{ "metadata": { "name": "2 - KMeans" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "The $k$-Means Algorithm\n", "====================\n", "\n", "Again, we start by generating some artificial data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.jet() # set the color map. When your colors are lost, re-run this.\n", "import sklearn.datasets as datasets\n", "X, Y = datasets.make_blobs(centers=4, cluster_std=0.5, random_state=0)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As always, we first *plot* the data to get a feeling of what we're dealing with:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1]);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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utGrVKgkObnrB9EKRoKBGsm7duqvuFx5eW2Bq7j5JYjZH6AnAdcDV2llsy8le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\nAAAASUVORK5CYII=\n" } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data looks like it may contain four different \"types\" of data point. \n", "\n", "In fact, this is how it was created above.\n", "\n", "We can plot this information as well, using color:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1], c=Y);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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e5eeff6Z169Z3JG9rl5WVxanTcTz7ZPZxRR9o+xgcPnz4rrKTJo5m7uR0Rr4M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\nwkpJAhdCCCslCVwIIazU/wHpAdejviYQKwAAAABJRU5ErkJggg==\n" } ], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Normally, you do not know the information in `Y`, however.\n", "\n", "You could try to recover it from the data alone.\n", "\n", "This is what the kMeans algorithm does. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.cluster import KMeans\n", "kmeans = KMeans(4, random_state=8)\n", "Y_hat = kmeans.fit(X).labels_" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the label assignments should be quite similar to `Y`, up to a different ordering of the colors:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1], c=Y_hat);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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2xu6T13Hq34xnKnrTrl07k2M7f/48ntV8sLKzx86tFDNmzMjNJQohiiCZhZJHSineHTmS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\n78LlOhoFNMtRDAkJCaSkpND8Xq4uURw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} ], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Often, you're not so much interested in the assignments to the means. \n", "\n", "You'll want to have a closer look at the means $\\mu$.