{ "metadata": { "name": "", "signature": "sha256:77216493d36a33d9c395283fedba43d615718fc05be51103ff969ba68bd7e932" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to data analysis using machine learning #\n", "\n", "## 02. Clustering with K-Means ##\n", "\n", "by David Taylor, [www.prooffreader.com](http://www.prooffreader.com) (blog) [www.dtdata.io](http://dtdata.io) (hire me!)\n", "\n", "For links to more material including a slideshow explaining all this stuff in further detail, please see the front page of [this GitHub repo.](https://github.com/Prooffreader/intro_machine_learning)\n", "\n", "This is notebook 2 of 8. The next notebook is: [[03. Clustering with other algorithms]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/03_Clustering_OtherAlgos.ipynb)\n", "\n", "[[01]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/01_The_Dataset.ipynb) **[02]** [[03]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/03_Clustering_OtherAlgos.ipynb) [[04]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/04_Classification_kNN.ipynb) [[05]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/05_Classification_OtherAlgos.ipynb) [[06]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/06_Classification_Decision_Trees.ipynb) [[07]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/07_Classification_Random_Forest.ipynb) [[08]](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/08_Dimensionality_Reduction.ipynb)\n", "\n", "***\n", "\n", "In this notebook, we will look at the popular K-Means clustering algorithm, using the fruit database outlined in the [last notebook](http://nbviewer.ipython.org/github/Prooffreader/intro_machine_learning/blob/master/01_The_Dataset.ipynb). The chief advantage of K-Means is that it's quick and robust, but its chief disadvantage is that you need to decide how many clusters there are beforehand ... except there's a way around that, the silhouette coefficient, which we'll see at the end of this notebook." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1. import libraries and datafile #" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pandas as pd\n", "import numpy as np\n", "from sklearn import cluster\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "from scipy import stats\n", "\n", "df = pd.read_csv('fruit.csv')\n", "# Since this is unsupervised classification, we'll drop the labels\n", "df = df.drop(['fruit_id', 'fruit_name'], axis=1)\n", "df.sort(['sweetness', 'acidity', 'weight', 'elongatedness'], inplace=True)\n", "df.reset_index(drop=True, inplace=True)\n", "df.tail(10)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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color_idcolor_nameelongatednessweightsweetnessacidity
169 4 orange 0.08 144 3.58 1290
170 5 red 0.11 182 3.58 1295
171 4 orange 0.11 144 3.59 1035
172 4 orange 0.09 143 3.63 1015
173 6 yellow 0.47 123 3.64 380
174 6 yellow 0.56 126 3.69 465
175 5 red 0.11 189 3.71 780
176 4 orange 0.19 144 3.82 845
177 5 red 0.09 191 3.92 1065
178 2 brown 0.15 152 4.00 1035
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 1, "text": [ " color_id color_name elongatedness weight sweetness acidity\n", "169 4 orange 0.08 144 3.58 1290\n", "170 5 red 0.11 182 3.58 1295\n", "171 4 orange 0.11 144 3.59 1035\n", "172 4 orange 0.09 143 3.63 1015\n", "173 6 yellow 0.47 123 3.64 380\n", "174 6 yellow 0.56 126 3.69 465\n", "175 5 red 0.11 189 3.71 780\n", "176 4 orange 0.19 144 3.82 845\n", "177 5 red 0.09 191 3.92 1065\n", "178 2 brown 0.15 152 4.00 1035" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2. Explore and normalize two numeric features #\n", "\n", "Since it's rather difficult to visualize more than two dimensions, we'll just use two of the five numeric features, ``acidity`` and ``sweetness``, which we saw exhibited some clustering in the first notebook" ] }, { "cell_type": "code", "collapsed": false, "input": [ "columns = ['acidity', 'sweetness']\n", "df[columns].describe()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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aciditysweetness
count 179.000000 179.000000
mean 745.849162 2.606034
std 314.332206 0.712020
min 278.000000 1.270000
25% 501.000000 1.925000
50% 672.000000 2.780000
75% 985.000000 3.170000
max 1680.000000 4.000000
