{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Sebastian Raschka](http://sebastianraschka.com), 2015\n",
"\n",
"https://github.com/rasbt/python-machine-learning-book"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Python Machine Learning - Code Examples"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 11 - Working with Unlabeled Data – Clustering Analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the optional watermark extension is a small IPython notebook plugin that I developed to make the code reproducible. You can just skip the following line(s)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sebastian Raschka \n",
"Last updated: 08/20/2015 \n",
"\n",
"CPython 3.4.3\n",
"IPython 3.2.1\n",
"\n",
"numpy 1.9.2\n",
"pandas 0.16.2\n",
"matplotlib 1.4.3\n",
"scipy 0.15.1\n",
"scikit-learn 0.16.1\n"
]
}
],
"source": [
"%load_ext watermark\n",
"%watermark -a 'Sebastian Raschka' -u -d -v -p numpy,pandas,matplotlib,scipy,scikit-learn"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# to install watermark just uncomment the following line:\n",
"#%install_ext https://raw.githubusercontent.com/rasbt/watermark/master/watermark.py"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Overview"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- [Grouping objects by similarity using k-means](#Grouping-objects-by-similarity-using-k-means)\n",
" - [K-means++](#K-means++)\n",
" - [Hard versus soft clustering](#Hard-versus-soft-clustering)\n",
" - [Using the elbow method to find the optimal number of clusters](#Using-the-elbow-method-to-find-the-optimal-number-of-clusters)\n",
" - [Quantifying the quality of clustering via silhouette plots](#Quantifying-the-quality-of-clustering-via-silhouette-plots)\n",
"- [Organizing clusters as a hierarchical tree](#Organizing-clusters-as-a-hierarchical-tree)\n",
" - [Performing hierarchical clustering on a distance matrix](#Performing-hierarchical-clustering-on-a-distance-matrix)\n",
" - [Attaching dendrograms to a heat map](#Attaching-dendrograms-to-a-heat-map)\n",
" - [Applying agglomerative clustering via scikit-learn](#Applying-agglomerative-clustering-via-scikit-learn)\n",
"- [Locating regions of high density via DBSCAN](#Locating-regions-of-high-density-via-DBSCAN)\n",
"- [Summary](#Summary)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from IPython.display import Image"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Grouping objects by similarity using k-means"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn.datasets import make_blobs\n",
"X, y = make_blobs(n_samples=150, \n",
" n_features=2, \n",
" centers=3, \n",
" cluster_std=0.5, \n",
" shuffle=True, \n",
" random_state=0)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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XWAVoNY/HbijOjqdTytClUimJx+M5z6/ckh+F6Pwl0VmbCPWFHd310UDZpFTI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\nQgIJDRQhhJBA8v8BCH8c16teZFwAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"plt.scatter(X[:,0], X[:,1], c='white', marker='o', s=50)\n",
"plt.grid()\n",
"plt.tight_layout()\n",
"#plt.savefig('./figures/spheres.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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dQPQDqFWrFu+sXs2wp57ikuRkXlXK7VO0FShJSeH7OnW432n+UzUgE+gFDFKK\n900mTgcalnl/Q+B0YIXJxG2pqcycN4/MN990TMEti6eR7/v372fkyJHUqFGDGjVqUKtWLQB+/vln\nxznO86tSUlLIy8vz+jdo2PCktIcPHy4XKzvttNNcxr7b+eWXX1zOLTv3aenSpXzwwQc0adKEzp07\ns2XLlrKXCJqYbnU0Ydw4zjnP9iy06+uvg7pWNKWuC8YjHKnrgn8opbjjrrvo0LkzXS66iLOPH6dd\nmXOuTU3lmvvuY/eOHVy4fHm5a9wJbKhdm0WnnMLH+/bxbn6+y9O9FbgqJYVfmzRhy/LlPuuiPI18\nb9y4MRMnTmTAgAEV0tPX6/Xr1+fgwYNorR2v79+/v1wWI0C9evU4cOCAY9/532DrYrJs2TIsFgvP\nPfcc1113XblzgiV20jnc0LBhQ24eejO33HxL0N5Tg4YNqZ6eTo2aNV226unpNGhY9nnpJGWDyEbD\nyPpFUrfKWLrzpJ89O9DTFivGMtDPr1GjRhQVF/MfN8eaW62kVq/OB2vW0A84BgxISaFjtWrsBdoA\nluPHmfrCC6wtLi43CLII+Li4mPfWrvWraNfdyPdPP/2U22+/nSeffJJdu3YBkJuby9tvv+3xOvbv\nD9hGvB86dIji4mKX485ceOGFpKSkMHXqVIqLi8nKymLFihXccMMN5a533XXXkZmZye7du8nPz3dZ\n4isuLmbRokXk5uZiNptJS0srV/YTCmLagwKYMf3pkFwnFKnr4oUJwRKJYYmeOlZ4m+xrBA9wxYoV\ndIyPp/qJE2wH7q5Wjb6FhTxYUsI1BQWMe/55zk9I4MfCQm5MSaHPwIFc2KwZFz30EDMLCrimpIRn\nZszg8oQEkoqLKQbWAd2wpTD3TEhg1apV3HzzzT5l8TTyfebMmRw/fpwbbriB/fv3k56eTo8ePejf\nvz9Q3ktyHg/frVs3zjnnHOrWrYvZbObIkSPlxsfHx8fz/vvvM2LECKZMmULDhg1ZsGABZ511Vrnr\n9ezZk1GjRtG1a1fMZjOTJ092iVUtXLiQu+++G4vFQrNmzVi0aFGFPxtPyMj3Ug4dOsQ5553HzJUb\nSK9lGwGd++cfjOrVkV1ff+2Xh1a7Th0pIBaCIpjx8JV57WicQlx21PjVPXrQ56OP+NNsZmpyMo8/\n/TQLZ88mYc8e5uTn09xkooHW/JWWxuwFC+jb1xZS37lzJwP69iX+l184YjYz88QJ2gI3pqbyc3Iy\nDQoKeD2Jeg3TAAAgAElEQVQvj63Agg4dWLlhQ0T1jHZk5HsIcE66sHtRgSZfRFMBsSCUJZxeUDQW\n8jqTl5fH6qwsDiUmEvfvf7P1vfdo0qQJt9x6K088+igXPv00hYWFqNNOI/vTT13+n2/evDnbd+/m\njptv5s233iIXaJeczIRJk7hn9GiefeYZ2k2cyBMFBWz8/HOOHTtGRkZG5SlrIORX04mKpK47r4M7\nv99OrKfASwwqdimrX6ylsGfUzHAsObnbqqW5z5Bzx5o1aygsKeGykSPZkJ3tKBQ1m808PHkySz/6\niPTq1WnUuLHbB9LU1FR69OlDCTC9QQM+3LSJUWPGYDKZGDVmDB9u2sT0Bg3IKypixYoVIfoLCOJB\nOeHsRWmtA05dD4UXFg4kNhZZonG5KxYJpVfWtm1bPv/8c9q0aeP2+CWXXMK3+/bx5ZdferzGgZ9+\nYsiAAfxv9uxy6eMtW7Yke88eRt12G/t//NFvuQTvSAyqDPZYFOB37Mnd+2eutK1DBxLDChcSG4ss\nwcR6whknCifhkNvfa3p7IIjGv1VVQ2JQIcSeuq6UchiVQDyQYL2wcCCxMcHIePK0KjvuJQSPGCg3\nlE1d9zbeIyUlhdxjrss1FSkgDucynF2ePkNvd8lQ/HjpYp/yZVXBeVBGwZd+shQpRDtioNxQttbA\nmwdi/fOXcu9354X5IpwzrioSG7MbzBMnTlBQUOByTOJW4SOS9UbRnnknCGKg/KAiHkigBcTX9u/P\nLwUWrh/5gMvri595irpJJoqKikLmRQE+vaeqMBQyGr2nUHoskdQvWgt5PbX/EWIDMVB+UBEPJND/\nMSaMG8fpTZuyYsE8h1HQaKwWC0op3n3nnZB5Uf7ExiRuFXqCHbUezUSj3HbvMFoTSwTfiIHyE08e\nSKjiGA0bNuQ/Z5/NaS3aMXTsoy7HQmUUAomN2c8984JWtLv0csD/uFWsEOkYVEVGrQdDrMfYfHll\nqdVSIyhN5In1zy8UiIHyE08eyPfff+/7zX4yd84cLunYkauH3RVwMoM/BBIbs+u7edVyh4GKhpqu\nWMCfSbaCb3x5ZUYvtBakDioggq2R8ofzmzd38aLs3tOLzz8fkuvbPwt/liCjsaYrlom2Gqdok6ei\nSDZibCJ1UEHgLu27Vq1aDLrpJkwmc9h+pJ29KPCdzBAogcTGorGmKxbx9QMqBIcYH+MiHpQHvHZf\nSM/g999tCQvhWCdu0ao1jc5vhdls9tt78lZHVXYomjO+Usbffvttbh0+HAif11hZRGqN3+6pjKo5\nKqIei9HroIweozG6fuJBBUFlZrEtX/Yu555/PuB/oa+3tHA7FUkZr127dsA1XUJsEM3GRxCgChmo\nQDs1+Fv7FI4nnEaNGrkYBXey21+zy96vXz9+t5i56f6JLuctmDaZH7I/44zW7StkbDt37kynTp1C\no1iUYeSnUxD9Yh2j6+cPVWaJryINU++4804XLyrUCQvecE5mcCd7SUkJ2mpFmUzExcXZzleKl9Zt\nLTdwce2aNXTv0SOoYYxCxbEv8TnXQbkj2pfUBCGU+LPEV2UMVFljY8eb0fEni82fdeJg++y5k33O\nY+OJS0hwqZkq+5qzbhU1tkZeB490DMoT4cqWM/JnB6JfrCMxKCcq0q4o2Cw2u2Fq1LixW+/NarX6\n1TbInezd+9/I+AF9XWqmnF8D1wzAQFsdCYIgVDZVxoOCii3ZBVP7ZF+aA9tDgj3F22q1kJJWnc59\nr6Fukon/PfNMOU+qrNd1z6hRHCmCG0Y9iMlk5o3//R8/bP+MM9q0d9HH/prWupxudv3dHYskVW2A\nolHqjQQhlMgSXxkqWng6+t4xKKUCbgBb1iAObX8e+f/87TiutcZsjsNqLR8HKxt30lqX/qgrUtLS\nUNrqEluy62N/DcobVHfGtjKMRVUboBjr6dyCEA5kia8MFV2y82aYvK0Tl12aa9+zD4lJSQx64GGX\n88pm0x08eJCePXuSl5hWLmb26pOPsDv7c7pechHnnnsu1193HcvnzQINAwcOpE2bNh7Twt21OvLV\ntfztt94K+Tp4tDSijdQaf2UZH6PHMEQ/4xPzBqqi6ePgf41RRVv2l+2CfvXwu7inVyeuvGWE1zjY\nfbffTuGJE2RlZ5eLma15cwElJcW8tvc75r/2WunSkAIFP+7dC3g3qGWPVYaxCGaAoiAIVYeglviU\nUknAJ0AikAC8p7UeV+acsC7xVWS5qKJLdhWh7LLiHZdeyKXX/ddjr72CggLq1awJQP9Bg/jTGucw\nHq9OeYTd2VuZumSVyz3G3dCHVLMiZ/u2oOSLZAp6ZabwC4JQ+YR9iU9rXaiU6qK1zldKxQGblFKX\naK03BXPdQAjEA7B7W088PhnAZVJsuOItLsuKVisKxZo35rtk2mVv2+aQZeXKlbRMSEADF7Vrx+gx\nYxyZd58sewutNbl//uFiTH75aa+L5xGIV1mRWVehQLIKBUHwRciSJJRSKdi8qcFa611Or4fVgwrE\nAwhHcN6fdWLn5ITr+vdn4aJFdL1mAGjNuqWLofTvY7FYqKYUjxcVoYGt11xD6qmnumTeaa19eh6B\n6ukteSSc6+CVnVVo9DV+0S+2Mbp+EUmSUEqZgBzgX8AsZ+MUCQLxACIZb3H2Yuxd0BWKp56aQl5e\nPu++8wZxcfE8t3oTtU6tB8BrTz3KuoXz6Ado4OFVq9j+1Ve0aNUKsMXMtNY+PY9A9aysruWe4oFV\nLQ1dEAT3hNKDSgc+BMZqrbOcXg97mrm/6eORjLd482KqV6/O8aNHMaGIi7c9I2itKS4qomNKCh/l\n29rh9KhWjc+Ki7GWlAAQFx8PQHJqKhf2vRar1eqoo3Lml19+oUWrVgHpGYlZV+5wFw+samnoglAV\niXgdlFJqIlCgtX7a6TU9ePBgmjRpAkBGRgbNmzd3uK72qZjB7r/59tv8VgRHDh+iVoKJ99591+35\nfa+6iqPFMHrGLABm3Hu71/ODlad5h64AnNuuvcv9zCYTWatWcX5RMXdbSuhe+vfaDpiBzkAxNosP\n0AoYnZDAhtRU7rrvPh559FGsFismswkFmEp/zIuLi6mWmsp1N9zAkSI4/2Jbo9cvNmVRL9nMgOuv\n9yj/6HvHcOjQIe4ccUfIPx9P++vXrwegS5cujuMzZs4krnYD/nvfQ3z9+WbH32/BtMlY//yF0SNH\nRkw+2Zd92Q/NflZWFpmZmQA0adKESZMm+TRQaK0rvAGnABml/04GNgDdypyjI8HBgwd19YwMXT0j\nQx86dMjnefM+/VLP+/RLn+f7Yv369T7vs3TPYb10z2GX+x08eFCnpafr9h266LOSkvSXtkiU2+0L\n0P9JSdE39uunc3NztdZaN2/ZSvcZMtxxbft2xU0364SkJJ2QmKjNcXE6PjFRxycmapPJrGvWquVV\nF6vVqq1Wq1/6hRNff7tQURm6RRLRL7Yxun6ltsGrjQk2BlUPeK00DmUCFmit1wV5zQrhrgjV03nh\njrcUFRVRq1YtRxGtfQTG8rkvMuCGGxz3GzhwIL+e0BQCl3y2kYVWK32sVpdrLTeZuCUpiekvvMBN\ngwc7arLsM6P6OfXiy/3zD9a/8yZd+13HsEeecrlO5pRHaFjNe+ymovVeoaayMgsFQYguDNXqyH4f\nXz+04Y632GMoJpPJMQID4PaubUlNTeGvP/8sJ0evrl05b9kyxpUxUFNMJn648UZenDu3XOLAyFGj\nXGZALZg2meqWApYtW1Yu/jTyio7s/iZ2RmtUtC2VIAixgfTi80JFinX9yS4rKirizrvvdjR2ffXJ\nR0hMTkZrzZ7srfTo3MElnXr0vWMAmD3zGXZqzZnAltJjFwLfAS2VIqlWLXJzc10SB3RpF4mXPrYZ\nQPuP+ONPPumSxWf3nmKtCLay09AFQQgfYqC84K+35Yy77DKrxYIG0tPTOfzzz9Rv0IDc3Fy01o7E\nBavFgrZqlMnE/n0/uXgBWms2bdrELd26sau4mEfi4pidnILWmtsKC5hUUsJ/4uM5p3dvTLXqlUsd\nf7D/5fynVTvMZrPjRzyU3kdWJdZihNvTrUzdIoHoF9sYXT9pFuuF4uLigGttru3fn4PHi7h5/GOO\n177+fDOff/QBa5e8ToOGDTlRVET3/gMZ9IDr6PX5//cYWe8toXbt2i6vK6V4Z/FiLrZYaAWos8/j\nqRdeBeDZEUNY+dVOLrFYiK9enTeXvF6uf92v+3/itwP7UepkLVHZONuAG26gZs2aFBQUlPMCnXWN\nthojf+OKgiAYkyrrQXmrtUlPT+fggQPl3nPo0CEuaNGCF9Z85mIk7rmiIxdf3oemtarzzz//sPj1\n1wF1clQGGqvFAlpTo2ZNlzoerTVNatfm12PHaN2mDXXOaeGIKc2f+hi/79rJtq1bqV+zJj379+dI\nsSrXRSIxIbHccqWz92E2mfjnn38wm82UlNZUAS4j46O1xqginq4gCNGPeFBe8NZtYe3bi6ienu7W\neCUmJbH05WcdXtSyuS/S7tLL+Wz1+8wt7fSwZMlSul830GUcO8CCqY9RL9n1mvn5+TQ56yyWPvss\ndevW5ZzzzqPvzXcAsP6dN9j19dccPnyY+0aO5N5Ro2jTrl25LhL169d3uaY9i3DQTYNQSlFYWOCS\nTGHntamPUXziBLdOfCLioy78RQyTIFRdqqwH5a2rRN++fclLqObWeKWV5LNkyRJeWPMZACN6XESn\nPlfTtFZ1RxD/6muvZeXKlby0bmvAHSt8JQb4kzjgkkVopzSbsKznN2P5OuLi4j3KZuR1cCPrBqJf\nrGN0/cSD8oK3WpvxY8f6nFe09OVnMZvNnN2qncN7svPszJmsWrWad+Y87/Cils990WcdT1FREfeO\nGkWrNm0AyNm+3dHl3B4f8meelTvvcM5j413keWf2c3To3Y9ap9ZjwbTJUmMkCELUUWU9KPBea+Nt\nXtGhQ4c4q1kzNJTznuw4e1Flr+0Ju+ejsD1UmMw2D6hsXOzBceOIM8d5TJF35x3+tPtrxg/oe7Im\nq1tbprzxPjVqnyo1RoIgRBxJM/cDT0tmvlK1h912G4sXv4HZbPLYmPasZv+h69U3EB8fR71ks886\nnrJG0c7cxx9yjOWwG6vfjxzxGp9xZ2B/2P4ZZ7Rpj9aaH7I/44zW7aXGSBCESsEfAxVULz5/NiLU\ni6+ieOvhd/uIEbrfrSP0Vbfcoe+4806XY1arVY8cNVpf2/86j9e++ZZbdUpqNb97yHnqQVctPUPP\n/iRbL91z2K0svq5l72O3detWh67O//Ymm5H7gRlZN61Fv1jH6PoRgV58MY+3Whtv8R6lFM/MmO7o\n1uuOV+bMpnr1NJQy+bV85i4utuyVFxyxorJxMH+vpUt7DrZp08ahq/O/ZWlPEIRopMov8YH3WpuK\ntETy99ruKLu0OKLHRTz7wQZHMkMgy3HuOjE4yxOobIIgCKFCsvj8xNsPdEUNkz/XdoeL52O1YlIm\n4uLiA/KenK9V1ktylifaDZNM1hWEqo14UEESjloFZ8/HXpOlK5jMEKyXVJm1GOGerGv0OhPRL7Yx\nun7iQcUozp7PvaNH+ax78ka0e0ne8NbtIxq7XgiCEFrEg4pSnD2fYONgsYq3bh9StyUIsY3UQRmE\nqpzM4K1gWhCE2MUfAyXrJEHiLc08VCilKs04RUI/b0wYN451S14n988/HIkiE8aNC8m1K1u3cCP6\nxTZG188fJAYVIiTjLDy4q+eSpT1BqBrIEl+ICHfGWVUm3JN1BUGIPJLFF2acvaZ+/fq5nbkkGWfB\nI5N1BaFqIh5UENSuU4e//vqL+Ph4WyKDm5lLsZ5xFi21GOFIFIkW3cKF6BfbGF0/SZIIM9f270/7\ny3rz+s4fWfzFT3S9+gbemzfLcdw+XypWjVM0UZmJIoIgVA7iQQVB2TqdP389zOi+3Xhu1UbA+wwo\nSaoQBKEqI3VQEaBsnc6D/S/nP63aYTabvdbrSFKFIAhVGUmSiABdO3fm1uHD6TP0dgB+3f8Tvx3Y\nj1LeWxPFShsfI6+DG1k3EP1iHaPr5w9BGSilVCNgPlAH0MBsrfWzoRAsVqhdu7ZLnc5NN91EYkKi\nz4wz+6ypPkNvd0mqCLRjuSAIglEJaolPKVUXqKu13qmUqgZkA1dprXc7nWPoJT4oX6dTv359wHfG\nmbTxEQShqhL2JT6t9a/Ar6X/Pq6U2g3UB3Z7faPBqGidjrMXBYj3JAiC4ETIkiSUUk2AT4BztNbH\nnV43tAdlXyeuaJ2O3Yuq6LyncGPkdXAj6waiX6xjdP0iliRRury3BBjpbJyqEhWt0bF7UVCxeU+V\njaTLC4IQLoI2UEqpeGApsFBrvczdOUOGDKFJkyYAZGRk0Lx5c8eTgb1jb6zu21+r6Pv37t3Lpd0v\npXHjxjRo0KDS9QlUv9p16nD8+HHi4+MBsJYaK43ts377rbeiSh/n/c6dO0eVPEbVz2Kx0LlzZ8xm\ns9fzLRYLWVlZmM3mmNIvXPtG0y8rK4vMzEwAhz3wRbBJEgp4DfhTaz3awzmGXuILBbE876lsoocd\nSfgQcnJyeGT8GFav2wBAz24deWzKDFq0aOH1vMu6deDRx5+mdevWEZdZiByRaHV0MfBfoItSakfp\n1jPIa8YU9ieEYIjmNj6+9HOe12Qn1HObwkUoPrtopjL1y8nJ4bLuHelVP4vc2VZyZ1vpVT+LHt06\nkJOT4/W83vU/oePFbejYvjU7duzweA/5/IxPUAZKa71Ja23SWjfXWrco3VaHSjgh+nGe12RHehAK\nj4wfw+Sr8ri9O6Qk2rbbu8Pkq/J4dMJ9Ps+bMRDyfskuZ9CEqoW0OhKCxrknIXjvQSgYH4vFQlJS\nArmzraQkuh7LPwHpw00UFhYBeD9vGPzvv7D6ty4sX/Wx2/sA5dqFCbGBdDMXIoKzFyXekxBKbuoA\nq9Z+4pIpmpOTQ5+eXUhKSiApKYE+Pbt4XQoUYhcxUEFi9HVif/Wzx6JiIfZkRz678GA2m+nZrSPz\nN5Y/Nn8jXN69E2az2fd5F4C5zC+Uc8zq/Xs9x7aMgNG/n/4gzWKFkCBTbwVnHpsygx7dOgB5DOpg\ne23+Rpi4LJVVa6ZisVgwm82ez1sCa8a6GjRwjVll7ToZswJbbMvdUqAQu0gMSggZsZwuL4SenJwc\nHp1wH6vWfgLAJRe2xGLRfLbNthxnTzvXWjNm5G1s+HQ7SsFl58OEK+HLAzaDtmbdRlq0aOF3bMso\nMSmjx9gkBiVElGhOlxciT8uWLVm+6mMKC4vYvHkLX3+zmxubZZdLOwdYv3EbWz7fyuWXdmbN1yY6\nPWHig1+6OIxTVUJibCcRAxUkRl8nNrJ+RtYNokc/s9nMYxMf8Jl23qZNG95fvZ7CwiIKC4tYvupj\nF+NUNmaVtevkPcouBcYqVSnG5g8SgxIEIaxYLBZWr9vAm7PLHxvUAe4e/okjJgXel7ScY1ZNatuW\n9uyxrTXrpnuVwde1owF/Y2yxok+wiAcVJPaeU5VJUVERBQUFbreioqKgrh0N+oULI+sGxtSvRYsW\nfLh2Ax/80oU+M0ykD/e+FBhLy2V2Q25PFul89sljg0rT7bdt2xYz+oQCSZIwALXr1OHYsWPlnqYs\nFgsZGRn8fuRIJUkmCDb69OxCr/pZpd7ASV5aCx/84r4Q1xe+vAj7ctnkq8pnEn64dgMtW7YM+J7h\nxGcSyDAT6WlJPN4vPyb08YUkSUSAaFjnv7Z/f/oMHsbrO3902XoPupX+110X1LWjQb9wYWTdIDr0\ns1gsWCwWHpsyg4nLUnlpre3HNv+EzThNXJbKpCc9L815Y+PGjV6XuPxttxQt+IqxNahTncf75ceM\nPqFADJQBiOWGrYIxKbu09vC4e/nf87P54JcupA/3vTQXLGWXy5wZ5KY7RbTgbMgLi50NeQqHjuTG\nnD7BIkt8BqHs2AsZdyFUFr6W1i644AIgvAH+WK6ZKls/dnn3Tjw8eSoXXdQuJvXxhD9LfGKgDII0\nbBWihXDEm2JZjopSNsYW6/qURQxUBMhymjZb2di9KK11yLynaNIv1BhZN6gc/SLpufjSb8eOHfTo\n1sGtJ1d2aTGa0rbtsmzcuNFFP3/0iSY9fCFJElWMWGzYKsQu9gSIaMU5Jd1T3Cua0tDLyjLugVEu\nsnjTR2sdNXqEFK11WDfbLYRIMWr0vXr0vWMqWwzBwGRnZ+vel3XWcXEmHRdn0r0v66xzcnIcx3tf\n1lnPGorWi1y3WUPRfXp2qdA9S0pKdElJSYVldvf+7OxsfUqNVD1rKDpvnm2bNRR9So1UnZ2dHfQ9\nA8GXLN70CfS90UKpbfBuP3ydEOwmBiqyWK1WbbVaK1sMwaD482OYk5Pj8RxnQ+bv/bwZw2DwZkhP\nq5cRlntWRBZfRj0cDwSRwB8DJTGoIJE4RuxiZN0gPPr5CtS/u+IjAL744otymWiTnpweUNzHVzbg\n33//XWH9fMXKqt8KR2fb5lGFuxjWkyxZu6Dtv7zH7WI5W1FiUIIghAxvtUXnNYasrPWOGMgj48cw\n6cnpbhu/+hv3CabQNtj4mFL+3TPa43CxjhioIDHyEzgYWz8j6waR0y/nJ7hqBkwdQLlRGl988YXL\n07tzt+6y5zp36/an0LZDh/IH/TV+gU7zLVsMG8rkCk+ydD7bd5d2f6cXxypioARB8AtPP4aPLIXJ\n1+KXp/PwuHuZ1Dc87Yf8NX52PLZfWgKTrgndffwhmFZQ4WgjFTX4ClIFu2HwJIn169dXtghhxcj6\nGVk3rcOjX9kEiL9fQZtNtn+XDdLnzUPHxZl0SUmJzs7O1r0u66RNCh1nRvdugc55wv25dnwF/8vq\nV5FkgezsbN2nZxdHQsRp9TL0+L7erxGupISyslzUprnfyRll39unZ5ewJ3YEC34kScg8KEEQPFI2\nkcFei/PohPu4e/gnpQ+h3pOgcnJyuOKyLky+Ko+35tpem78RejwFHz4ILU93/z7n2U/lC1Onk5ub\n6yJnIDOn7Nin/tr13LFjBz0v7USjWuU7hq9ZN73C9/GHsrJs3Oh/n8Ky743lZT1nJItPEIRy5OTk\n8Mj4MaxeZ2ud1bNbRx6bMsNtFt5Vvbp7zezTWns+/gUsH+O5XY+7vnRlswEB9u3bxxlnNOXvObpC\n2Wwu+mpb5/BDR3JRSrncM5az5qINaXUkCELABDpHyVsLnlVrsrw3OR0G//svPLK8fPshZ3x5Btf3\n6sW2rVt4oM9fAfeq86xvCh98mEWbNm1cZHBnkC1WeHktrP4t9nriVRaSZh4BomHmTjgxsn5G1g0q\nrp+v9O6yqdX+tBTyhNUKq37t7PNcs9lczjjZ9SsoKODDjz/mz7+P89C7KQEnC3jWN5/JDz9YLmPv\nn+P/MG5JEi+thU+/gyumQuJguHs+/P3P3yFrMWT076c/BG2glFLzlFK/KaW+CoVAgiBUHoHUOjmn\nVttjIGXrnnylQV9xWWfeX70+qJlQa9asoWVCAi2Tkpjw8OMBGUpf6ewffJTFZd07uGTs3XBWNiYT\nzN7+Hy6dAn1bwt+vwD9z4YazsoPK5hNcCXqJTynVATgOzNdan+fmuCzxCUKM4CnGkvMTXPZ/tnTy\nQMeNB9JVvCLcdM01XPjOO2hg6zXXMH/JEr+TBXzFlOqOsNV3uVs2fGp1BmN7HjPM+ItIE7EYlFKq\nCfC+GChBiH3ctTPq8zT0au7+h9q5xZG3JAR/kh0CpaioiLo1avB1fj4aOC8lhV+PHiUhIcHva3hq\n3/TiGrhngc07shsvi9X23/wTkDHM5jVJskTFkBhUBDD6OrGR9TOyblBx/coWfv5TAKu+wPMy2Jr1\nJCbGe+2oUHYJ8N0VH3H++ee7vb+n9kGtL7iA9ORkx5aakECt6tVpbTJRH2gAtDaZqFW9ust56cnJ\ntC6d4uuPvvbY1cPvpaCU7Scy5yebkU4aYtuue9aPP2SQGP376Q9ioARBcKFs0kON27w+5AJw9GXt\nV0eFL774gqt6dXcbx/LVPujFOXM4JSODK6xW9hQW8mZxMYdOnOCD48cd56w8fpxDJ05woLCQPYWF\nXG61ckpGBi/OmeO3vvbY1Ucfb6Jn9448/q5tebNXc8idY9uubAVpyRi2xVC0EJElvsGDB9OkSRMA\nMjIyaN68uaNPmP0pQfZlX/ajb3/dunUAzJz2OL3qZ9GsPrbjZ9v+e+8C2PIDbH7Utp+1C5Znw15s\nMRjn6+Xk5NCl08Xcckkhj19nO/+ht2DupiRefOkVRt19Gze1y6PH+dCxme2H/sG3k5g2/X8MHz4c\ngJUrVzJjyhR+3bGDN/Lz+ZNSeUr/m1X635rADSkp1G/ZktFjx9KrV6+A9O3WrRsAc+bM4d57bmPa\nAM3t3W362fWf8CbMWK24o6sup0/Whs20aNGi0j+/aNrPysoiMzMTgCZNmjBp0iSJQQmCEDweEx2W\nwJqx0KLJyXM9xWCcYz32WI7ZFHjCgdaa+ZmZ3HfXXcwrLKSP1erynuUmE7ckJTH9hRe4afBglPL8\nG+grmcJisZCUmEDuHA9jOYYpLr+0E6vX2gqaQxVbqwpEJAallFoMbAbOUkodVEoNDfaasYT9CcGo\nGFk/I+sGodXP3TLYA4vhvXtdjZMn7Onc5zV2jeX0eRrOaQgHfz3mtXO5c0xKKcXgoUO5sEMHvnFz\nr13A1f37M2jIEI/GyXk5MTExnt6XdfZcv+TlJ1QpxbIVa92OFQkWo38//SFoA6W1HqC1rq+1TtRa\nN9JavxoKwQRBiC7KJjp06tSZLw+UP89TDEZrzVUzXGM5vZpDv2cCl8VqtfLppk1cU+o9bSndAK62\nWnl/2TKsZTwrO/bOEeclZHHpOVYUmtVrP6Fbh9a8/vrrLueazWYubtfCY6zpkgtbOoqIJeYUeiRJ\nIkjsa61Gxcj6GVk3CJ9+9h/jQMY8mM1mGtap7nYsx+P9oUaa2aMRaFC7Ol9++aXL65s3b6ahycTp\nwAjA+JgAAA4HSURBVMT4eK5OT6dfejoT4+NpCtSyWvnss8/cyv/I+DEMuySPOVm2ItvcObZU8iev\ns3LbrTeVS/CwWmHcm5TTc9ybtmPhwujfT38QAyUIQoUIpMWRxWLh5yP/eFzGO3bcysRlbtoULYGB\nbY6Vywxc+vrrtM7Lo2NqKlvbtSNnzx527NnD523a0Ck1ldZ5eSxdvLjcvexLjTsPuJ9hNe0GK49M\nGONy/mfbdrDifltj2/Rhtu2DL2Dl/bB5a45M1A0j0iw2SLKysgz9pGNk/YysG0ROP3vdkrdlLn+6\ngG/evIX+V/bg0G/HUMo21XbSNbYYl3OyhNaaJrVrc/joUaY88QT3PvAAJpPtWdtqtTJj6lTGT5hA\n/Zo1+enIEZc4lMViITExHoUmd47vItuycjsnd4S7INfo308p1BUEIeTYDZJzokFqajJX9eruMdHA\nn9HkLVu25Off/+bobCjMtI3hsCdgOCdL5Ofn0+Sss3j+xRe5b+xYh3ECMJlM3Dd2LJ9u2cJpZ55J\nfn6+Wzn8fWYuK7fZdHIUvNQ7hR/xoARB8IuyM5PSkuCOblYmXGU77qs3n6+efOeff35EZi3t2LGD\nbh1a8+R1Vr/S2sPdS7CqIh6UIAghwZ755ujqPcfKk9dZmb0e9hwuP5LDHb5iVv54WaHwVlq0aMHz\nsxdw/xsmvxI8ghknIgSJr5nwwW62WxiX9evXV7YIYcXI+hlZN61Dq1/vyzrrWUPRepHrNmsouk/L\nk/t589BxcSZdUlLi9XolJSVuz8nJydGn1EjVs4barpU3z3aPU2qk6pycHJdz165d6/M+3sjOzta9\ne3bWcXEmHRdn0n16dil3j7KyepI7HBj9+1lqG7zaD/GgBEHwiq+ZSau+OJk84Os6zp0b3HlD/ngr\n9thXjx6Xem1Q64uWLVvy/qr1Hots3fUG/PLLLyXmFEEkBiUIgld8ZuANsyU12NsWlY3huMSugJ7d\nOvLYlBlel8c8ZQYGOo6+okTqPlUZiUEJghA0vmJDPc6DE8XuYzhlY1d/vWTl8rqeO577ygz0NY4+\nVETqPoIPfK0BBrshMaiYxsj6GVk3rUOrn6fYULVkkzablccYjj12lf04uncLdJzZtrVsgu7YvrXL\nudnZ2R7jT9nZ2bqkpETHxZl03jxbvGv9hMBjX/5Q9j7OWyjv4wujfz+RGJQgCKHAU2xow6fbOXGi\n2G0Mx7lBbNl5SsO6wLbt29m2bZvjfPFahLJIDEoQhIDwNaLC+bykpAQuPcdK35bux8Wv/KUz769a\n71enicLCIq7q1d3teHZ3sa9g8DQGPtT3qcr4E4OKi5QwgiAYA3+z2MxmM5d17cDqtZ+wZGT544M6\nwN3DNwTUy+6xKTPo0a0D4K5odrrX9wZCpO4jeEeW+ILE6DNbjKyfkXWD6NDv0See9qutkL9Fus5L\njWm3qoCLZouKiigqKvJ5XqCNcMPRMDYaPr/KRgyUIAhho3Xr1nRo38qv7hD+ju+wz6Vas+Yj8vIK\neHfFRz6N06JFi2hSP4PkpESSkxJpUj+DxW66nTtTdv6VP3VSFanHErzgK4si2A2DZ/EJguCdQLpD\nZGdn6z49u/js7pCdna17X3ayC0Tvyzq7PU9rrRcuXKhTEil3/5QE9MKFCyukk6+MQ8E3+JHFJ0kS\ngiCEnZycHB6dcB+r1n4C2DynSU9O9+j5eEvECLSItkn9DMb2zHWb8PDUhxns+/lowPpIEkXw+JMk\nIQYqSIw+s8XI+hlZN4hO/fzNAPSG3Tg0qw+dzz75ujvjUFRURHJSIv/MdT/7Ke0WKCg8QUJCQkA6\nRKLrejR+fqFEOkkIghBVeBtqWBZ3yQc++wKWzowSjIEYqCAx8hMOGFs/I+sGsaufv8kHzt6TJxIS\nEmhUN91jkkajehkBeU/gf8ZhsMTq5xdKxEAJghA1lJs7NdtKr/one/dVxDhMmT6LMYsolx04ZhFM\nefrFCsnpb8ahECS+siiC3TB4Fp/R+2UZWT8j66Z15ekXzMwkr3OnenbRWp/MChzd03dWoJ2FCxfq\n0+pnaJNCmxT6tPoZ+vXXX6+wjlr7n3FYUYz+/UR68QmCECmCrQvyN75kL6Ld8mdzvyfcDhw4kH0/\nH6Wg8AQFhSfY9/NRBgwY4HKOv0W8dnzVSQnBI1l8giAETSjmJ1UkOy4UWYGLFi1iwv13cvDXXAAa\n1U1nyvRZ5QyYEFoki08QhIgQik7kFYkvBZIV6I5FixYx/Jb/MrZnLv/MhX/mwtieudw65EYWLVpU\n4esKoUEMVJAYvV+WkfUzsm4QOf1CmfodSPJBKPSbcP+dTL+RcoZ1+kCY8MBdQV8/GIz+/fSHoA2U\nUqqnUmqPUup7pdSDoRBKEISqSSBNWoOlqKiIg7/mejSsB385FlBMSgg9QcWglFJm4FugO/AzsA0Y\noLXe7XSOxKAEweCEo/VPKOJL3ghHlwnBfyIRg2oL7NVa79NaFwNvAFcGeU1BEGKMcNQFBRtf8kU4\niniF0BKsgWoAHHTaP1T6WpXB6OvERtbPyLpBZPWL5NKcnVDoF44i3lBh9O+nPwQ7UdevtbshQ4bQ\npEkTADIyMmjevLmjjYf9Q4jV/Z07d0aVPKKf7FfWfsuWLbn3wYcZeZ+Fzp07YzabycrKIsup6Wk0\nyQtQr149Rt03nqcyX+TOzGNoDXVqpfJK5hwGDBhQ6fIZaT8rK4vMzEwAhz3wRbAxqAuBR7XWPUv3\nxwFWrfX/OZ0jMShBEKIee0KELOtFhkjEoLYDZyqlmiilEoDrgeVBXlMQBCHiJCQkiHGKMoIyUFrr\nEuAu4ENgF/CmcwZfVcDuwhoVI+tnZN0g+vVzN04jEKJdv2Axun7+EHQdlNZ6ldb631rrM7TWU0Ih\nlCAIxiXYnn1C1UF68QmCEDFC0bNPMAYy8l0QhKgiHAW9QmwizWIjgNHXiY2sn5F1g+jTL9Tj2qNN\nv1BjdP38QQyUIAiCEJXIEp8gCBFDlvgEO/4s8QXbSUIQBMFvHpsygx7dOgDlkyTWrKtYzz7BuMgS\nX5AYfZ3YyPoZWTeITv1C2bMvGvULJUbXzx/EgxIEIaK0bNmS5as+Dvs4DSH2kRiUIAiCEHEkzVwQ\nBEGIWcRABYnR14mNrJ+RdQPRL9Yxun7+IAZKEARBiEokBiUIgiBEHIlBCYIgCDGLGKggMfo6sZH1\nM7JuIPrFOkbXzx/EQAmCIAhRicSgBEEQhIgjMShBEAQhZhEDFSRGXyc2sn5G1g1Ev1jH6Pr5gxgo\nQRAEISqRGJQgCIIQcSQGJQiCIMQsYqCCxOjrxEbWz8i6gegX6xhdP38QAyUIgiBEJRKDEgRBECKO\nxKAEQRCEmKXCBkop1V8p9Y1SyqKUahlKoWIJo68TG1k/I+sGol+sY3T9/CEYD+oroB+wIUSyxCQ7\nd+6sbBHCipH1M7JuIPrFOkbXzx/iKvpGrfUesK0jVmWOHTtW2SKEFSPrZ2TdQPSLdYyunz9IDEoQ\nBEGISrx6UEqpj4C6bg6N11q/Hx6RYot9+/ZVtghhxcj6GVk3EP1iHaPr5w9Bp5krpdYDY7TWOR6O\nS465IAiCUA5faeYVjkGVweNNfAkgCIIgCO4IJs28n1LqIHAhsFIptSp0YgmCIAhVnbB3khAEQRCE\nihCRLD6l1GSl1BdKqZ1KqXVKqUaRuG8kUEpNU0rtLtXvHaVUemXLFEqMWpCtlOqplNqjlPpeKfVg\nZcsTSpRS85RSvymlvqpsWcKBUqqRUmp96ffya6XUPZUtUyhRSiUppT4v/b3cpZSaUtkyhRqllFkp\ntUMp5TXZLlJp5lO11hdorZsDy4BHInTfSLAGOEdrfQHwHTCukuUJNYYryFZKmYHngZ7A2cAApdR/\nKleqkPIqNt2MSjEwWmt9DrYQw51G+vy01oVAl9Lfy/OBLkqpSypZrFAzEtgFeF3Ci4iB0lr/47Rb\nDfgjEveNBFrrj7TW1tLdz4GGlSlPqNFa79Faf1fZcoSYtsBerfU+rXUx8AZwZSXLFDK01huBo5Ut\nR7jQWv+qtd5Z+u/jwG6gfuVKFVq01vml/0wAzMBflShOSFFKNQSuAF7BS4IdRLBQVyn1hFLqADAY\neCpS940wNwMfVLYQgk8aAAed9g+VvibEGEqpJkALbA+HhkEpZVJK7QR+A9ZrrXdVtkwh5BngfsDq\n68SQGSil1EdKqa/cbH0AtNYTtNaNgcxSAWMGX7qVnjMBKNJav16JolYIf/QzGJIZZACUUtWAJcDI\nUk/KMGitraVLfA2BjkqpzpUsUkhQSvUGjmitd+DDe4LQ1UGhtb7Uz1NfJ8a8DF+6KaWGYHNZu0VE\noBATwGdnFH4GnBN1GmHzooQYQSkVDywFFmqtl1W2POFCa52rlFoJtAayKlmcUNAe6KuUugJIAqor\npeZrrQe5OzlSWXxnOu1eCeyIxH0jgVKqJzZ39crS4KaRMUrR9XbgTKVUE6VUAnA9sLySZRL8RNk6\nVM8FdmmtZ1a2PKFGKXWKUiqj9N/JwKX/394d4kQQRFEUvX8ZCASGTWBmGSMw43E4NsACSNjCZDSK\nkBlJggLHAtgGyUN0W1BN90/nnqR0fVUvqX6VZiVnZpK7JOdJLoAtcPotnGC+b1D345XRB7ABbmfa\ndw4PDMWPl7E2+bj0QFNa44PsJN/ADfDM0CQ6JPlcdqrpVNUeeAUuq+qrqnZLzzSxK+Caod32Pq41\ntRbPgNN4Xr4BT0mOC8/0X/68bvehriSpJX+3IUlqyYCSJLVkQEmSWjKgJEktGVCSpJYMKElSSwaU\nJKklA0qS1NIPRUwpEB6DluYAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.cluster import KMeans\n",
"km = KMeans(n_clusters=3, \n",
" init='random', \n",
" n_init=10, \n",
" max_iter=300,\n",
" tol=1e-04,\n",
" random_state=0)\n",
"y_km = km.fit_predict(X)\n",
"\n",
"plt.scatter(X[y_km==0,0], \n",
" X[y_km==0,1], \n",
" s=50, \n",
" c='lightgreen', \n",
" marker='s', \n",
" label='cluster 1')\n",
"plt.scatter(X[y_km==1,0], \n",
" X[y_km==1,1], \n",
" s=50, \n",
" c='orange', \n",
" marker='o', \n",
" label='cluster 2')\n",
"plt.scatter(X[y_km==2,0], \n",
" X[y_km==2,1], \n",
" s=50, \n",
" c='lightblue', \n",
" marker='v', \n",
" label='cluster 3')\n",
"plt.scatter(km.cluster_centers_[:,0], \n",
" km.cluster_centers_[:,1], \n",
" s=250, \n",
" marker='*', \n",
" c='red', \n",
" label='centroids')\n",
"plt.legend()\n",
"plt.grid()\n",
"plt.tight_layout()\n",
"#plt.savefig('./figures/centroids.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## K-means++"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Hard versus soft clustering"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using the elbow method to find the optimal number of clusters "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Distortion: 72.48\n"
]
}
],
"source": [
"print('Distortion: %.2f' % km.inertia_)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"distortions = []\n",
"for i in range(1, 11):\n",
" km = KMeans(n_clusters=i, \n",
" init='k-means++', \n",