\n", "\n", "The means in $\\mu$ can be seen as *representatives* of their respective cluster." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.scatter(X[:,0], X[:,1], c=Y_hat, alpha=0.4)\n", "mu = kmeans.cluster_centers_\n", "plt.scatter(mu[:,0], mu[:,1], s=100, c=np.unique(Y_hat))\n", "print mu" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[[-1.47935679 3.11716896]\n", " [-1.26811733 7.76378266]\n", " [ 1.99186903 0.96561071]\n", " [ 0.92578447 4.32475792]]\n" ] }, { "output_type": "display_data", "png": 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fu3cvH3/8MRs2bMBms2GxWFi5ciV//etfe3rJQeeDD9bR1BRGYuI47HYrH36Y\nR3x8HJGRkdccV1xczF/+sgaIwu12sHv3Uf7pnx6/LsRbWlqoq6sjMDDwumuIwSciIoKvPv88VVVV\n6HQ64uLietwfbbVa2fjee4wNDiY4MJCm1lY+efddnv3+92/6CcLtdtNUV8eEK8viav38MF6ZsSkB\nLqAXfeA//elPKS0tpbCwkPfff5+77rrrtgpvj8dDaWktUVHJAOj1/qhUwdRfmT33RTt27CMwMI3E\nxHRSUkZjNvtz8uSpa44pLi7mV796ldde28qvf/0ueXmfDcj7EL2j0+kIDQ0lNDS0Vw/qm5ub8XO5\nCL6yGmFIYCAap/OWu9RrNBoi4+IorakBwGq30wzyIFJ06LOJPLfbKBS1Wk1ERDANDdWYTNG43S7c\nbssNp4Xb7Q602quLDWk0OlwuV8f3iqLw3nvrCAwchdFowu12sXXrfjIyhhETEzMg76cv2O12bDYb\nRqOxR10IvsZisbDq7bdprqzEDUy8+26mf2lZ2q4yGo24tFqaWlsJCQyksaUFj07X6SbHix99lFVv\nvUVpaSlutZrZS5fKpzfRoU8CfNasWR0PbW4njz66mDfeWEVpaQmKYmPevIk3nPE3YcIoPvxwH5CB\n02kHakhLy+143el00tJiJympfSqzRuOHWh10y7uvwebQoXzWr9+Fx6MhJiaIxx9/6LZfw3rr+vX4\n19QwJjERp8vFoU2biE9KYsiQId2+lr+/PwuXL2fDe++hNptR9HruXbGi01UGw8PDefL552lubsbf\n319WJRTXkKn0txAbG8u3v/0kZrOZgICAm64lMXFi+3Tsw4dPo9drmTPn/mv6KNv7T8Opri4iOjqF\ntrZmVKrm61aXs9ls7N17gJoaM8nJsUyalD0odhCvqKhgzZrdxMZOQqczUFl5mdWrN/LVry7zdmld\npigKe3bt4uiePWg0GqbMndvp8rZVxcVkXdlbUuvnh0mjwWw29yjAAdLS0nj2+9+npaUFo9HY5TDW\naDQd66R4i9Vq5Uh+Pm3NzSQNHcrw4cO9Wo9oJwHeCX9//07HzqpUKrKzJ5CdPeGmxyxffh/vvrua\n0tLP0OvVPP74wmv+QnC73bz11gcUFXkwGiM4fvwE1dX13H//vX32XnqqfWPiUHS69odtUVFJFBXt\n8XJV3XPo4EFObNjAuIQE3B4Pu/7+d4KMxlvu1h6ZkEBlYSFDYmJwud00ut29DlKDwdBvwx77i8Ph\n4L3XXkO5dCthAAAgAElEQVRdUYFRr2fzrl00P/AAEydN8nZpdzwJ8JuwWq3s3Lmbysp6kpJimDFj\naq/GgZtMJr7+9SewWq3o9frr7qyrqqooLm4mOTkHgNDQKA4f/ox58+7y+vjd4OBg3G4LbrcLjcaP\nhoZqYmJ8a23qy2fOkBoRgf+Vu96EgACKLl26ZYDPXbSID998k5qyMhweD2Nmz2bo0KEDVfKgUVhY\niLu8nMyUFACi7Xb2bt0qAT4ISIDfgNvt5u23P6SkRCE4OJpLly5TXV3P8uUP9uphrUql6sa+iwrc\ndJWNgZWcnMycOaPJy9uHWm0gKEjhoYeW3vIcq9WK3W7HaDQOim6gAKOR5tJSIq7027c6HER3Mlbf\nZDLx1W98A7PZjE6nu2OXY/V4PNc8tNao1