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ " acidity sweetness\n", "count 179.000000 179.000000\n", "mean 745.849162 2.606034\n", "std 314.332206 0.712020\n", "min 278.000000 1.270000\n", "25% 501.000000 1.925000\n", "50% 672.000000 2.780000\n", "75% 985.000000 3.170000\n", "max 1680.000000 4.000000" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For many parametric algorithms, it's important to standardize (a.k.a. normalize) the data so that every feature has a mean of zero and a standard deviation of one." ] }, { "cell_type": "code", "collapsed": false, "input": [ "col1 = columns[0]\n", "col2 = columns[1]\n", "plt.scatter(df[col1], df[col2], s=44, c='#808080', alpha=0.5)\n", "plt.xlim(df[col1].min(), df[col1].max())\n", "plt.ylim(df[col2].min(), df[col2].max())\n", "plt.title('before standardization')\n", "plt.xlabel(col1)\n", "plt.ylabel(col2)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ 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NlJSUkJ2dzdixY6mtrWXSpEmX+OwLCwvp6OigvLw85P7j+YxF22NLp9Iy4Sj/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\nH86IESNwuVw0NDQAHheRt0Hatm0bFy5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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "col1 = 'acidity_normal'\n", "col2 = 'sweetness_normal'\n", "df['sweetness_normal'] = (df.sweetness - df.sweetness.mean()) / df.sweetness.std()\n", "df['acidity_normal'] = (df.acidity - df.acidity.mean()) / df.acidity.std()\n", "plt.scatter(df[col1], df[col2], s=44, c='#808080', alpha=0.5)\n", "plt.xlim(df[col1].min(), df[col1].max())\n", "plt.ylim(df[col2].min(), df[col2].max())\n", "plt.title('after standardization')\n", "plt.xlabel(col1)\n", "plt.ylabel(col2)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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wIFb0zxskktOR7PU7sjXRLRcZLr+FzRw8yHBYIjMbWLhwIT/84Q954oknmDp1KmVlZZw7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\n9OnTOXjwIBMnToyaQOYmueupp54iLy+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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make a numpy array of the (x, y) values of the above ``sweetness_normal`` and ``acidity_normal`` features" ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = np.array([list(df[col1]), list(df[col2])]).T # a 179 x 2 array of instances x features\n", "data.shape" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "(179, 2)" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3. Showing the steps of k-means centroid convergence #" ] }, { "cell_type": "code", "collapsed": false, "input": [ "k = 3 #number of clusters\n", "\n", "start= np.array([[ 1 , 0], [ 2, -1], [ 2, -2] ]) # starting points for the clusters\n", "\n", "steps = ['Set initial centroids',\n", " '1A: assign clusters by proximity',\n", " '1B: move centroids to mid-cluster',\n", " '2A: re-assign clusters by proximity',\n", " '2B: move centroids to mid-cluster',\n", " '3A: re-assign clusters by proximity',\n", " '3B: move centroids to mid-cluster',\n", " 'Final centroids and clusters']\n", "\n", "centroids = []\n", "\n", "for i, stepname in enumerate(steps):\n", "\n", " num_iterations = [1, 2, 2, 3, 3, 4, 4, 100][i]\n", " kmeans = cluster.KMeans(n_clusters=k, max_iter=num_iterations, init=start, n_init=1)\n", " kmeans.fit(data)\n", " labels = kmeans.labels_\n", " centroids.append(kmeans.cluster_centers_)\n", " \n", " plt.xlabel(col1)\n", " plt.ylabel(col2)\n", " plt.title(stepname)\n", "\n", " if i == 0:\n", " #plot every point in grey\n", " plt.plot(data[:,0],data[:,1],'o',markerfacecolor='#808080')\n", " for j in range(k):\n", " lines = plt.plot(centroids[i][j,0],centroids[i][j,1],'kx')\n", " # make the centroid x's bigger\n", " plt.setp(lines,ms=15.0)\n", " plt.setp(lines,mew=2.0)\n", " else: \n", " # plot every label in a different color\n", " for j in range(k):\n", " subset = data[np.where(labels==j)]\n", " plt.plot(subset[:,0],subset[:,1],'o')\n", " # plot the centroids\n", " if i in [1,3,5]:\n", " # from previous step\n", " lines = plt.plot(centroids[i-1][j,0],centroids[i-1][j,1],'kx')\n", " else:\n", " lines = plt.plot(centroids[i][j,0],centroids[i][j,1],'kx')\n", " # make the centroid x's