" n_init=10, \n",
" max_iter=300, \n",
" random_state=0)\n",
" km.fit(X)\n",
" distortions .append(km.inertia_)\n",
"plt.plot(range(1,11), distortions , marker='o')\n",
"plt.xlabel('Number of clusters')\n",
"plt.ylabel('Distortion')\n",
"plt.tight_layout()\n",
"#plt.savefig('./figures/elbow.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Quantifying the quality of clustering via silhouette plots"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"from matplotlib import cm\n",
"from sklearn.metrics import silhouette_samples\n",
"\n",
"km = KMeans(n_clusters=3, \n",
" init='k-means++', \n",
" n_init=10, \n",
" max_iter=300,\n",
" tol=1e-04,\n",
" random_state=0)\n",
"y_km = km.fit_predict(X)\n",
"\n",
"cluster_labels = np.unique(y_km)\n",
"n_clusters = cluster_labels.shape[0]\n",
"silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
"y_ax_lower, y_ax_upper = 0, 0\n",
"yticks = []\n",
"for i, c in enumerate(cluster_labels):\n",
" c_silhouette_vals = silhouette_vals[y_km == c]\n",
" c_silhouette_vals.sort()\n",
" y_ax_upper += len(c_silhouette_vals)\n",
" color = cm.jet(i / n_clusters)\n",
" plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
" edgecolor='none', color=color)\n",
"\n",
" yticks.append((y_ax_lower + y_ax_upper) / 2)\n",
" y_ax_lower += len(c_silhouette_vals)\n",
" \n",
"silhouette_avg = np.mean(silhouette_vals)\n",
"plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
"\n",
"plt.yticks(yticks, cluster_labels + 1)\n",
"plt.ylabel('Cluster')\n",
"plt.xlabel('Silhouette coefficient')\n",
"\n",
"plt.tight_layout()\n",
"# plt.savefig('./figures/silhouette.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Comparison to \"bad\" clustering:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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WHS+1YeOmj5qUgzpjyKmcecZpUctEOfXdxnJvVlRUsLikhL+0acMrxx/P2g8/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\nRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"km = KMeans(n_clusters=2, \n",
" init='k-means++', \n",
" n_init=10, \n",
" max_iter=300,\n",
" tol=1e-04,\n",
" random_state=0)\n",
"y_km = km.fit_predict(X)\n",
"\n",
"plt.scatter(X[y_km==0,0], \n",
" X[y_km==0,1], \n",
" s=50, \n",
" c='lightgreen', \n",
" marker='s', \n",
" label='cluster 1')\n",
"plt.scatter(X[y_km==1,0], \n",
" X[y_km==1,1], \n",
" s=50, \n",
" c='orange', \n",
" marker='o', \n",
" label='cluster 2')\n",
"\n",
"plt.scatter(km.cluster_centers_[:,0], km.cluster_centers_[:,1], s=250, marker='*', c='red', label='centroids')\n",
"plt.legend()\n",
"plt.grid()\n",
"plt.tight_layout()\n",
"#plt.savefig('./figures/centroids_bad.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cluster_labels = np.unique(y_km)\n",
"n_clusters = cluster_labels.shape[0]\n",
"silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
"y_ax_lower, y_ax_upper = 0, 0\n",
"yticks = []\n",
"for i, c in enumerate(cluster_labels):\n",
" c_silhouette_vals = silhouette_vals[y_km == c]\n",
" c_silhouette_vals.sort()\n",
" y_ax_upper += len(c_silhouette_vals)\n",
" color = cm.jet(i / n_clusters)\n",
" plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
" edgecolor='none', color=color)\n",
"\n",
" yticks.append((y_ax_lower + y_ax_upper) / 2)\n",
" y_ax_lower += len(c_silhouette_vals)\n",
" \n",
"silhouette_avg = np.mean(silhouette_vals)\n",
"plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
"\n",
"plt.yticks(yticks, cluster_labels + 1)\n",
"plt.ylabel('Cluster')\n",
"plt.xlabel('Silhouette coefficient')\n",
"\n",
"plt.tight_layout()\n",
"# plt.savefig('./figures/silhouette_bad.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Organizing clusters as a hierarchical tree"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Cg5VEMfGU3Kc7mTVCVWW0c/suhVsxHT6ssD4lkXom96MB/Wz+ODKYjcS6oZj2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QGSlvt8Wl2pnmlZWueAOtx1j39gC5fXNoHX3lYf2jy3Acw0TcHGCBl3nyAzW25eZa8HIHnXc3Pt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\nXl9F0uspB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Ng0FyGnI2FS4Y5sSH/yyAHJFDKGrNEhpbjxAxRR3FFZNz18kT1xUNYCsMTj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h+UBzBvOErOIDZFlTf/vtt3swS9xBgwb50wo4tYBxwdjV+JVb7PSI9YsUiBSIFIgAthN5QEIG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\nZCxAAiRAAiRAAiRAAiSQSwL/A13kqhIGoT+6AAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {
"image/png": {
"width": 400
}