bi/8JBeeI8E+A3U1tZSXGwhKWkyAMHB4Zw5s7uj77I/\nxMTEMGRICJcvnyQwMByLpZxp0zI67r4VRWHPnn3s2pWPWq3mrrtymDRpYr/U8mVnzpyhuLiS2Nhg\nJkwYybhx427Zf3vw4CHWr/8MRdESFeXPV76y1Ot9uNNmz+b9ixdpLi7GrSgo0dFd2uJNq9XecqOH\nO0FSUhKfGo0UVFYSEhDA5fp6MufM8XZZAgnwG1Kr1SiKB0VRrsyI8gBKl+++FUXh0KF8Dh8+hV6v\nY86cqaRc+fh5MxqNhscfX8q+fQeprW0gKWlCx8NRgKNHj7F+/VHi48ehKB5WrdqL0RjIiB4ulNRV\nZ8+e5a23tmIyDcfjcbN+/X7i4+NJvLId2Je1P/DcS1xcDjqdgaqqQlat2sCTT67o1zo7Ex4ezsrn\nnqOoqAi1Ws3QoUO5cP48l06fJiAoiMkzZ96xd9idCQwMZPmzz/LZ9u2YLRbGTZ/OpJwcb5clkAC/\nocjISEaNiuPkyWMEBITT1lbN1KkZHTMra2tryc8/htPpIStr5HVhduhQPqtW7ScqagQWi41XX13L\n17/+SMfIlObmZt58803+8IfXqK2tISjIyCOP3M83vvF1cnNn3LCms2cLMJmGoNe335EbjcmcP1/Y\n7wF++PApQkLSCA1tH3tst1s5dercTQO8vr4etfraB57FxYNj0pLRaGTMmDFA+/6Wh1avZojJhMVm\n491z51j59a/32ycsX2cymViy9NbdZmLgSYDfgEql4pFH7iMt7SjV1Wbi43MYNiyN8+fPY7FY+OST\nPShKLBqNHwcOfMRTT913zdCyw4dPExmZQVBQe7dBa6uFS5cKiI2N5dSpU+TmzsVmi6a1dSxgora2\nmV/+cjO//vXveP/9t7j//vuvqykoKJC2NgsmU/vHeZutmeDgG4doX9JqtbjdV/s73W4nWu3N/7MJ\nCQnB47n6wLO+vpLY2Ih+r7O7juzaxdj4eAKvjAhpKyqisLCQsT3Y+UYIb7kjAryiooKamhqMRiND\nhw7tUleIn58fkyZlA+2LGr388l9padFTWHgWi0XPwoVT0Wg01Nfr2bPn8DUBbjDosFjsHd+73Q60\nWi1ms5lZs+7GbJ4GfDEownC5knG5Cli27CucOXP8utEOM2dO5vz59ygubsXlchAcbGX8+EW9+r10\nxYwZ2Zw9+yFlZVY8Hjf+/mbGj5930+OTkpKYOzeT7dv3oVbrMRrp9IGnN6jU6msWC1JUqttuNrG4\n/d32AX706DE++GAnarUJt9vC5MlDWbJkQbf+Z928OQ+nM4akpBRaWtwUFxdSXl5OUlISKpUKt/va\nVcPmzJnKq6+uobW1CbfbSXi4ldGjR/H73/8BqzWBa8P7i1JxOrP43//9Nb///W+uecVkMvGNb/wD\nmzdvYdu2Q6hUkfzlL++zcuWDREVFdfO30nXx8fF8/evLOHPmPGq1irFjF3baVzx79kyyssZgs9kI\nCwsblLMHJ82eze4PPiDZaKTFZsMRFnZHDhEUvq3Hy8l26eJeXk7W7XbzX//1EuHhk9Dr/a8sULWf\n555b2q3V3F5++XUcjmQCA0Noaqpj/fqPSE0dQVpaGs3NBTzxxELS09OvOae6upqLFy+h0+kYOXIE\nQUFBJCenU1IyE7hV10cjAQGv0tLSdN1fMvX19fz6128RGTkBgyGAuroKAgOr+Na3nunGb0V87ty5\nc1w+dw5DYCDZkydL/7cYNPp9OVlf4HQ6cblUHQ/+1Go1arUem83WretkZAxh27ZLJCePxWAIZPTo\neEaONBIW5mLixHtvOBkkOjr6uuFntbVVQGcTYEJxOOxYrdbrxow3NDQARgyG9p9HRMRRUnIRu90+\nKO9yB7uMjAwyMjK8XYYQPXZbB7jBYCA1NZrLl88RG5tKU1MdAQHObo/rnTVrOq2tVg4d+gyXy8GI\nEdEkJsYzalR6pwvyf1FgoBGrtRW41WQeG4qi3HC6dUhICIrSjNNpR6vV09hYS2iov+wUJMQd6rZf\nE/SRR+5j1Ch/6usPYDLV8+STS7sxG7Kdn58fS5Ys4LvffQqj0UhNTQjHj9v4y1/WcebMmS5fZ9my\nh9FqT97yGJXqBPPnL7rhcq2RkZEsWTKNqqqDlJUdxO0uYPnyJfLwTYg71G3dB97Xdu7cxa9+tQqX\ny4/AwACGDUsnIcHN1772D106/9KlS2RmTqStbQVwo08BTQQE/JUtW9Yy7Uv7Htrtdi5fvozH48Fk\nMqFSqTCZTB136p/P1Nyz5ygajYY5cyYzblxWL9+xEMIbpA+8H2zfvoe6Oh0pKdnY7RYOHz6EyZTe\n+YlXpKWl8dprf+KJJ/4Jm20KipIJGAAncJKAgL3813/9