXevu6vt9mN1bCexZStn8O3AVzxw7YxUZR0XVHIRjdmXahDFEkmyGBSRm68p40XRMpB2kY+3/ImVWuJMUY8RhIRRm9w6C+5YT6dxyyDewu3RO4ilPRR9OpJNI5+ZMm6EYQ3J6UZgdaqNjzQ+xA/tAaIBEc5dQeuK3Rxw67Zt0Pr07HhtdQw83pE2k4z08pUdn2hLFGJGzPQopbdprv4vlr4suxLKDSDuEHWyibeV3RuxncEJNoOmjbO3hh9W9M9MmKMaQnBWKSNtanEg3AyMUJTiRARGIQ263YwM4Qwt+OqKRWTyroxh1clYozO4d0UVPCZB2iEjX1hG1K3SP6lEMhnDjrjgp01YoxpCcFQrNXQSaO/FOYaC5S0bUrrfyFFAe/RQINJcPV/Eswm1rsYMtmTZIMQbkrDPTO/40ujffn3inEORNPDPl+dKOEGp6k1DzOwjNhbfqg3gqTkL3lpNXfTGB3U+lwerDAylctK/8DkIzkI6Ju3QOJcffjOYqyLRpijSRuz0KVwHFx34x1qvY/zU00NwUzvoUuq8y6blOpJvWt26me9MfYlmqltP13s9pX/U/SMekYPpHYrMoioFIZLgVnEh0KbtjEml7j7aVt+LY2RKmrhhtcrZHAeCr+gCuomn07lmK5d+NkVdFXvXFuAqnJTxeSgdp9dK18XfYoZa49Q3SDmF2baF39xIKpl2Bu2wukbY1Y/VV4vC+soeC+9ejtwSxx/nwf3YOocXZtbI2Hhu7t56W1z9DwaxPkT/l/KRHSulgdm3DMXtwFdage8vH0E7FSMlpoQAw8idTfMyNKY+RUhLYswT/zseQZi9Jczk4EXp3PUne1EuQVnD0jR0C3lf2UHTPGrRwVMSM5iBF90QFK7vFIiq2PZv/grRN8iYvRjN8cfsjnZvpXHd3LKmOhpQmnooFlBz3lQMrWRVZicimUNwFCxbI2traUW+3e8sDBOueRzpDi63Q3CU4kc5Rt2MoVHziOYzmgSJlVfpoffDCDFg0QoSOq+Roio++EaNgMnawhda3bho4U6W58VTMp3Tu1zNjpwIAIcQqKeWCZPsP+4G4E+kmULd0yCIRPSczIgGgtyTuySTbnrVIG7NjA20rvoUVbKa3bikyUYIcJ0K4tRb74NWriqwi54TCDrURbnsXs2f3kNZ1RDrWI0TujLDscb5hbc9uJNIO07vz8WggW5IgLSFcmN07xtg2xXDImSfIsQJ0vXcP4fZ1CM2FdGx0bwWlc/8bo2BK8hNzbPbC/9k5cT4KAMej4//snAxadSg4hFtWYiRxMEeRamo1y8mZp6jj3bsIt62LLnW2AuCEsQMNtK38Do7Zm/Q8d9nxyETZm7KU0OJqum86EavShxRR30T3TSdmvSMzJUInb8r5SR2WQvfgKlELzLKZnOhRmD27Mbu2gDx4nl4inQjBhlfJn3ppwnM1I4/Cmdfi3/bwsPwUmSS0uDq3haE/wsA34QN4KhbgGbeQcEvtAYemMBCaQckJ/6UKDmU5uSEU3VtJmujViRBpfy+pUADkT70M3TuOnu2PYPfWJT1OkQaERt7USxFCUHzcTYRbagnUPY9jduEuOYa8qZdg+MZn2krFIOSEUGhGPkJoSXIxCTR3cdJzQy2r6N3xKFbvXjR3Eb7JFxLc+yrI3OhdHA5YvXXonhKEEHgrF+KtXJhpkxTDJCeEwlNxEslStgnNjW/S4oT7enc9Rc/2R/qK99jBAMG9L4FMVjxHMeo4EQL1L+IpOz7TligOgZwYGArdQ9Gcr4DmIc5k3YN34lm4EzjCHLOHnu0P9avwFUNaJK+ypUgHTmRgHlIpJZu3NPDmW5tp3Je8hqsiO8iJHgWAb/wpGHlV9O5+GrN7G7onusrTkyQvQrh1NQid4dXTECRPNqsYEZormoe0Hzt2NHHLrQ/S2tKDrmtETIuTTprO9+64hoICb4YMVaQiZ4QCwFU4lZLjvjKkY6VtJi2VB/SV95PSIVp0HQpmfYqeTb8fDVOPHDQPvomLCTW9iTQHRrQKYZA3+by+z93dQb7wpfvw+4NxaT9WrdrON775AL+5N/W6HUVmyCmhGA5OpCt5ujbNQ+FR12HkV2H17EJzF+OpmI/Q3YSb3yHS/u7YGpvTOLhLZhFseHngLs1F6fzb4woGPbt0FWbEGpAbyDRtNm7ay9atjcyaVZVmmxXD5bAUCulY9KZIPCOEhm/C6QjdPcC/UXjUp2lfsSlpmj1FPzQXnnGn0L3pjwlrtAqhRyuQFc/q27ZmzQ5C4cTDQSFg46b6nBKKXbuaWbV6Bx6PizNOP5qSkvxMm5QWDkuhsHrrE9fS3I/hQ+iJ0+i5CqopW/B9ujf9EbNrK4ef41NEK7DbEZDJCzAPBaOgGl/VGURaE6/4lXaIQP3LeMef2retpCQfIUTCdTqaJigszI01LZGIxa3f+Tu1q6KFqjVN4+6fPsUN15/Dxz/2wZTn1te38dcHXuPtd7bgdhtcdOGJfPTqM7LaP3NYCsX+Gh/J0AYp8OMqmk75oh9hmwE6194ZFYwUVc1zB4Fv0jkUzvoEwcZ/49/2f1FfzkjEUHNRfMznowmAUiDtQNznyy5dyMuvrCMUGtirkBJOO/Wo4dtyEOvW7eYf/1xOY0MHs2dP4qMfPY2aqckzno2Ee36xhNrabYQj8cPbe3/zPH/68ytcdeUpXPe5xXi98S+kzVsa+OKX7iMcNnGc6D36fw++zvPPv8uf//SlrBXKw1IojPzJsbdmgqAq4cI7IbXi70d35VF20nfx73ycQN1zSLMHzVOKt+pMpBUm0r4OO7gvde8l3RgFYPUy1Nkaq2cXmquA/OoLyZv0IXp3PxOrZn6QP0foGAVTsXv3Jgh9F+iecozCaWieUmRSX5ALd/mJcZuOO66aSy9ZwDNLavvEQtc1DEPntu9ejccz9CptW7c28tAjy9i2rZGJVWV89OrTWL1mB3/7+78Jh02khC1bG3n+hTXcfttHOOvM44bcdjLCYZNXX32PJc/WYlmJBTYUMvn7Q/9m+ZubeOAvX8UwDmR1/9GPHyMYjH/pRCI2zS1dPPi3N/jC55NnB8skh23imlDLKjrX3R3fExA6mruEilN/iuYqHHabUkqEOBBKLu0I7au/h9Wzs9/6BVeCNSnpQKNk/h14y+bgmL10b7ovmihYaKmLH2kuxp3x2zgHo3/7P/Dvejz6SpcWQveieSsom/8/9O58nMDel2O/RwmaB6EZlC38Aa6C6HqUrvW/Jrhv+UG9LoEw8qg4/VfoB0XOSilZsXIb/3j0TVqau5gxYwIXXnAiJ544DZdraO+uF15cw513PYlpWjiORAhwuwws28a2B97TXq+LJU9/m7y8AwvT2tt7CIctKiuL0fXBQ4refmcL3/nuQziOk7BHlIi8PA+f/cyH+I+rTqGnJ8hVH/kJppn4xVJRXsjTT90ypHZHm8ES1xy2QgEQ6dhIz7a/YXZtjWbanvABCmdekzLke7hIaRNuXU2o8Q2kY+MZfyqh5hVEmt8ceLDmjdY1tXqIBo71eyMJAyF0NN8EXCWzCTW+MTBYLIaeP4WSud/AlT8xbrtjBXHMbtre/m+klXhFrdC9lJ/8E4yDzrWCTYT2LUdaAdylx+Iun9e3UCvStYVg/cs4kU5cZceRN3ExmuuA0046Ft2b7yfY8GosM7eFkTeRkuNvSpkCoK2thzv/9wlWrNiKrmtoQvCRj5zG9dedk/LB7ekJctnldxJO4hRNhMulc8XlJ/OlL17Ajh1N/PiuJ9i5swld