},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='./images/11_05.png', width=400) "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" X | \n",
" Y | \n",
" Z | \n",
"
\n",
" \n",
" \n",
" \n",
" | ID_0 | \n",
" 6.964692 | \n",
" 2.861393 | \n",
" 2.268515 | \n",
"
\n",
" \n",
" | ID_1 | \n",
" 5.513148 | \n",
" 7.194690 | \n",
" 4.231065 | \n",
"
\n",
" \n",
" | ID_2 | \n",
" 9.807642 | \n",
" 6.848297 | \n",
" 4.809319 | \n",
"
\n",
" \n",
" | ID_3 | \n",
" 3.921175 | \n",
" 3.431780 | \n",
" 7.290497 | \n",
"
\n",
" \n",
" | ID_4 | \n",
" 4.385722 | \n",
" 0.596779 | \n",
" 3.980443 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" X Y Z\n",
"ID_0 6.964692 2.861393 2.268515\n",
"ID_1 5.513148 7.194690 4.231065\n",
"ID_2 9.807642 6.848297 4.809319\n",
"ID_3 3.921175 3.431780 7.290497\n",
"ID_4 4.385722 0.596779 3.980443"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"\n",
"np.random.seed(123)\n",
"\n",
"variables = ['X', 'Y', 'Z']\n",
"labels = ['ID_0','ID_1','ID_2','ID_3','ID_4']\n",
"\n",
"X = np.random.random_sample([5,3])*10\n",
"df = pd.DataFrame(X, columns=variables, index=labels)\n",
"df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Performing hierarchical clustering on a distance matrix"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" ID_0 | \n",
" ID_1 | \n",
" ID_2 | \n",
" ID_3 | \n",
" ID_4 | \n",
"
\n",
" \n",
" \n",
" \n",
" | ID_0 | \n",
" 0.000000 | \n",
" 4.973534 | \n",
" 5.516653 | \n",
" 5.899885 | \n",
" 3.835396 | \n",
"
\n",
" \n",
" | ID_1 | \n",
" 4.973534 | \n",
" 0.000000 | \n",
" 4.347073 | \n",
" 5.104311 | \n",
" 6.698233 | \n",
"
\n",
" \n",
" | ID_2 | \n",
" 5.516653 | \n",
" 4.347073 | \n",
" 0.000000 | \n",
" 7.244262 | \n",
" 8.316594 | \n",
"
\n",
" \n",
" | ID_3 | \n",
" 5.899885 | \n",
" 5.104311 | \n",
" 7.244262 | \n",
" 0.000000 | \n",
" 4.382864 | \n",
"
\n",
" \n",
" | ID_4 | \n",
" 3.835396 | \n",
" 6.698233 | \n",
" 8.316594 | \n",
" 4.382864 | \n",
" 0.000000 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" ID_0 ID_1 ID_2 ID_3 ID_4\n",
"ID_0 0.000000 4.973534 5.516653 5.899885 3.835396\n",
"ID_1 4.973534 0.000000 4.347073 5.104311 6.698233\n",
"ID_2 5.516653 4.347073 0.000000 7.244262 8.316594\n",
"ID_3 5.899885 5.104311 7.244262 0.000000 4.382864\n",
"ID_4 3.835396 6.698233 8.316594 4.382864 0.000000"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from scipy.spatial.distance import pdist,squareform\n",
"\n",
"row_dist = pd.DataFrame(squareform(pdist(df, metric='euclidean')), columns=labels, index=labels)\n",
"row_dist"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can either pass a condensed distance matrix (upper triangular) from the `pdist` function, or we can pass the \"original\" data array and define the `'euclidean'` metric as function argument n `linkage`. However, we should nott pass the squareform distance matrix, which would yield different distance values although the overall clustering could be the same."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" row label 1 | \n",
" row label 2 | \n",
" distance | \n",
" no. of items in clust. | \n",
"
\n",
" \n",
" \n",
" \n",
" | cluster 1 | \n",
" 0 | \n",
" 4 | \n",
" 6.521973 | \n",
" 2 | \n",
"
\n",
" \n",
" | cluster 2 | \n",
" 1 | \n",
" 2 | \n",
" 6.729603 | \n",
" 2 | \n",
"
\n",
" \n",
" | cluster 3 | \n",
" 3 | \n",
" 5 | \n",
" 8.539247 | \n",
" 3 | \n",
"
\n",
" \n",
" | cluster 4 | \n",
" 6 | \n",
" 7 | \n",
" 12.444824 | \n",
" 5 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" row label 1 row label 2 distance no. of items in clust.\n",
"cluster 1 0 4 6.521973 2\n",
"cluster 2 1 2 6.729603 2\n",
"cluster 3 3 5 8.539247 3\n",
"cluster 4 6 7 12.444824 5"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 1. incorrect approach: Squareform distance matrix\n",
"\n",
"from scipy.cluster.hierarchy import linkage\n",
"\n",
"row_clusters = linkage(row_dist, method='complete', metric='euclidean')\n",
"pd.DataFrame(row_clusters, \n",
" columns=['row label 1', 'row label 2', 'distance', 'no. of items in clust.'],\n",
" index=['cluster %d' %(i+1) for i in range(row_clusters.shape[0])])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" row label 1 | \n",
" row label 2 | \n",
" distance | \n",
" no. of items in clust. | \n",
"
\n",
" \n",
" \n",
" \n",
" | cluster 1 | \n",
" 0 | \n",
" 4 | \n",
" 3.835396 | \n",
" 2 | \n",
"
\n",
" \n",
" | cluster 2 | \n",
" 1 | \n",
" 2 | \n",
" 4.347073 | \n",
" 2 | \n",
"
\n",
" \n",
" | cluster 3 | \n",