x3Xh3dbWxquvvktlJahUaoKDrTzzzPJr\nulkOHz7C+vVHiYsbi8fj5u9/34nRGERaWlrfvHkhxKBz23eh3IzNZsPtdnf5eLfbTWurm/DwCJqb\nG/B4NLS02ElP795kmkcffZSdO7ewaFEAOt1LBAT8Bq32l8yebWf9+r/zz//87evOOXLkKFVVWlJS\nxpGcnInNFsWnn167nOvp05cID0/DYAggIMCIv38CFy4Udqs2IYRvuePuwK1WKx99tJ5z50pRq2HR\nopldWhRKrVYTHh6CyTSEioo67HYnERExjBs3rts1ZGdn8/HHH9LW1kZDQwPBwcG3HMJmsbSh119d\nOS8gIBiLpeGaY4KC/CkpaSYkpH3Wo8PRRmBg/40PF0J43x13B75p03bOnWsjMXEmUVE5rF69h+Li\n4k7PU6lULF06D7u9gPBwiI62s3BhNgkJCV1q1+PxUF9fT0NDQ0ffVkBAAPHx8Z2OP05LS8ZqLcdm\na8XptFNfX8DIkddOOsnNnYpWW01x8UmKio4REWG7ZjEsIcTt5457iPnii39Erx/VMZa6pOQsS5ak\nM6mLi9PX1tZSU1NDQEAAKSkpXRoBYrPZeO+9VRQU1AMexo8fyn33LezWOtmHD+ezdet+XC4X06eP\nY9as6deNVLFYLB2r7aWmpnp9IwghRM/IQ8ybiIoyUVJSh8GQhKIouN3NXZqB53Q62b//IFVV9SQk\nRDF8+PAuD9/Ly9tNQYGTpKSpeDweDh06QkrKCcaP73r3y8SJE5g48eZbtkH7zjmyGJMQd447rgvl\n3nvnoNdXUVqaT0nJfiZMiOt0g1ZFUfjb31azceM5Ll5UsW7dSVavXt/lNsvLawgNbZ+6r1arCQiI\npLKytlfvQwgh7rg78IiICJ5//qtUV1ej1WqJi4vr9E66rq6Os2erSU6egkqlIjw8luPHd3PPPU2E\nXNmi61YSEqIpLCwjODgcj8dDa2sNsbG33tm8ubmZmpoawsPDe7ybjaIoVFRU4HA4iIqKIjAwsEfX\nEUIMTndcgEP7TvOd7ZBzIz2d8Thr1jQqK1dTULAXj8fNpEmpZGbevKtjx45P+cUvXqOtTUVAgIfn\nn1/BokULu9WmoiisXr2e/Pxi1Go9AQEOnnxy6R2/PZgQt5M77iFmT3g8Ht566++cP99GcHA0TU2V\nZGaaePTRrm9y7PF4aGhoQKPR3PKOurKykmee+TGQickUS0NDCR7PCf7whx+TnJzc5ZovXLjA669v\nJSUlB5VKRV1dOZGRTTzzzFe6fA0hhHfIQ8w+pFarWb78QfbuPUBlZS0JCSOYPHlSt+7I28eRd7YS\nIZjNZpqbNSQktN8ph4YmUFx8hMbGxm4FeGtrKxqNsaPGkJAIams7Hy4phPAdEuBdpNPpbrpfZV8K\nDg4mKEihqakWkykai6Uaf39VtzfcjYqKQlEasNut6PX+VFVdJjMzqZ+qFkJ4wx03CmWwS0xM5Nln\nF+Nw7Keo6BNaW/fwjW88TFJS98I3Pj6epUtnUV9/iJKSnaSl+bFw4dx+qloI4Q296gMvLS1l5cqV\n1NTUoFKpePbZZ/nmN7959eK3SR+4N3w+YSgmJqZLXS8343a7cblcsuGDED6kq9nZqwCvqqqiqqqK\nrKwsWlpamDBhAmvWrGHEiBHdKkIIIcRVXc3OXnWhxMTEkJXVvuZ0UFAQI0aMoKKiojeXFEII0UV9\n9hCzqKiIo0ePkpOTc83PX3jhhY6vc3Nzyc3N7asmhRDitpCXl0deXl63z+uTceAtLS3k5ubyH//x\nH9x///1XLy5dKEL0mdbWVnbv2kx9XSHBIbFMn7mwx7N0fZHb7aagoACn00l8fPxt/d4HpA8c2hd5\nWrRoEQsWLODb3752MwIJcCH6hqIorPrwNZJjixk+LIKS0gaOnw3h4WXfQKvV9lu7zc3NlJWV4efn\nx5AhQ/Dz887IY5fLxbq1b6NXnyfYqOFyiZY5854mPj7eK/X0twHpA1cUhaeeeoqRI0deF95CiL7T\n3NyMva2QieMTMBoNjBoZS5B/PXV1df3WZm1tLas//C3VJe9w6fTrrFn1Bg6Ho9/au5Xz588TqDvH\nwnlDmD41idnT9ezbs84rtQwmvQrwPXv28Pbbb/Ppp58ybtw4xo0bx6ZNm/qqNiHEFVqtFocTHA4X\n0L40Q5vV0693xPv3bmLKBDe5M5JYcE8K4cYCTp861W/t3YrNaiXMdPW9hpkCsVktXqllMOnVv/3p\n06fj8Xj6qhYhxE34+/uTPuJu1m/axJBkP8orXIRHTSEiIqLf2rS2NRIRfnUrv4hwHc3Wln5r71bi\n4uPZsRmGprRiNBo4lF9BfMJMr9QymMhiVkL4kEuXLmGuryU4xNStTUV6