bigger\n", " plt.setp(lines,ms=15.0)\n", " plt.setp(lines,mew=2.0)\n", "\n", " plt.show()\n", " " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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duj1r1iwee+yxXsc2btyYyvaPi9bWVubNmxfI4V1QHvPmzYstpTr4j6pqLnde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\nknymVPU1yS93+BjQVnQqUDvVg6nK1VY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IFdHjZ9dEI3ySHErdsa6DyxZdxp4LBu/LnF7vkMvslJSIpVL9LGPHjmX9+vX9\nymDatGmsX7/e02yVrTRylQsLv4pjifs3c//xikg5Uoi2tqtKVhSZNuKXX34eeA3HHTe2KuzFQZAr\nNLjWUpBE4Uso9h5JWN/k1cECLFy9kD3H7PG8Jt/sIQkJFctdGe5HecStNMB/dtwuERkHnIujMH6r\nqvnnUVXO4PQQG3GsbcnJSptUai0FSalpRIpRBKXcI+4cYrk62OOOHEf3X3TDr72vyzd7SMJ2t/lW\nhvuVI5/ySILSAHyv4/gE8Hvg++5rOzCzFKdKWC9KcI5n0t6+QZubF2tj41Jtbl5c0Ek42Pnr7Qg2\nh6+RK0gg33ejWMd1KfdI38drfVNYZDq7x7xzjKcje/S7RjvvL0d5H7Gsd/Bca/FRf/duvKzR87ka\nL2ssWo5Mx3dDQ4M+/vjjgz77daDng5B3AGwFzlV3liEiJ+KMCe4IUIfFRikjtsE24uTai414KcWX\nUGxizlL9FVFmGRgyw9ieo2DaUjbR/Xs/IDDmz2NYfn00YbXlzBqC9LNkzzzOPvtsgHhnGi5+kxwK\n8GLG5z2UkQYkaZQSYfLyy5mWuvjtxWk6OjaSSrXS1NRGKtVKR8fGyGUwBijFl1CsIkiCv6IQQzrj\nI97lJo6dSP2WevcD8H6oP76eW6+/NbK1GOVEZy24eMGA/C71D9cz/6LS/Cxjx45lzZrBi5TXrFlT\nstLoWNdB6ooUTZc3kboiVVId4N85vha4T0R+hKMwZpEVCVXJlDZiewVYjOPXaM547xCHwzcJG/cY\ngynFl1CsIojbX+GHIZ1xPY7N4gMDh8b9xziWXe3s4hnnxk/lzBqC3riqp6eHWbNmDTo2a9askmYc\nXn6lUvGrOK4G/hp4L45z/CZVvbPsuyeEUkZsxx13CvB+nICzYcBuYC7HH/8npkw5NRaHb7XsPVJN\nlBIMUKwiqISAgyGd8UT37x3ACYDC+NeN7+9g41zpXW50VlAbV2U7wtesWcOsWbMKhurmwssEVyp+\no6oU+Jn7qmiyo1XOP/9kXnxxF3V1n6Ov75v95fyNCqe6rwGmTFnia+/zMEI0w47Nr7oUFRE9T7G+\nhFIUQdy7VBbCqzPmaZw4zYnOx1f/+9UYJBtKEra7zRU95Xedhxe5THAl4ceDDvwN8H/Ay8AB9/Vy\nKd74sF74iKoaGq2yISM77gaFVq2rm62TJ19VMMKknEymYaV7mDTpc57RNZMnX1VWvWHKHBfV9jyV\nQHtnu6ZFBBfCAAAgAElEQVSuSOmod41SprqRUxmRRyPfMdKy6erQaKrs6KlC53PhmZKlxKgqv51y\nN1k5pJL28qM4hoYtlhdGW2o4Y6nhk4WYNOnTCouy6r1GJ036dFn15pN58uSrigpjTgph/Q/Cothw\n8STT3tmuI6eMHNyBvddRJJWSVyos/CqFUpSHV5hxqYrDr49jlw7dla/iGGrKKc+042Ue8GP+CMuk\nNNTvchiYwXHH3V9WvZBb5m3bDtDXN5ARplKc8UlOuZFNtQU9tExv4fR/O52t928dyEHxJmAi9D1T\nGXmlwqCYxX2lmK28THD3cV9JsvpVHA+JyBqcDZ3SuwCqqv68pLvGxFAneLBhjH5/4GGFT+byu9TV\n+U9cl0vx5ZK5r29w7stKccZXQghrmrCCHuL0WU04aQJbJw5NWlZxO+EFyB133FHUivBs5eEntXq2\n416+V+KqCj/TEuAW4HvZr1KmOGG9KNvHoUX5Kbzwa/4Ia6e3cuvNZ/f3OldXN8f1DQ1+3sbGpWU9\nRxRU0m57jY1LPb9X5bRz3D6e9s52HTd93CCzybgPjqt5H8eqVauKXhG+e/fuklKqq2q4pipVvTzf\neRG5RlW/Uprqig6vaJUpU85h8+Zgwhj9mj/CCp8st958I9t0pFhm3T09h9iyZWjdSRy1Z1MJIaxp\nwpgdJSJ0+yD9K8OrI2Vq+ZSyGdPYsWNLuq4c/JqqCvEJIPGKA8INWyzmBx6WHOXUW0jxZdftmOaS\nvfAsH0kIYfVjLgpjgV/cPp4VP1rBrvfvGnRsF7uKSgZoxEdQisOgMlbw5qPYka2fUXvUW2FWEn59\nYmHMjuL28VT6pks1Tyn2rewXsCWIesqUoSQbX9BEnXE0SIK2+8exFWYlEWdIcNw+nkrf5rVaIORw\nXMMnpYboJoGgR7YzZ87kxhtv9B0uGOdWmHEQp7kobh/P+Wecz6Y7N9E7o7f/WNSbLhllUIq2yX4B\ni4Kop0wZAtC/wRN39ErchLmgKQ6CXIhXaYsQg6J/IdrlOCvIG51V40u/tjRu0WoOQl45fgNwHHA0\nTk7Ll4DZpdzQo+4ZwFM4KU2+lKPMCvf8o8CkHGWCbtNAqNXOIZOwUihETdCDgLjNRXFhZqrkUKri\n8LsfR7OqvgxcgLMFSz3wxTImOgCIyDBglas8GoCLROSMrDIfBt6kqm8GPgt8c0hFCSbu6JUkkF6o\n1NDQ0G+26ulx9jNJzFaYPihl35Z8tLRMZfnyFKnUEhob20illrB8eTJDgoPEHOOVj18fR7rcBcBP\nVXW/iAQReX0e8LSqbgcQkduBjwKZ6U0+AtwKoKoPiMgoETlJVXcHcP/QiTt6JSl4pUjITBOddKUB\n4QwCkhASHDVB7pJnxIPfGcfdIvIU8BfAr0VkLBDE8GAC8FzG5+fdY4XKnBLAvSNhwYJm6usXDzrm\nhOhOj0mi+MieeZx99tkVozTABgFBEfQueUb0+F05/o8icgOwX1UPicifcGYG5eJ31pKdUMXzura2\ntv73TU1NNDU1lSRUkMQdvZK0iK70Vpjp/ZOhvK0wo6SS1+kk6XuQhP0uapWuri66urrKr8iPIwSY\nCRznvl8C3AlMLsWpklXvFGBtxudryHKQA98CLsz4/BRwkkddAbmLqockRnRlOsLTryQ7xLOpxHU6\nSfweGMmAkKOqHnf/vhfowvF1/LaUG2bVOxxnr4+JwGuAR8ja9wP4MHCPDiiazTnqCrxRK52kRXRl\nR089/vjjFRFNVekk7XtgJIdSFYdfH0faiHsB8B1VbccJzS0LVT0EzAPuA7YBa1T1SRGZIyJz3DL3\nAL8TkaeBm4Cryr1vrZCkiC6v6KmzzjorZ7SVERxJ+h4Y1YHfqKodIvJtYDrwVRGpw79jPS+qei9w\nb9axm7I+zwviXpVCUPbopDhz84XclruPslGYpHwPjCrCz7QEOAb4a+DN7ufxOGs7yjJVBfmiSkxV\nQdqjk7DArNpWjicdr5XtSfgeGMmEEk1V4lxbGBF5H85CvO+JyInAsar6u8A1WYmIiPp9liSTSrXS\n2Xmdx/GBPTGKoaNjIytXrsuI6JpOS8vUSKJsil3cV0mLAZOIV7bd+vrFLF+eAvD8Hhi1jYigqsVv\nA+hHuwBtwN3A/7qfJwD/WYqmCutFBDOOIPMU5SKM3d6yiSrKxrLjRos5wY1iIeTsuB8DJgH/7fbQ\nO0Tk2KK1VAXjd++EconCHh3V7m/p/TSK2Y8j7fO44447mDjxbFKp1kSsPagEzAluRIVfxXFQVY+I\nODMaETkmPJGSSVSdbRSLzPJ1MEGbsErdCnPixLMjUdTVhDnBjajwqzjuEJGbgFEi8lngU8DN4YmV\nPILsbPOVj2Klea4O5sCBFxPTWSdiT+wKo5JXthuVhd+UIzeISDNwAHgLsERVS0sJWqEE1dn6MXmF\nnfguVwejejAxnbWZXYon7vQ2Ru3gewdAVe0EOkOUJdEE1dnmGkn/0z/NjSyXUK4O5oYb7vcsH0dn\nbWaX0qjFbLtG9PhSHCLyN8BXgZMYSDioqnpcWIIljaA621wj6W3bDtDXt7r/c9gmIq8OZsUK73FB\nHJ21mV0MI7n4nXF8HbhAVZ8sWLKKCaKzzTWS7ut7w6DPcZiIktRZm9nFMJKLX8Wxq9aVRi6K7Wy9\nytfVXUlf38VDykZtIkpaZ21mF8NIJn4Vx0Misga4C3jFPaaq+vNwxKociu1svcr39Bxiy5ah5eMw\nEVlnbRhGIXylHBGRW/DYPElVrwhBppKo5JQj3qkiFtXE/tOGYcRHqSlH/CqO96rqfxQ6FieVrDgg\nd04pwzCMsAhbcTysqpMLHYuTSlcchmEYUVOq4sjr4xCR84F3A2NF5O8YCMU9FrCVWDlI0v7OXiRJ\nviTJYhiGPwo5x1/DgJLITGr4MvDxsISqZKJKhlgqQcpXbqef9LYyDCMHflLoAm9w/x5TSgreKF4k\nZCOnpKe2Dkq+IFKzJ72tDKPaIeQ9xyeIyDbgKQAReYeI3BiCHqt4kp5jKSj5cich9J/CLOltZRiG\nN37XcXwDmAH8AkBVHxGRxnJuLCKvB9YAbwC2A59Q1X0e5bbjmMYOA6+q6nnl3Ddsis2xlG3uOf/8\nk/nNb14IzeafT75iTE9BdPqWj8owKpNikhw+m96Pw8X7V++ffwTWqerXReRL7ud/9Lo10KSqfyjz\nfpFQzEpyLxv//fdfyaFDFwNOhx20zT+XfFOmnFKUvyGITj9JKU4MwygCP/Ys4KfAe4AtOA7zfwBu\nL8U2llHnU8BJ7vtxwFM5yj0DjPFRX1Bmv7Jpb9+gqVSrNjYu1VSqNafdP5eNH1pDtfl7yVesv8Hb\nx3FN0dvP+m0rwzCCh5C3jv0csBxnr/EdOOnVi9/abTAnqepu9/1unMy7XijwKxE5DNykqt8p8745\nCSo01G/ajlzmnuxI56Bt/l7yFZvlN6i8VpbixDAqD78bOb0IDM3CVwARWYczm8hmcVb9KiK5Vu+9\nR1V3isiJwDoReUpVN3kVbGtr63/f1NREU1OTb1njCA3NZe5x3DkDRGHzL8X0ZJ2+YVQWXV1ddHV1\nlV+Rn2kJ8Fbg18BW9/M5QGspU5yMOp8Cxrnvx5PDVJV1zVLg73OcK2vKFkdoqJe5Z/jwzypsKMv8\nE5QsUd3bMIx4IGRT1XeALwLfcj8/DvwYuK4MnfVL4DLga+7fu7ILiMhrgWGqekBEjgGagWvLuGdO\n4ggN9TL3TJnydjZvXkdf3/2RpjVPWkp1wzCSi1/F8VpVfSAdVaWqKiKvlnnvrwI/EZFP44bjAojI\nycB3VLUFx8z1c/e+w4EfqrOFbeDEFRqaJHNPkmQxDCO5+FUcL4rIm9IfROTjwM5ybqxOeO0HPY6/\nALS4738HvKOc+/jFQkMNwzD84Tc7bj3wbZyEh3txQmQvUdXtoUpXBEFkx63m1OaWTNAwjGxCTaue\ncZNjcHwOLxd7o7BJSlr1JHbQ3htFLWb58lTsshmGER+hpFXPqLwb2Axscl9bi71RJVKsEkhqttfc\neaWWmOIwDKNo/Po4zgTeBbwX+GcReQvwuKr+VWiSxUwpSiBJHXSm0nv00ec8y1gyQcMwSsFvdtxD\nwKs4K9OOAC/irPauWkrJ/pqUbK9ppdfZeR0bNrSxb9+pnuUsmaBhGKXgV3G8DPwbjlP8MlWdoqpz\nwhMrfkpRAknJ9jpU6TWTtVjfjRibHqlchmFUB35NVRcB7wOuAv5WRP4L2KiqvwpNspgpRQkkJaR3\nqNJzzGSjR1/EOee81Rb3GYZRFn5zVf0C+IWIvA34MPB54GqgLkTZYqUUJRDE6utcDvliHPXeSm8q\n5523jrVr23zLYhiG4YXfqKqf4SzE6wY2ArOB34YoV+yUqgTKWX2dyyH/4INPcNttO3I66r02g0rC\nzMcwjOrE7wLAq4FvqerLIrIEmAwsU9WHwxbQL0lZx1EOqVQrnZ1D03+NGTOLPXvWeJRfwvz50z3X\naFx66QQ2b95ZlYsZDcMIhlDXcQCz1dmp773AB4B/xkl4mOhtXCuNXA75Q4dGeh7v6xuWM/pr8+Yl\nrF27LHAZDcMw/EZVpT3CF+AkIGwHjg5HpNoll0P+yBHvhfp1dYcTEwJsGEbt4Fdx7BCRbwOzgA4R\nqSviWsMnCxY0U18/OGx23LgvMGwYZIfTjhv3BebPn56YEOAk09GxkVSqlaamNlKpVjo6NsYtkmFU\nNH5NVZ8AZgA3qOo+ERmPsz+HESBeDvmengNs2fJznJiEJTjbyh5m/PgD/eXNEZ6bpKaBMYxKpqgk\nh0mmGpzjXjQ1tbFhQ9uQ442NbXR1OcerOatvueQKOEilzAdkGGE7x42Y8GOKimoDpiRm/i2E+YAM\nI3hMcSScpKxGr1STj/mADCN4THEknKTsBR5W5t+NHR10rljB8IMHOTRiBM0LFjC1paVccftJiuI1\njGrCFEcFEOVe4Lk68jBMPhs7Orhv4UKu7+7uP7bYfR+U8kiK4jWMaiI2xSEiM4E24G3AublWoYvI\nDOAbOOFEN6vq1yITssbI15GHYfLpXLFi0L0Aru/uZsnKlYHOOqJUvIZRC8S5FuNx4GM4caaeiMgw\nYBVOKHADcJGInBGNeLVHro583cqVnmtMyk3NPvzgQc/jw/r6Sq7TMIzwiW3GoapPgRMOlofzgKdV\ndbtb9nbgo8CTYctXi+TryMMw+RwaMcLz+OG6qk26bBhVQdJ9HBOAzH1Pn8fZwtYIgUIdedAmn+YF\nC1jc3T1olrOovp4Z8+cHdg/DMIInVMUhIuuAcR6nFqnq3T6qKGpFX1tbW//7pqYmmpqairm85jn5\n/PO5ctMmvtXb238szI487cdYsnIlw/r6OFxXx4z58wP1bxiGMUBXVxddXV1l1xP7ynERWQ/8vZdz\nXESmAG2qOsP9fA1wxMtBXq0rx6Mi7RhPdXezDicS4cmRI2m8+mquylDIhmFUD5W+cjyX4A8BbxaR\nicALOEkWL4pIptgJe41DJpmO8X5jVG8vSzZvDuV+hmFULnGG434MWAGcgJNxd4uqfkhETsZJ3d6i\nqodEZB5wH84g+N9VtSYc416hsVdu2sQPTz+dEydM8K1E/CqfUiOcolRuQVGJMhtGkogzqupO4E6P\n4y8ALRmf7wXujVC0ROAVGvut3l6WbN3Ksq1bfS2UK2aBXSkRTkEs4Iu6E49i0aFhVD2qWhUv51Gq\nh6WNjaow5LU0431rKpW3jsXNzZ51eF23ob1dF9XXDyp3TX29bmhvD6R+L7zuuajAPculXJkNo5pw\n+82i+9uk+DiMLHLOADLeFzIj+TU/pUf9L9XVMWvMGMaPH8+xEyYUjHAqdwFfVCvHM7FFh4ZRPqY4\nEornGgecJfRpCi2U82N+8jTdjBrFdB9hseUu4IujE7dFh4ZRPrb9a0KZ2tJCavlylqRSfP6ss5j5\nmtcwg4GIpy+MG8f0AusrmhcsYHF9/aBji+rrB12XL81IPjZ2dLDrxRf5XFaHO2fkSMZPmZL/4Vzi\n6MT9tIlhGPmxGUeCmdrSwtSWFjZ2dHDrZz7Dul27uB/HXPWyz+sh/wK7Ukb96VnKzd3d3IgTI32G\nK9clvb3cd9ttbDz33IKO+7Ti+WbGvcJeOW6LDg0jAEpxjCTxRZU5xzMJ06FbSt2Z1yz2uLbQ9ZlO\n8Q2graCz6+r0qsmTQ3WMe8mxuLlZlzY26uLm5kjvbRhJAHOOVy9h+gJKyReVKU+uL1A+2bIXG04F\n6OtjyYknRjbyt7BcwygdUxwVQJi+gGJMN+noq6cfe2xAthz15pMtCZFNcUR0GUa1YIqjAgg7+WDa\nl5KPzBH6RmAxcD3QnPHer2xJiGxKgvIyjErFFEfC2djRwY7bbuPi3l6WkJF88NJLAxkZ+1257ZXL\nagnw7OjRHD1xInNFOPHYY305m8NKp17MKvQkKC/DqFRMcSScMJMPFmPnzx6hp30Tn58wgdedeOJA\nZ+0jQimMyKZifRa2F4hhlI4pjoQTpkmlGDt/rhH6zu5u1jzxRP9nvw5mP+axYijWZ2FhuYZROqY4\nYqaQeSVMk0oxSslrhD5n5EjmZvhdID4HcykKNmjlZRi1gimOmNjY0cH3lyzh6CefHLQALnvEHqZJ\npRil5DVC5/nnmbp165CycTiYzWdhGNFhKUdiIG2PH7dlyyClAUPTfWSmHmlrbGRJKsWM5csDGSn7\nTb+xsaOD1lSK+2+4AVXl/V/8IsvWruXECRM8642js/Z6ljkjR9Lz/PO0plJs7OiIXCbDqFZsxhED\naXt8W47z2SN2vyaVG9va2LBqFSMPHaJ3+HAa583Lu+2rHzt/PqdzkhzMmc9yYMcOdnZ3M7e315kR\n+dy/xDAMn5Sy3DyJLxKcciQ7tcXCs84qOV1HLlYvXapzhg8fVM+c4cN19dKlZcleKCXJhvZ2bU2l\ndGljo7amUolI22F7bhiGP7CUI8nEa8Q+a+RIoLjFc4Wc6BtWrWLNocHruL916BAXrlqVd9ZRiEJO\n58zZUFrG+2+4IdYtWW1xn2GES5x7js8E2oC3Aeeq6sM5ym3HSQZ7GHhVVc+LSsYg8AoTndvby5Uj\nR/avBF8C/L6ujmMbGpj15S8P6Wz9rFEYecg7+UddjuN+8et03tjRwV2f+Qz/umtX/7G/e+wxuPnm\ngllyg9w6dmNHB09mhAfnk9kwjBIpZZoSxAtHYbwFWA9MzlPuGeD1PuoLZu4WMLm2gP3smWf6NvH4\nMb18YswYzzKzxowpSe60ee2zZ56pc0aOHFSn15ayn5s0yfP+V02enPceQW4dm65vA+iiLDkKbYNr\nGLUIlWaqUtWnAETET3FfhZJIrhH72FNOYdnatb7q8GN6aZw3jyuvv55vZcww5gwfztR584qQ1iF7\nhrMRx7w2vr4+55ayf3rmGc+6/pjjOASfaDC7vnSKlqfGjOGqgCLRDMOojKgqBX4lIoeBm1T1O3EL\nVAxBRB75MRdd1dbGjcCFq1ZRd+gQfa7SKMW/kd0BTwWm9vayZMKEnMruYI4BwCt57hO0LyKzvv50\n7UDbWWeZ0jCMAAlVcYjIOmCcx6lFqnq3z2reo6o7ReREYJ2IPKWqm4KTMlyCSG3hV/lc1dZWliM8\nTa4O/bnNm2lNpWhesABgkG9CR49m8d69gx39wDETJ+a8T9CL9mwRoGFEQ6iKQ1WnB1DHTvfviyJy\nJ3Ae4Kk42jI6zaamJpqamsq9fSCUm9oi6rxKuTrgU/fvZ1lnJ59+7DGOh0GO8E+PG8ezo0axZN8+\nhuFEMuwaN47Lly3LeZ+g14EkaV2JYSSRrq4uurq6yq5HHP9IfIjIeuAfVPW/Pc69FhimqgdE5Big\nE7hWVTs9ymrcz1IteEVxLQJm4Jh/WoHrPK77zKRJjB87tl+5Tfeh3DZ2dLAuQyH6uSbK+gyjmhER\nVLVoH3JsikNEPgasAE4A9gNbVPVDInIy8B1VbRGR04Gfu5cMB36oql/JUV9FKo6gw1GDlGvdypU8\nt3kzp+7fz3QyfAbuK5u2xkbacoxmkvqchlHLlKo44oyquhO40+P4C0CL+/53wDsiFi0ykrzvddq8\n1ppKsaxz8ASv2O1ik/ychmEUjyU5jJFc4aiZSQ7jxit54AvjxvF34wbHPHglR0xTCc9pGIZ/KiEc\nt2qphNQYXo75y10F4ddZXwnPaRiGf0xxxEgp4aNx+ApyRYX5va+FyRpGdWGKI0aKDR+tVF+Bhcka\nRnURezhuUFRyVJXf8NHWVIrrOodEIrMklfKdviQuLEzWMJJHxUVVGQ7FLA6sZF+B7e9tGNWDRVVV\nEOYrMAwjCZjiqCAK7RGe3hu8ranJ9tk2DCM0zFRVQeTLWVWpjnPDMCoPc44HQDpE9sUdO9i3axfj\nx4/ndSefHFlajY0dHay+7DLW7Nkz5FzUjvPVq1czc+ZMxo4d6/uanp4e7rjjDubOnRuiZIZhZGPO\n8ZhIj/RT3d3cB9wEsGcPPPFEJCP+9P3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rWE3NQqqrh3vWaylISov/+qbcO0yWivFvHs+ot41i72f28vva39M2vo0FqxbQ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\nCwuTNYzkUWhUlc04YiafxYHl7Cuw/b0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TYpRIdiT7rhAujE+SvHLLHnRzX3q5t53wNt4+4e1QR2QjlsL8jjs7O+ns7Ox9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\nKajyuaK1Na+iSMdLaYwYMaLPADyCNOX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T/2o2cGlK+ScDPaqqIjIFEFX9cyEKHzas1+d6eRmqkslmJFFdXc369esHhMku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\np9DrQKK0rsQwokhnZyednZ155xP6Og4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z6RGRduB0nC1dEnMt1SzNR0n1fhKYrKqfd88vBc5U1VlJZQ4H3lLV10XkXGCR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\nqc2lYRE5ClgBnAA8A1yoqq9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PNQYnnHBV3nWVg1z7Q/uRPvMoZ2p1v4V/5567wGYiMSFOYaGlIOi6FeMIhBWO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\n8kw56zOMakZEUNW8fciRKQ4R+VtgBTA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MtBQkxQ4khSiCYtqIe5D1k/nIA0fS9X+64Lfe9+VTbEnY7nag2FmCuuOeD1wD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\nJ3GA9vQYq6sjtXx57LIZhhE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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 4. Evaluate the reproducibility of k-means clustering this dataset #\n", "\n", "Since the final K-Means clusters can be dependent on the initial centroid positions chosen (usually randomly), let's run the algorithm 100 times and find out how often instances are assigned to different clusters. (Ironically, with K-Means clustering, the most inconsistent results can occur in datasets that exhibit the best clustering. This should not be an issue with out data, but it's best to be sure.)\n", "\n", "First we make a 179x100 numpy array to hold the cluster assignments ('labels'): 0, 1 or 2 (since we have predetermined there are three clusters)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "for i in range(100):\n", " kmeans = cluster.KMeans(n_clusters=3, max_iter=100, init='random', n_init=1)\n", " kmeans.fit(data)\n", " labels = np.array(kmeans.labels_)\n", " if i==0:\n", " all_labels = labels\n", " else:\n", " all_labels = np.vstack((all_labels, labels))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the numbers of the clusters (0, 1 or 2) are not consistent from run to run, we will choose three datapoints that are representative of the clusters. Going through the data, I chose points 10, 144 and 160 in the lower left, upper left, and upper right, respectively." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(df[col1], df[col2], s=7, c='#808080', alpha=0.5)\n", "plt.scatter(data[10,0], data[10,1], s=72, c='#dddd22')\n", "plt.scatter(data[144,0], data[144,1], s=66, c='#dddd22')\n", "plt.scatter(data[160,0], data[160,1], s=66, c='#dddd22')\n", "plt.xlim(df[col1].min(), df[col1].max())\n", "plt.ylim(df[col2].min(), df[col2].max())\n", "plt.title('chosen characteristic cluster points')\n", "plt.xlabel(col1)\n", "plt.ylabel(col2)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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MWZtkqrDu/cBNZOVT2pyDpCOAdcBFzSoHSccBH46I4yQdCpwbEYe1mFepKod2eCeVr6w7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\nmmnaaSJqNoS5mfW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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Go through each repetition and assign each point to the cluster that each of the above three points represents, then find any points whose cluster assignment has a nonzero standard deviation." ] }, { "cell_type": "code", "collapsed": false, "input": [ "regularized_labels = np.zeros(all_labels.shape, dtype=np.int8)\n", "disagreements = []\n", "\n", "for i in range(all_labels.shape[0]):\n", " cluster0 = all_labels[i, 10]\n", " cluster1 = all_labels[i, 144]\n", " cluster2 = all_labels[i, 160]\n", " for j in range(all_labels.shape[1]):\n", " if all_labels[i,j] == cluster1:\n", " regularized_labels[i,j] = 1\n", " elif all_labels[i,j] == cluster2:\n", " regularized_labels[i,j] = 2\n", " \n", "for i in range(regularized_labels.shape[1]):\n", " disagreements.append(regularized_labels[:,i].std()) # standard deviations" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualize all the points that are ever assigned to two different clusters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(df[col1], df[col2], s=12, c='#808080', alpha=0.5)\n", "for i in range(len(disagreements)):\n", " if disagreements[i] > 0:\n", " plt.scatter(data[i,0], data[i,1], s=72, c='#dd22dd')\n", "plt.xlim(df[col1].min(), df[col1].max())\n", "plt.ylim(df[col2].min(), df[col2].max())\n", "plt.title('points in different clusters after 100 runs')\n", "plt.xlabel(col1)\n", "plt.ylabel(col2)\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 5. Cluster with different values of k #\n", "\n", "What does the clustering look like with 2, 3, 4 or 5 clusters?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# comparison of different values of k\n", "def compare_kmeans(k):\n", " \n", " kmeans = cluster.KMeans(n_clusters=k)\n", " kmeans.fit(data)\n", "\n", " labels = kmeans.labels_\n", " centroids = kmeans.cluster_centers_\n", "\n", " plt.xlabel(col1)\n", " plt.ylabel(col2)\n", " plt.title('k-Means for k = ' + str(k))\n", "\n", " for i in range(k):\n", " subset = data[np.where(labels==i)]\n", " plt.plot(subset[:,0],subset[:,1],'o')\n", " # plot the centroids\n", " lines = plt.plot(centroids[i,0],centroids[i,1],'kx')\n", " # make the centroid x's bigger\n", " plt.setp(lines,ms=15.0)\n", " plt.setp(lines,mew=2.0)\n", " plt.show()\n", " \n", "compare_kmeans(2)\n", "compare_kmeans(3)\n", "compare_kmeans(4)\n", "compare_kmeans(5)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ltbr7LNBsZrC0x9unXREEpXgwvv/+v7B168HABHpXHtDV9SL5/PJU3HezPX+o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\nq5zC8/fhbNyrsP9u+/e0T0M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V0EG5i7IaUmnbgiiO8vpJtYbRhs1HiGrlvE+MGdMrn+Qq0E+MGVPTdSvJfPnY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\nbmCIiBycsEwQ428IQFVXAdsqNIm7n4L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+Mym2KGx322f8LH486MBngC3AD93XZmB8Pt74Ur3II6oqkWzF+pJJLLcxzatO\nRIbSG3Pnzs05WmrHjh0VX/ytEsmnjEiu0UH5lrFYsmyZxhobta6xUWONjUWLPkpXRiQxiuuYMWM8\ny5McdNhhzud77lGuvjqUfIdCorPqGhs9/y3qIrrjISUuOTIdGKHuKkNEjgWW4ewtVPbks49FYrmN\ndA8xncM3nxXD4MGDy3ql0VfJp4xIrrPWfP0Vpdof22tVnbIqeuutngvc8iTcfDMHtmyB9na4/HLn\n3EMPwUEHccwbbzD7G98IZNZeyKohKn6WUuNXcQiwM+HzLgooAxI18qmg2/n2293vvQtFhOPwtTIf\n0SKfMiK5KoKoDVbxCU7iLpcpg/H+pO/vKo8T77yTAe+9RwfAOefAOedQs2BBYEoDCgsciIKfJRPJ\nJrh88as4lgJPiciPcBTGBJIiocqZfIr1/RWYhuPXaEh4HycMh28UdwDs6zQ2NtDRMa2Xj6OmZiqT\nJyfvYt9DroogioNV8uo4ZTD+h3+A+fNh4sTuQ0N++lPumzULCKa+VjoKUcRB1gfLFS9fGM3NefXl\nV3HcAlwBfBzHOX6/qi7O644RJJ8KuicecQQX4ISb9QN24Gzp+u6RR3LSqFGhOHyjuPdIXyfuAG9u\nnpFQRmRsRsd4roogyoNVnJTB+JxznL+33w4nnwwHDnD8/v3dMocpe6GKuFQmwELxMsHli9+oKgV+\n5r7KmmRTzgnnncf2nTv5clUV/52wwsi2YugaMIDzgeT//jNGjfK193kpTEqlLnNeaWawIMJkwVEe\nufSbjyKI6mAVx2sw5pln4NJLu5XI3773vZCk6005KOJ8SGeCywe/e45/Cvg2cBw9vg1V1SOKJkkA\nJJtyVgE/Wr6c+V1drMJZPWypquLw2lom3H57xkExW7n2XOSA4piUEv0uiex85528+4xTaWawYu+2\nV2yirghyJXEwfvqVV3jzmGNg5MielQfQsW0bLcuXR+J7V9rzh/QmuLzwE3oFdABn5BO2FdQLH+G4\nyTvW5RpGm0y6cu25ylGsnfNuGD5cpyb1eSvoDcOHF9RvJpm/cu65OYUxR4Vi77ZXaqK0T3WhLFm2\nTAdedlnvkNWrrlLuuSe0nfD6Al5hxpQ4HHe7pu7KV3Ykm3JyDaNNxisz2o85p1QmpWS/y36cfXmX\nH1H4wjCdzO9s2MC8BLnLZRVS7N32SkmlZSOPu+ACTn3gAda7obYcONC9+ti7aVPY4lUsXia4p/Ls\ny6/i+K0KObnaAAAgAElEQVSILMTZ0Cm+C6Cq6s/zvG8oJDvBix1G69ecU6rtbNP5Xdpy6Ded4ksn\n87AkZVcuzvhi77ZXSkqVjRxmTaWhgwez/oorUo5XWr5D1Eg2wcmcOXn1k7U6rsuRwHs4kaeXuK9/\nyuuOIZJcsbUBUqrjTq2pYUyeYbTpoprakkLe0lWOzfe+xeo3rvjubG2laeVK7mxt5akpU1jV0uLZ\n95eqqhjj0U85VLptbGygpmZar2NOmKzXNwqXUhQkzKf6bDFpvOwyhsyf3+vYkAcfZPKllwZyf6Mw\n/EZVXZ/pvIjcqqp3F0WiEuJVJ+nsUaOYsWZNUeom+TVBlapeU6H9ZgrnjUeKJfbd1dnJ+WvXpvRT\nDpVu8wmTDYtSJPhFoqbSu+92Z4Zz4AC8914w9zUKplg7Fn0GiLzigPQVW4tBLiaoUslRSL/ZFF9y\n36taWpiWZJorp0q3uYbJlgI/5qJSJPiFvXfFnEcfZfuUKb2ObYfKKwZYoQSz1V0foZAQ3SiQq++l\nr1W6LTZ+nd6lyCsIu0xJ2IrLKAxTHEWk3AfSfBRfKVdwlU4u5qJi5xWEXaYkbMVlFIYpjiKTb4hu\nFCh3xVduhDnrDjs7+rxTT2X17NnsSTBXhV1fy/BPsRRHRZRXLwXllnFtK4jMFLNMSdiz7rCyo1uW\nL2fB+vXsqa/vdo4P3LqVay65xPwbZYLfkiOzgDuAPTiVcs8BblbV/wFQ1X/LVwARGQvcg5OzNl9V\n/92jzRzgIpyQ4OtVNTWUJ6JY4cHKodhlSsI2F4VFLxOdW3JkD7BmccXUTa14/K44GlT16yJyOc7u\nf1cAq4H/KeTmItIPmAt8AtgGPCsijydmqYvIxcBpqvoBEfkI8N/AqELuGySlLjxoBMecOa29lAZA\nR8ddNDfPyEtxhG0uCgtzjJc/fhVHvN0lwE9V9S0RKUbFrJHAK6q6GUBEfgxcCiSWN/kk8AMAVX1a\nRI4SkeNUdUcR7l9ySpUlbgRPKcqUVGIxvWyEbaIzCsdv5vgvRGQj8PfAMhEZTHEmCEOBPyZ83uoe\ny9bmxCLcOxBKlSVuBE85lSmJMo2XXUaNG3Ycp2bBAssaLyP8Zo5/0/VzvKWqXSLyLs7KoFD8rlqS\n17ae1zU1NXW/r6+vp76+Pi+hiknYkUrlEtFVDuSzm19UCLMuVTJ91UQXBdrb22lvby+4H1EfNdpF\nZDzwlKq+LSIzgHOBO1T1uYJuLjIKaFLVse7nW4EDiQ5yEbkPaFfVH7ufNwJ1yaYqEVE/36Uv4RnR\nVVNDbPZsUx550tKyiubmtoQyJWNCzz7PhleiYc3DDzP7yittsO7jiAiqmvMOT34VxzpVPUtEPg7c\nCfwH8C1VHZm7qL367Q/8H3Ah8DrwDHClh3N8kqpe7Cqae1Q1xTluiiOV6bEYd7a2phyfEYv52qXQ\nqAxijY20elSijS1ezNLZs0OQyIgK+SoOvz6OuBH3EuBBVV0CvC/XmyWjql3AJJyy8BuAhar6sojc\nKCI3um2eADaJyCvA/cBXCr1vX8EiugywKCaj+PiNqtomIg8AY4Bvi0gV/pVORlT1SeDJpGP3J32e\nVIx7lQvF8ktYRJcBFsVkFB+/iuMzQAyYpapvisjxwNdLJ1bfpZiZ5uVedNHIHS8neF9NNDRKhy8f\nB4CI/CNOIt73RORY4HBVjcw+j5Xi4yi2X2JVSwttCRFdY9yILou2qjwyOcEBmh97rCeK6dJLzTFu\n5O3j8FtypAknh+ODwPeAg3Gyxj+W6w3LmSAG22L7JdIVXSyn+lmGPzJV2106e7YpCqNo+DVVXQ4M\nB34HoKrbROTwkkkVQYIabIPwS5RL/ayWthbm/GgO+3QfA2QAjVc1Mm5MdOSLGuYEN4LCr+LYp6oH\nxP1hisihpRMpmgQ12Abhl8i0qomKCaulrYUp86bQMbznOXTMc96b8vDGnOBGUPhVHItE5H7gKBH5\nZ+ALwPws11QUxRxsM7UPItM83apm5zvvRMaENedHc3opDYCO4R00P9JsiiMN5gQ3gsJvyZFZItIA\nvAP8HTBDVdtKKlnEKNZg68fkVeo9MdKtavapRsaEtU+9FfXeA2Z4SYeV8jCCwvdGTqraCqSG+/QR\nijXYpjN53fStbwVmIkq3qlk+a5Zn+zASBgeIt6KuOsgML5noi9V2jeDxG1X1KeDbwHH0FBxUVT2i\nVIJFjWINtulMXu9s2MC8hGtKbSLyWtW0zpnj2TaMhMHGqxrpmNfRy1xV81wNkydZDophhI3fFcd3\ngEsSa0j1RYox2KYzeQ1LUjRhmIiilDAY92M0P9LM3gN7qTqoismTJpt/wzAigF/Fsb2vK4105DrY\nerX/UlUVV3msUII2EYVdAj6ZcWPGmaIwjAjiV3H8VkQWAo8Cf3WPqar+vDRilQ+5DrZe7bs6Ozl/\nbeo26mGYiErtmDcMo/zxW1b9+3hsnqSqny+BTHlRziVHvCKtptbUMNb2zTAMo4SUej+Oj6vqr7Id\nC5NyVhyQvqaUYRhGqSi14nhOVc/NdixMyl1xGIZhBE1JihyKyHnAR4HBIvKv9ITiHg70y1nKPkLU\nayxFSb4oyWIYhj+yOccPpkdJJBY1fBv4dKmEKmeiXmOpmPIVOuhH/VkZhuGNX1PVMFXdIiKHquq7\nAciVM1ExVcU+H6O1OjXBPrYlxtKHwt/nu1jyeQ36NWtrmH3TbN+DftSflWFUOqXec3yoiGwANro3\n+7CI3JvrzfoCUa+xVCz5MhUhDFoWwzCCxW8exz3AWOAxAFV9XkTqCrmxiBwNLASGAZuBz6jqmx7t\nNuOYxvYDf1PVkYXct9TkWmMp2dxz3hnn8ZuXf1Mym38m+XIxPRVj0Ld6VIZRnuRS5PA16b1RTFeB\n9/4m0Kaq3xGRb7ifv+l1a6BeVf9c4P0CIZcaS17mnuU/W05XbRec4nwuts0/nXyjPjYqJ39DMQZ9\nq0dlGOWJX8Xxmoh8DEBEDgYagUJLkHwSiK9afgC04604oCeaK/LkUmPJy9zTdXEXLAeqnc/F3oMi\nnXy57n9RjEHf6lEZRnni1zl+LDAb+ATOIN4KNKrqrrxvLLJbVQe57wX4c/xzUrtNwFs4pqr7VfXB\nNP0V7BwPOjS0/vp6Vp6yMvXECmB0z8e6V+to/357yeTIJEume7e0tfQe9K+0Qd8wyomS5HHEUdWd\nQM7biIlIGzDE49S0pP5VRNKN+h9T1Tdc5dUmIhtVdbVXw6ampu739fX11NfX+5Y1jNDQdOae5OIu\nQdj88zE9WRFCwygv2tvbaW9vL7gfvyuODwL3AkNU9UMicjbwSVW9M+8bi2zE8V1sF5HjgRWqenqW\na2YCf1HV//Q4V9CKI4zQUC9l1b+lP10f6uo2VdU8V8PsSf5DXIspS1D3NgwjHEq64gAeBL4O3Od+\nXgc8AuStOIDHgeuAf3f/PprcQEQOAfqp6jsicijQANxWwD3TEkZoqJeNf9SnR7Fm4xr2vhqszd/8\nDYZh+MWv4jhEVZ+OR1W5pqW/FXjvbwM/EZEbcMNxAUTkBOBBVR2HY+b6uXvf/sDD7ha2RSes0NAo\nmXuiJIthGNHFr+LYKSKnxT+IyKeBNwq5sRte+wmP468D49z3m4APF3Ifv1hoqGEYhj/8+jhqgAdw\nCh7uBl4FrlbVzSWVLgeKFVVVqVFCVkzQMIxkSlpWPeEmh+L4HN7O9UalJiq1qqI4QBejrpRhGJVH\nSZ3jItIBrAFWu6/1ud6oHMlVCUS12muuyX2GYRiZ8Ovj+BDwEeDjwH+IyN8B61T1spJJFjL5KIEo\nDdCJSu+FjS90h/cmYsUEDcPIB7/VcbuAv+Fkbx8AdgI7SiVUFMin+mtUqr3GlV5rdSsrT1nJmwen\n1I4ErJigYRj54XfF8TZO7sb/A+ar6p9KJ1I0yEcJRKXaa4rSqwGWARcmHLKIMcMw8sSv4rgS+Efg\nK8AXReTXwCpV/WXJJAuZfJRAVEJ6U5RetfNn0JJBnP2hsy25zzCMgvBbq+ox4DEROR24GPgX4Bag\nYm0d+SiBYmRfp3PI5+Ko91R61TBSRtrOeoZhFIzfqKqf4STidQCrgGuBZ0ooV+jkqwQKyb5O55B/\ndu2zLPj1grSOeq/NoDp+Hf7KxzCMysRvAuAtwH2q+raIzADOBe5Q1edKLaBfopLHUQjpCi0e03IM\nu8alVrCPbYkx+crJnjka13z0GqfmVQUmMxqGURxKXeTwWnenvo/juFj/A6fgYaS3cS030jnkuw7y\n3mxx74G9aaO/1mxcY2YpwzBKgt9w3P3u30twChAuAd5XGpH6Lukc8gf2HvA8XnVQVWRCgA3D6Dv4\nVRzbROQBYALQIiJVOVxr+KTxqkZq1tb0OjbkV0Pod1A/J5w26fjkKydHJgQ4yrS0tRD7fIz66+uJ\nfT5GS1tL2CIZRlnj11T1GWAsMEtV33Q3Xvp66cTqm3g55DsP7mTtpWudwvPLcTbuVTj+sOO720ch\nBDiqRLUMjGGUMzkVOYwyleAc98LPXuCVXNW3UMLY2dEwyoVSO8eNkPBjigpqA6YoVv7NhvmADKP4\nmOKIOFHJRi9Xk4/5gAyj+JjiiDhR2Qu8VJV/S72KiYriNYxKwhRHGRDkXuDpBvJSmHyCWMVERfEa\nRiURmuIQkfFAE3A6MCJdFrqIjAXuAfrhVOb998CE7GNkGshLYfIJav+SIBWvYfQFwszFWAdcjlP7\nyhMR6QfMxQkFrgWuFJEzghGv75FpIPfKMal5robJV+Zv8jHHtWGUJ6GtOFR1IzjhYBkYCbyiqpvd\ntj8GLgVeLrV8fZFMA3kpTD7muDaM8iTqPo6hwB8TPm/F2cLWKAHZBvJim3zMcW0Y5UlJFYeItAFD\nPE5NVdVf+Ogip4y+pqam7vf19fXU19fncnmf57wzzmP14tXsGbun+1gpB3JzXBtGsLS3t9Pe3l5w\nP6FnjovICuCrXs5xERkFNKnqWPfzrcABLwd5pWaOF4t58+Yxfvx4Bg8e7Hm+2zE+qAM2AQJVf6pi\n9GmjeeLRJ4IV1jCMQMg3czwqhQrTCf5b4AMiUi0iB+MUWXw8OLHCpVjF+ebNm8ekSZMYPXo0nZ2d\nnm26HePVwAXACNjbuZcnH3uSefPm5f0dDMOoPMIMx70cmAO8H6fi7lpVvUhETsAp3T5OVbtEZBLw\nFE447ndVtU84xr1CY1d/azWn/tepDD1uqO9EuZa2FhatXsQhRx7Chg0bGDFyBM8+82zKyqOXY/wv\nwA+AnXDIkYcwfvz4jP2XWxmScpTZMKJEmFFVi4HFHsdfB8YlfH4SeDJA0SKBV2jsnrF7WL98Peur\n1/tKlOulfE4CfgCvbXnNU3l0O8YTlAbHwsgLR2Y3bxWQwBf0IF6upVMMI0pExVRlJJEuNDZu1Ivn\nV2Sil/I5DLgOONZRHslmq8arGhm2ZlgvpTHs3GF87Qtf89c//uWKEx/EW6tbWXnKSlqrW5kyb0pJ\n98soVGbDMExxRJZ0obGJcWbZEuVSlI+rPOJmq7jyaGlrYdZ3Z7H9V9thJww4bAD1F9Yz76vzMs7C\nC03gC2MQt6RDwyicqOdx9Fm8chz4JXBaz8dsiXKeyucwGHnRSDpf7Oz2eRw49QBbX9rqmKmOhSF/\nP4SvfeFrWU03hSbwhTGIW9KhYRSOrTgiyrgx45h902xiW2Kc+bszOfhnBztKo9o5H986NhPpyoR8\n7QtfY8WKFdTW1vLaltfYumJrt3mK62DLqC1ZZ/0tbS3s7NxJ1dLeA+7ApQMZdfooX98xjEG8FKVT\nDKOvYSuOCBPP1G5pa2HinRPZvmk7vIrvtMhsCXYLFy7krLPO6rng0zjmLDLP+rsdzCM74BlgEU5s\nnMKe0/ew4NcLGNE2IqvjfmfnTqo2VrF3bM+9Sp05bkmHhlE4oScAFotKTgAsxfannZ2djB49mg0b\nNvQcdFccHJa5717yLAMu9GiT4fpekU2bgU1Q9W4VtUNruX3S7aGXkDeMvoJtHVvBFNsXkKg0Th52\nco+PYyfwAyeaavJX08/6e8mTxtiZSbZeTvFq57WXvRy75dhAlYaF5RpGfpiPowwopi8gUWnU1tby\n7DPPct+t91F/YT2HHHkI7ATdqIw4Z0TKtfFM9hfXv9hz8ID3fTLJFoXIJgvLNYz8McVRBpx3xnkM\nXDqw17F8HLrJSmPFihUMHjyYcWPGseKRFbz6+1e7HebJeR6JORe7z9ztmKgAauh571O2KEQ2RUF5\nGUa5YqaqiNPS1sKCXy9gz+l7YDkgMPCtgVxz5TU5mVTSKY1kO//UmVP5t9v+rTvPI94uxbwEsBwG\n7RtE9THVyHPC4YMO9+VsLlU59Vx8FlFQXoZRrpjiiDheA/Ye9rBm4xrffWRSGil2/h91cNvM21KU\nR8oMvdp5Df3dUI495tjuwXryldkjlEoR2ZSrz8L2AjGM/DHFEXGKYVJZtGhRitKA9Hb+/1n6P6xY\nsaJb2SxatCjtDL3jjx289Pcv9Xz26WAu9qZQue5fbmG5hpE/pjhCJpt5pRgmlZtuugkgZT+OTEpp\n8ODBrFixgkWLFnHTTTdR3VadMkMfuHQgez68p9e1mQbrUpKPgi228jKMvoIpjpBoaWthxj0zePnP\nL/dKgEuesRfLpBJXHolkU0qDBw/uvs5rhr510FbWV69PuT4MB7P5LAwjOCyqKgTi9vi176ztpTQg\nNSQ0sfRI3at1xLbEmD1pdlFmyn7Lb8TDcGc9PAtV5etXf52lDy1l6HFDPfsNY7D2+i4Dlw5k6/at\nBW2CZRhGKrbiCIFue/wK7/PJM3a/JpWm7zQxd9Fcuvp10X9/fyaNn0TTLU1p2/ux82dyOkfJwZz4\nXbb9aRsdf+xgz4f3sL56Pevxt3+JYRj+sJIjAZDsx3h91+uOQzmPch3paPpOE3f97C66Lu7qPtb/\nif5M+9S0jMojG9nKnbS0tfRWPD6iqkpNKUq0GEYlYiVHIorXjH3g2oHw9/QkzyUoj3Qz9mxO9LmL\n5tJ1SVeva7ou7mLuT+cWpDiyOZ0TV0NxGWc9PCvU2k+W3GcYpSXMPcfHA03A6cAIVX0uTbvNwNvA\nfuBvqjoyKBmLgecWsMP3OBFJY92IpOWZi/z5yVHo6tdbacTpOsj7uF/8Op1b2lqYOGsi2z+2vfvY\ni7NeZD7zs1bJLWahwZa2Fl5a/xKckl1mwzDyI8wVxzrgcuD+LO0UqFfVP5depOLjOfuthlN3nMqJ\nW05kr+6lqiazicdPjkL//d7/lP0P5PdPHB/Qt+3YxsCNCUoO71XRjOYZvZQGwPaPbedbc7+V9nsV\nu9BgvL9dZ+7yvZIzDCN3QlMcqroRHBubD3K2wUWFdDP2E4ec6Nve7sf0Mmn8pFQfR0t/Jn16Ug7S\nOvQa0KuBzTDw0YHUnFTD0PcP9UyUe7XzVc++Xt3hfRxyT9rLRkp/bomWY947htl3FScSzTCM8vBx\nKPBLEdkP3K+qD4YtUC4UI/LIj7ko7seY+9O5dB3URf8DjtLIx7+RMgBXw57qPQzdMjStspP9aXT7\n/vT3KbYvold/1XSXaDnz1TNNaRhGESmp4hCRNmCIx6mpqvoLn918TFXfEJFjgTYR2aiqq4snZWkp\nRmkLv8qn6ZamghzhcdIN6Gs2rCH2+RiNVzUC9PJNDKoaxO5lu3tHif0SqgdXp71PsZP2LAnQMIKh\npIpDVccUoY833L87RWQxMBLwVBxNTU3d7+vr66mvry/09kWh0NIWQddVSjcAvzXgLVqrW3nxzhdh\nAL18GkM2DeGovUfx5vI3HcOiwhAZwh3/ckfa+xQ7DyRKeSWGEUXa29tpb28vuJ/Q8zhEZAXwNVX9\nnce5Q4B+qvqOiBwKtAK3qWpKkH6U8zjKDS+nNb8ETsMx/6TJPxn+zHAGHzc4p5yOYueBRDGvxDCi\nSr55HKEpDhG5HJgDvB94C1irqheJyAnAg6o6TkROBX7uXtIfeFhV707TX1kqjqjuex0fgNdsWMNb\nA96CU+nZh2MFMDr1mrpX62j/fnva/qL4PQ2jL1N2CYCquhhY7HH8dWCc+34T8OGARQuMKO97HTev\neWZh57hdbJS/p2EYuWNFDkOkHPa99ioeOIQhDPnf3jEPmbaLLYfvaRiGf8ohHLdiKYfSGJ6O+RmT\nU49lcNaXw/c0DMM/pjhCJJ/w0TB8Bemiwvze18JkDaOyMMURIrmGj5arr8DCZA2jsgg9HLdYlHNU\nld/w0XIuF25hsoYRPcouHLfYlKviyIX66+tZecrKlOOZwmANwzDSka/isKiqMsJ8BYZhRAFTHGVE\ntj3C43uD119fb/tsG4ZRMsw5XkZkqllVro5zwzDKD/NxFIHETY+279zO8ccfzwnHnBBYWY2Wthau\nm3oduy7ZlXKuHBznhmGEQ9mVHKkUumf6gzrgL8AlsItdvMRLgcz4u3e9OzRVaYAl2RmGUXzMx1Eg\n3eU0OkipGBtEWY3u++dYP8owDCNfbMV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PsfWSrfTfuz/t7e28+PiLHLLykDilcejxh/KDb/4gVz8pJfkoJBkUFolUegS94vgF0ATc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\nZDZ+7rkHvvnNrsMjGhp4buX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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Find the maximum silhouette coefficient #\n", "\n", "The silhouette coefficient compares inter- and intra-cluster distances to find the value of k that best separates the points into clusters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.metrics import silhouette_score\n", "\n", "def kmeans_silhouette(k):\n", " kmeans = cluster.KMeans(n_clusters=k)\n", " kmeans.fit(data)\n", " labels = kmeans.labels_\n", " score = silhouette_score(data, labels)\n", " return score\n", "\n", "silhouettes = []\n", "for i in range(2,10):\n", " silhouettes.append(kmeans_silhouette(i))\n", "\n", "plt.plot(range(2,10), silhouettes, 'ro-', lw=2)\n", "plt.title('Silhouette coefficient plot')\n", "plt.xlabel('Number of clusters')\n", "plt.ylabel('Silhouette coefficient')\n", "plt.ylim(0, 0.6)\n", "plt.xlim(1,10)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "(1, 10)" ] }, { "metadata": {}, "output_type": "display_data", "png": 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