1/B63Xz+P8/jskuTh5Y3NLTzsU/cQyQy/MJHHo/BzJlV3Prtq/jcdfcmFZnCQi8vPHfbsNsfDTImFEKIO4AbgP2D2G9LKZemOiddqfDGGikl4dY1+Hc8jB1oRBiF5E+9BFfRDNpX3ZHA3yHQPGWUzv0GwaY3CdQ9308kBKDhnXAarsJpeCoXYeSlnhVoX/NDIq1rSDQcEUYelWf+GZGGQsyOFYiuqXEVYuRNSHlsKBThYx+/h5bWbmz7gGB6vS7OWXwC377lqqTnLnl2FT+/55kBXfjBcLk0fF4P4Yg1QGS8Xhdf/tJFzJ8/HZehU1VV2td7bGnp5hOf+gU9PSPPMub1uvn6/7uMX/16KV1dgQH7hRCcespszjt3LoFghHlza6ipGV2/SioGE4p0+yh+LqW8O83XyDqEEHjHnYR3XHzUaOf7v0gSBCZxTD9WcB+BuucOEhIJ2IRbVlJ87BeGlIS2YPrVtLe/P0CQhOYhv+aKtIgERJf0u/tNhabihRfX0tnVGycSEB3fv/jSWq6/7hwqKxP3/Hp6gljW8P1Cpulgmokf9lDI5Kc/ewqv143jOFRUFPHVr1zEG29s4Nmlq4d9rYHtR1iypJbPfPpsfn/fiwN6FZomeOvtLbz5VrRKvK4L5s+fyV0//sSw/DbpIifWehwuWP56ks0wCKETbAm5nMkAABMBSURBVPhXimhSEQ1LHwLu4lmUnPD/0FxFCN0bjULV3ORNvZT8mitGZvwo88YbG5J2wXVdY/Wa5KnxjjlmUpyDcLSQEoLBCOGwxd697XzzWw+Oikjs5921u/jlr5YihMDl0vF4DAxDJy/PjW07cVPGti1ZsWIrP7rzsVG7/qGQ7h7Fl4UQnwJqgf8npTyiV/8Y+ROxenaSaEggpR1LPptYSKR0cMyeIV/LO24BnjP/GM1FaUcwiqYPSJ9/KHR1BejxBxlfWTxkB2R/3O7k55imhd1vRqGtrYf2dj9VVaUUFHiZe0INkyeVs337PpyDhs4ej0E4nL0FlKWUA4ZMqXpHr7zyHkfNnkQ4bDJ16jgMXcOyHI4/YSqhYISHHl7G2nW7KCnJ56orTuGss+agaaP//j8koRBCvAwkGozeCvwW+D7Rp+L7wE+BzyVo40bgRoDq6sMkq1MS8qsvJdS8IoGPQsPIq8Izbn4sZiOxE9NVNHNY1xNCH/JQYKg0NLTzwx89xvvr92AYOkIIPnbtGXzm02cP6wa98MITWbFya0I/g2U5/On+Vzh2zmR++tOneXftLqQjkYDH42JqdQVbtzUmbDebRWIkOI7k9/e92DdTIgS43S5sy+573ewfvm3cuJdXXl3H97937aiLxZjMegghaoAlUsqUE9mHizMzFb17ltKz9QFAghOdihRGPuULf4gwfLQs++LAGQthxILAfpwRm/fT1RXg2o//jO7uYF+wEEQdgR++bBFf++rFQ27Lth2+dvOfWbNmR9Ka0LquDfBhKFLj87m5/bar+eAHjh3WeRmr6yGE6O+avwJ4P13XyiXyqy9i3On3UjD9WvKmXkbxnC8z7ozfoPvGobkKKFv4A3Tf+JhvIQ80N+6SYyg98dZMm86TT71DMBiJEwmIOgKfePKdhN78ZLS0dHPuOSekzJWpRGL4BIMRbrv9Yf77Gw/w8itrR+T0TUQ6fRT/K4SYR3TosQv4zzReK6fQveUUTLs84T5XQTUVp9+L1b0dO9yBUTB50OnQseLf/96YtGvvcum8//4eTj89dTbt3t4Qt93xCKtWbcfQNRxHicFoE4lYLH9zE2++tYnS0me599c3MLV63CG1mTahkFJ+Ml1tH+4IIXAVzyTzk2LxDDZNl8pBuZ9v3vIg7723G9O0ORxWz2QzUkJ7u5+vfu1PPP7Pbwwp+jQZanpUMWQuuWQBXm9ysZg7tybl+dt37GP9+j1JQ5gV6aG3N8yKFVsPqQ0lFIohc87i45k+bfyAnoPH4+K/v/7hQXsUGzfujVsroxgbTNNiT92h1XY9LFePKtKDy2Vw769v4JF/LOfJJ1fg94eYfdRErvvshzjxxOmDnl9Y6Es5bScESWdAFCPH5TKYML7kkNpQQqEYFh6Pi0998iw+9cmzhn3uKScnj+kwDA0p1UxHOjBNi5pph7ZuRA09FGlj85YGHn5kGU88+Q6trd14PC5uv+1qvB4XmnZgCOJ2G1kpEuc2r+ex2ntZtvzHPFZ7L+c2r8+0SSPCsmxuuPG31O9tG3Ebh/Uyc0VmCIUifONb/8f77+3Bdhw0TUNKyWc/czaf/tTZ7NrVzEMPL2PjxnrKygtoaupk9+5DG0OPNuc2r+db25fi67f2JqgZ3DnjIl6qzL3K8kIIzjpzDj/8wceS7c9MwJXiyOXunz7NunW7CYVNTNMmHDaJRCz++sBrLH9zEzU1ldzyrSu5665Psn17E3v2jPxNly4+v+e1OJEA8DkWn9/zWmYMOkSklCxbvnHE5yuhUIwqvb0hXn5lXcIEL6GQyV//+lrf5+/e9hAdHf6EiXYzzfhw97C2ZxIhopm08vM9pJpUOniF6nBQQqEYVZqaulIuAa+rjw4xGhrao6s/newTCYAmT9GwtmcSKeHWW65k6ZJbmT49ecKguXNrRjw9rYRCMaqUlxdimslXcI6riD5ora09GEb2Trr9rvosglq8fUHN4HfVZ2XGoEE47bSjcbkMvvbVixNG0Ho8Lr70hQtG3L4SCsWoUlycx8KFMzGMgbeW1+vi2mvOAGDylPKUgpJpXqqcw50zLqLRU4QDNHqKstaRWVKS1ycOC+bP4K47P0F1dQUul45h6MyYMYF7fvZZjj02ef7SwVCzHopRp6PDz+e/+HtaW3sIBiMIIfB4DM4+6zi+c+t/9HV/v33r31j+5uasFoxc4H/u+CjnnjN3wPaODj+aplFcnDdoG0d0Fm5F5rAsmzf+vYF33tmKz+fmvPPmcewxk+OO6Q2E+cY3HmDjpvo+X8VIslwfqRiGxo03nMeECSUYhsbCBTPJzx9ZtTElFIqsZtmyjfz6N89RX9+GoWvYjsy6wKtso7g4jx98/1qWLdvIE0+uiA3zBLbt8J83nss1Hz1j2G1mOgu3QpGUxx5/m3t/81xfkt2Io1aVJmJ/eLvLpTN5cjm/+sX1PLNkJU89vZJIxCLSb73+fX94iaqqMs784PAyXA1qw6i2plAMkWAwEicSisQcc8wkLr14Ad09IY4/bgrz5k3DcSQP/u2NhL+7UMjkj396WQmF4vBg9eodh5RI5Uihunocl19+cty2ri5/SoHdsyd14eiRoP5Sioxg2c5Q6yof0dTXDQxvz8/3poywLCgYmUMzFapHocgI8+bWYI5S4tfDmVmz4vOlbthYz6P/fBOfz41lBQfk73C7DS7/8KJRt0MJhSIjFBZ6+ch/nMpjj7+t/BRJEELwiY9/sO/zXx74Fw/89TXCESthj8Lnc1NTUzmiXCGDoYRCMWZEIhb3/+VVHn/8bXr8IcrLC1i0cCbvrt1NIBDCshw0TcSt/3C5dCzLQQgSrgvRdY3582fQ0x1g85aGrF07MlyEgG998wqqqkp5+ukV3PeHl2jvSFKhXggWLZzJxRfP56wz56Sl3KISCsWY4DgON//X/WzYUEc4FlTV1uZnxcptXHD+iVx//TkYusbadbvp7PDj7w3T2emnrKyQU085irt+8gQbNtTHJbz57GfO5orLTyY/34tl2dz/l1d59J9vEQiEc1owPB4Xjz36dcrKCrnvDy/x8CPLUva6fF4X5503j3MWn5A