Yvdn27E3b2PW9CSsVicb\ntlaSM/0fe7SSZ184f+4cB/d/jNNpJSl5HLNmL+jX/n9vGrCHmH1RhBBiYCmKgsViQa1W33RHKpfL\nxc5PN1FUeAiNRsf4iQsZm9n9TbxF90mACyFuyOl0snnjR1gaTuHxQET0eObOu++me7QqitKvd/ri\nehLgQtzG6urquHD+FIqikD58NJGRkV0+d9/endgtm5g1IwVFUdieV0xYzP1MmJjT+cliQMh64ELc\nJqqrqzl0YBt2WzNxCSMJNUWye+c7ZGepUKlg4/rPmLfwH7u825K5vozMjFBUKhUqlYrUIUEUlJV3\n6Vyr1cpnOzdRV3uZIGMU02feS1hYWG/enugFWU5WiEGssbGRzRv+TMaQQjJH1PHJmv/k1T9+naa6\nXTjsdjLHJJKdqXDqxIEuXzMkNIbikvYheIqiUFzSQkhoTKfnKYrC5o1/JzQgn8X3aElPLmTDutew\n2+09fn+idyTAhRjEiouLSUu2kZYaxclTl3h4sY4Z2W08+kAIRYUnKS0zo9f74XZ3fYJN9qTpVDek\n8eGaYj5YU0KzfTTjxmd3el5bWxvNTZeYNDEJo9FAxvAYQoyNHD58mIsXL9LW1tabtyp6QLpQhBjE\nNBoNdkd7X2hDg5mkyf7UN4ZTWeUixGjn3Pkq6hsDyJ7a9dEher2e+x/8B+rq6lCpVERERHTpIaVW\nq8XlUmG3O9HrtThdLo4dO05KcjPWRiMH9gazYNFTvVq/XnSPBLgQXqYoCm1tbRgMhutGgqSlpXHy\neCx79hXR0qKwfVcdU6fNxuOBbbsPExkTT+7s+0hNTe1Wm2q1mqioqG6do9PpGDV2Pus2rmNoioZj\nJ8ox6LQ8vmwkKpWK8xeq2b93C/cuXt6t64qekwAXwovq6+vZvOEdPO5aXG4902Y8wrD09I7XDQYD\n9z/4NKdOHid1ZDaXC/I5eMRDS6uHWXO+y7Tps/uslra2Nt577z3++ubvqKqqJjQ0hIcffoInnmy/\nqy4qKkJRINA0E7sqBIPxEvdkXeq4e4+MCOLEOXOf1SM6J8MIhfASRVF4/93fkT22ibTUKBoaWlm/\npZElD/4zISEhNzzH6XRiNpsxGAw3PaYnLly4wPx5MxmV3sqzK1pIGwKV1fDGB/5syvPjv////yEk\nsJj0VD9qap3YPWPJGJnN8UOvsfCeeAwGP3btLkETcBczZt7dZ3XdqWQYoRCDnN1ux2GrJi21fcNq\nkymQmEgz9fX1Nw1nrVbb5eGCXWWxWJh3zwz+7blannnsamiMGAZ3TbeybRc88k/fZNeWf2X0qHgU\nRWHtJ6fQ66czdPgDvL96I4rHRWLyJGZPmXXTdmRCUN+TABfCS/R6PagCqatrISIiCIfDRZ1ZIesm\nU9tvxel0UlNTg1qtJjo6GrW6awPMFEXhN795iQljmq8J7y+6eyZ8baWLP726g9/+6iuoVCoCAzQ4\nnU7GT5jEuPHZeDyem87kPHhgL6dObEVRPKRnzGTa9Nldrk/cmgS4EF6iUqmYdddyNmz/K1HhjZgb\nPKRlLOjWrEpo3xFr/cdvEqCrxOlU0PqPZOGiRztdatbtdrPxkw94+6//x+//23rLY7+2UmFk7n7+\n80cPUlffSlVdENNiYzvex83C++yZM5QXfczyBxPQaNRs+3QrR48EyazPPiIBLoQXpaSkEL70O5jN\nZgIDA3u0POz+vTtIT6lmfFYSiqKwY+cpThxPZ/yEW4/tPnv2LH7KMRoarYwYdus2EuLa//nReitR\n0cksWLSAgICATmurKL/EmJFB+PvrAMgcY+LomQvAjQNcURRaW1vRarXtn1DELUmAC+FlRqPxpisC\ndkVzczVj04OB9rvh+Fh/qhvrOz2vpbmJ2BgtwUYdtfU2Ym/Rtd7aBnaHwsonvodOp+tybf4BwdTV\nW0m7Msqxvt6Kv/+N97JsbW1l04b3sbYU4nSpGDV2AZNypna5rTuRdEQJ4eMiIodw7kIDiqLgcrm5\ndLmNiMgEAEpLS9m0aRObN2+msrLymvOiomO5WOBiyb0TeOujG3eBfO69NTB/3ix0Oh1OpxO3292l\n2rLGTaKoIo4t24vZsbOEE+eCmDjpxhsx7MrbQEpcEY8/msSKpTGUFKyjqKioS+3cqWQYoRA+zuFw\nsGXTKhrqT+F2w5C0mcycNZdDB/eyZePvMBpKCAxQMLcMYe78b18zbf7QwX3s2P4uP//Fn8j70Enm\nqOuvX1kNU5YE8KdXVuF2NlFVcQJUfozNms/E7Mmd1me32ykuLkZRFJKSkvD397/hcW+/+T88sNCf\nwMD2rpP8oyUouvuYmN35NP/bjQwjFOIOodPpWLRkGeXl5dTU1GA0GmlpaeHQgdUkxTaw/MEUVGrY\ns7+OA/s+ZOSosR39y9mTpjBufDaJSZO5Z8Uz/OhbNlY+rBBsBLsdPvwEfvRiAP/0tR+i1ypo1MdY\n8FgydruL9ZvWYgqL7HQWqF6vJ/0Lk5NuxhgcTVl5CcPTo/F4PFRUuRk+pu/Gut+OJMCFuA2Ul5ez\nfcurpCQ4qCj0cLAtGZXiwBSiQatt7ykNNvqhUTuw2+3XPCD08/NjxWOPMSw9nf998Sf82y+2Ehqi\npbHJyeSc8bz8h/+PBQsW8Ld3f8O83ChUKhUGg5b0VC011RWkpKRw+fJl7HY78fHxmEymHr2HGbMW\ns2Hda1y8XEprm4ewyMkMG9bJ09U7nAS4ELeBvbs/5q7pehLi25eF3bClgNKSAC5cdnDpchMB/nDu\nkpuAoBQMBgO7P9tORdkZDP4h5EyZR3R0NNnZ2fzt7+tpbm7umEz0xTAODIqgqvoSoaEBKIpCda2D\niPgg1n/8Hn7KaUKCNRw95MesOU+SlJTU7fcQFhbGw8uep7a2Fp1OR2RkpEz86YT0gQtxG/jr6z9j\n6WIjAQHtI0QO5RdjVeZxueAYx/K3oNGoyBw3lyX3r+TI4b147LuYkBWNuaGNPYfg/oeeJzg4+JZt\nmM1mNqx7lagwC21WN2rdKFKHZVFy8W0W3DMEgIrKRj47EMCjK57r9/d8O5M+cCHuIHHxozh8ZD/T\npiRhsVi5UKDirnnDmDlzJjzxzWuOLbx8kJWPJqPVajCZAimvLKGsrIyRI0feso2wsDAeeuQ5Kisr\n0Wq1xMfHc+LECcJMV0ewhJkCsdma+uU9iuvJMEIhbgMzc+dj82Tz+rsVrNviYOLkx4m9MlPyy/z8\n9LS1Xd0Aoq3Ng1ar7VI7/v7+DB06lMTERNRqNXFxcVwsVFFf34LL5eZQfjnxCaP75D2JzkkXihC3\nka4sGHXq5AlOHXuPEel+mM0u6ptTue+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} ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "$k$-Means on Images" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this final example, we use the $k$-Means algorithm on the classical MNIST dataset.\n", "\n", "The MNIST dataset contains images of hand-written digits. \n", "\n", "Let's first fetch the dataset from the internet (which may take a while, note the asterisk [*]):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets import fetch_mldata\n", "from sklearn.cluster import KMeans\n", "from sklearn.utils import shuffle\n", "X_digits, _,_, Y_digits = fetch_mldata(\"MNIST Original\").values() # fetch dataset from internet\n", "X_digits, Y_digits = shuffle(X_digits,Y_digits) # shuffle dataset (which is ordered!)\n", "X_digits = X_digits[-5000:] # take only the last instances, to shorten runtime of KMeans" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's have a look at some of the instances in the dataset we just loaded:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.rc(\"image\", cmap=\"binary\") # use black/white palette for plotting\n", "for i in xrange(10):\n", " plt.subplot(2,5,i+1)\n", " plt.imshow(X_digits[i].reshape(28,28))\n", " plt.xticks(())\n", " plt.yticks(())\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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4GNPpFF6vFx6PBxaL5b2hNlJ22kGQxZp2AhTCo2K1ZDIJm83GX087E0mSsL29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\nUBo0aNCg4Uni/wBre6u6A6BSUAAAAABJRU5ErkJggg==\n" } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Warning**: This takes quite a few seconds, so be patient until the asterisk [*] disappears!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "kmeans = KMeans(20)\n", "mu_digits = kmeans.fit(X_digits).cluster_centers_" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's have a closer look at the means. Even though there are 10 digits, some of them are over/under-represented. Do you understand why?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(16,6))\n", "for i in xrange(2*(mu_digits.shape[0]/2)): # loop over all means\n", " plt.subplot(2,mu_digits.shape[0]/2,i+1)\n", " plt.imshow(mu_digits[i].reshape(28,28))\n", " plt.xticks(())\n", " plt.yticks(())\n", "plt.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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OMGfMHvcXImpApVoD+dwZJAR4OH8qCXn79m3HeBRbgDaX30EWz9T0sgI4fX4z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} ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Playing with $k$-Means" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This website allows you to play with the $k$-Means algorithm on another artificial dataset, the \"Mickey Mouse\" dataset.\n", "\n", "You \"step\" through the algorithm by pressing the buttons in the correct order. \n", "\n", "Try to get a feeling of how the algorithm proceeds." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import HTML\n", "HTML('')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "" ], "output_type": "pyout", "prompt_number": 11, "text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Playing with this Notebook\n", "==========================\n", "\n", "Try to see what happens when you\n", "\n", "- Increase the standard deviation of the clusters in this notebook\n", "- Choose a \"wrong\" number of clusters by:\n", " 1. changing the number of clusters generated\n", " 2. changing the number of clusters used by KMeans\n", "\n", "- What happens to result of the $k$-Means algorithm when you have multiplied one axis of the matrix $X$ with a large value?\n", "\n", " For example, the 0-th axis with 100:\n", "\n", " `X[:,0] *= 100`\n", "\n", " Why does the result change?\n", "\n", "- Combine the $k$-Means algorithm with the PCA algorithm" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 } ], "metadata": {} } ] }