2m5RQKMaElbXb2bR5b59I7CcUMln63Go++YkzKasq5QNnHJPw/Ht/dQM7djSxZWsDxUX715MceHMahs4N15/L9dedQyhk0tsb4pOf/uWwihJlC8ceM5myskK6ugL8/aF/Dxqtalo2XV2JexujhRIKxZjwr3+9n7DOKES7zm++uYmrrjo1ZRvTp49n+vTxKY8RQuDzuRECenqCI7Y3naRKIiyE4JRTZgOwsnYbhqEPKhSGoXPU7ImjbWYcanpUMSakXiogR3Wm1DQtbrv9kawdflRXj+PPf/oiNVMHVu+SUvLn+1/luedXM5TMEbquMWFCCfPmTRt9Q/uhhEIxJpx55hx8PnfCfVLS9xYdDX5973OsrD20gjfpZN++TqbVjOfaaz+A2z3Q8RgOm/zs589wwgk1KWuHulw6s2dP5Jf3XJf2eilKKBRjwsmLZiUsHuT1ujj3nBOYPKl8VK4TDps8s6Q2aY3UoVBc7Itzmo42QkRL/T27dBWRSHIh2L27mY9/7AMDqrPpukZlZTG//93n+dMfvkh5eWHabN2PEgrFmKDrGr/65XVccfkifD43miYoLs7jc59dzC3funLUrtPS2p3y7SoEKUVACMHiD52Ay5U+953jSEpK8jEHc1KaNtdfdw4333QJ48eXIERUWC//8CL+9uBNHH3UpLTZeDDKmakYM7xeN1/76iV85csXYZo2brcx6l3m0pL8lN31SZPK+cH3P8b1N9yLZQ1czu7xGJx37jymTRvPPb9YknDJe57PTXFxHm3t/oSOxoNjQfrjcumcdVZ0GHbmmXPYsaNpwEwQRPN5HH/8VIQQXHrJQi69ZCGWZaPrWkbKMqoehWLM0TQNj8eVlhs+P9/LaacdnTDoyOt1cc3VpzN7VhVXXnHygC69x+NiwfwZHH98NVddeQp33H41FRUHkulOmlTGb++9gZdfuoNH//F1xo8vGbCwTdc1KiqK+MU9n6OsrCAuK7bP52bq1Eq+/l8fBuCiC0/Cl+ce0MPxel1c89EzBqzZMAw9Y7VbDylxjRDiI8AdwDHAIillbb99twDXATbwVSnlC4O1pxLXKEaDrq4AN37+d7S2dsdS8YHH4+bkk2fxg+9di65HCxItebaWB/7vdZqauigtyefqq0/jo1efPkBkIhELw9AG1E1ta+vh29/5G1u2NGAY0QjSaTWV/PhHH2d8rNbnho31vBIrX3DqqUdx8qJZvP76en77+xdobOxAE4Ki4jy6uwPouo7HY/DpT57FNdecMaaikNYMV0KIYwAH+D3w9f1CIYQ4FngIWARMBF4GZkspU64CUkKhGC1M0+L1NzawfPkmPF4X5583j3mHkK4+FXV1rezd286EqhJqpqau8fnU0yu45xfPEg4fiLTUNEFRUR6/vOdz1NRUpiUEezDSmuFKSrkxdpGDd30YeFhKGQZ2CiG2ERWNtw7legrFUHG5DM5ZfMKQw5r37Gnlwb+9zpp3d1JY4OPKK07mggtOHNJDO2VKBVOmVAx6nGla/Pre5+JEAqLOzUAgzGuvr+f6mVVJzs4s6fJRTALq+n2uj21TKLKOd9fu5DOf+xVLn1vN3r3tbNq8l5/d8ww3/df9KR2jw2Xz5oakEZmRiMUrr743atcabQYVCiHEy0KI9xP8+3Cq0xJsS/grEkLcKISoFULUtrSMfmYehSIVUkpuv+MRQiEzbqYiFDLZsKGOF19aO2rXGmzYkxk35dAYdOghpTxnBO3WA/2rjUwGGpK0fx9wH0R9FCO4lkIxYjZvbsDvDyXcFwqZPPHkO1x04Umjcq2jjpqIniSGw+02OO+8gbU5soV0DT2eBq4RQniEENOAWcCKNF1LoRgxvYFQygCsZCIyEgxD56abLhlQ8k/Xo0V6rrwi9aK4THJIzkwhxBXAr4BxwLNCiHellOdLKdcLIf4BbAAs4EuDzXgoFJlg1syJmGbiW9MwNBbMnzGq17vwgpMoKszjd79/gR07m/qcrl/8wvkUFflG9VqjiSoApDji+enPnmbJs6sGzEb4fG4efOBrVFWVpuW6juMMiM3IFKoAkEIxCF/76sVomuCpp1ficuk4jqS0tID/uf2jaRMJIGtEYiioHoVCEcPvD7F9+z4KCrxMnz4+Y+HSmUD1KBSKIVJQ4GXu3JpMm5GV5E7fR6FQZAwlFAqFYlCyykchhGgBdh+0uQJozYA5yVD2pEbZk5pstWeqlHJgEs8YWSUUiRBC1KZysow1yp7UKHtSk6v2qKGHQqEYFCUUCoViUHJBKO7LtAEHoexJjbInNTlpT9b7KBQKRebJhR6FQqHIMFkpFEKIjwgh1gshHCHEgn7bzxVCrBJCvBf7/0OZtCe27xYhxDYhxGYhxPljYU8C++YJId4WQrwbSwK0KBN2HGTTV2K/k/VCiP/NtD0AQoivCyGkEGLwvHXpteMnQohNQoh1QognhBAlGbLjgtjfaJsQ4lspD5ZSZt0/olm9jwJeAxb0234iMDH283HA3gzbcyywFvAA04DtgJ6B39eLwIWxny8CXsvw3+9sogmVPbHPlVlwT00BXiAap1ORYVvOA4zYz3cBd2XABj12v04H3LH7+Nhkx2dlj0JKuVFKuTnB9jVSyv2ZstYDXiGEJ1P20C+JsJRyJ7A/ifBYI4H9BSiKSZJNbAz5AnCnjCZXRkrZnGF7AH4OfIMkKRnHEinli1LK/VV/3iaaAW6sWQRsk1LukFJGgIeJ3s8JyUqhGCJXAWv234wZIluSCN8E/EQIUQfcDdySARv6Mxv4gBDiHSHE60KIhZk0RghxGdHe5+glwBw9Pgc8l4HrDuvezdjqUSHEy8CEBLtulVI+Nci5c4h22c7LsD1DTiJ8qKSyD1gM3CylfEwIcTXwJ2AkuU5Hyx4DKAVOARYC/xBCTJexPm8G7Pk2o3ivHKo9++8nIcStRDPA/W0sbYsxrHs3Y0IhR5a0FyHEZOAJ4FNSyu0ZtmfISYQPlVT2CSEeAL4W+/go8Md02DAMe74APB4ThhVCCIfomoK0pVlPZo8Q4nii/qO1sfwSk4HVQohFUsp9Y21PP7s+DVwCLE6ngKZgWPduTg09Yt7hZ4FbpJTLM20P2ZNEuAE4M/bzh4CtGbChP0/G7EAIMZuosywjC6GklO9JKSullDVSyhqiD8hJ6RSJwRBCXAB8E7hMShnIkBkrgVlCiGlCCDdwDdH7OTGZ9P6m8MheQfQPGgaagBdi278D9ALv9vuXdo96Mnti+24l6j3eTGzmIQO/rzOAVUQ91+8A8zP893MDDwLvA6uBD2X6nupn2y4yP+uxjah/YP89/LsM2XERsCV2/96a6lgVmalQKAYlp4YeCoUiMyihUCgUg6KEQqFQDIoSCoVCMShKKBQKxaAooVAoFIOihEKhUAyKEgqFQjEo/x94qMmE2r7U3wAAAABJRU5ErkJggg==\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "history = zip(centers_hist, labels_hist)\n", "for x, y in history:\n", " plt.figure(figsize=(4,3))\n", " plt.scatter(X[:, 0], X[:, 1], c=y,\n", " s=50, cmap='tab20b');\n", " plt.scatter(x[:, 0], x[:, 1], c='red') \n", " plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 2 }