" 3 | \n",
" 5 | \n",
" 5.899885 | \n",
" 3 | \n",
"
\n",
" \n",
" | cluster 4 | \n",
" 6 | \n",
" 7 | \n",
" 8.316594 | \n",
" 5 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" row label 1 row label 2 distance no. of items in clust.\n",
"cluster 1 0 4 3.835396 2\n",
"cluster 2 1 2 4.347073 2\n",
"cluster 3 3 5 5.899885 3\n",
"cluster 4 6 7 8.316594 5"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 2. correct approach: Condensed distance matrix\n",
"\n",
"row_clusters = linkage(pdist(df, metric='euclidean'), method='complete')\n",
"pd.DataFrame(row_clusters, \n",
" columns=['row label 1', 'row label 2', 'distance', 'no. of items in clust.'],\n",
" index=['cluster %d' %(i+1) for i in range(row_clusters.shape[0])])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"
\n",
" \n",
" \n",
" | \n",
" row label 1 | \n",
" row label 2 | \n",
" distance | \n",
" no. of items in clust. | \n",
"
\n",
" \n",
" \n",
" \n",
" | cluster 1 | \n",
" 0 | \n",
" 4 | \n",
" 3.835396 | \n",
" 2 | \n",
"
\n",
" \n",
" | cluster 2 | \n",
" 1 | \n",
" 2 | \n",
" 4.347073 | \n",
" 2 | \n",
"
\n",
" \n",
" | cluster 3 | \n",
" 3 | \n",
" 5 | \n",
" 5.899885 | \n",
" 3 | \n",
"
\n",
" \n",
" | cluster 4 | \n",
" 6 | \n",
" 7 | \n",
" 8.316594 | \n",
" 5 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" row label 1 row label 2 distance no. of items in clust.\n",
"cluster 1 0 4 3.835396 2\n",
"cluster 2 1 2 4.347073 2\n",
"cluster 3 3 5 5.899885 3\n",
"cluster 4 6 7 8.316594 5"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 3. correct approach: Input sample matrix\n",
"\n",
"row_clusters = linkage(df.values, method='complete', metric='euclidean')\n",
"pd.DataFrame(row_clusters, \n",
" columns=['row label 1', 'row label 2', 'distance', 'no. of items in clust.'],\n",
" index=['cluster %d' %(i+1) for i in range(row_clusters.shape[0])])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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mSWqO4SZJao7hJklqjuEmSWqO4SZJao7hJklqjuEmSWqO4SZJao7hJklqjuEmSWqO4SZJ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\nao7hJklqjuEmSWrO/wOQQ5UEi+khlgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.cluster.hierarchy import dendrogram\n",
"\n",
"# make dendrogram black (part 1/2)\n",
"# from scipy.cluster.hierarchy import set_link_color_palette\n",
"# set_link_color_palette(['black'])\n",
"\n",
"row_dendr = dendrogram(row_clusters, \n",
" labels=labels,\n",
" # make dendrogram black (part 2/2)\n",
" # color_threshold=np.inf\n",
" )\n",
"plt.tight_layout()\n",
"plt.ylabel('Euclidean distance')\n",
"#plt.savefig('./figures/dendrogram.png', dpi=300, \n",
"# bbox_inches='tight')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Attaching dendrograms to a heat map"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# plot row dendrogram\n",
"fig = plt.figure(figsize=(8,8))\n",
"axd = fig.add_axes([0.09,0.1,0.2,0.6])\n",
"row_dendr = dendrogram(row_clusters, orientation='right')\n",
"\n",
"# reorder data with respect to clustering\n",
"df_rowclust = df.ix[row_dendr['leaves'][::-1]]\n",
"\n",
"axd.set_xticks([])\n",
"axd.set_yticks([])\n",
"\n",
"# remove axes spines from dendrogram\n",
"for i in axd.spines.values():\n",
" i.set_visible(False)\n",
"\n",
"\n",
" \n",
"# plot heatmap\n",
"axm = fig.add_axes([0.23,0.1,0.6,0.6]) # x-pos, y-pos, width, height\n",
"cax = axm.matshow(df_rowclust, interpolation='nearest', cmap='hot_r')\n",
"fig.colorbar(cax)\n",
"axm.set_xticklabels([''] + list(df_rowclust.columns))\n",
"axm.set_yticklabels([''] + list(df_rowclust.index))\n",
"\n",
"# plt.savefig('./figures/heatmap.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Applying agglomerative clustering via scikit-learn"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cluster labels: [0 1 1 0 0]\n"
]
}
],
"source": [
"from sklearn.cluster import AgglomerativeClustering\n",
"\n",
"ac = AgglomerativeClustering(n_clusters=2, affinity='euclidean', linkage='complete')\n",
"labels = ac.fit_predict(X)\n",
"print('Cluster labels: %s' % labels)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Locating regions of high density via DBSCAN"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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ncW2Q/hYBn0nHrY9TOl/V6Z14ZmXuRWNPtmpOVjrvVBfy947h/C0CgtOq5gCC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\nHQUJp3MOgjIvDAFDoB4QoIxCUP75z3/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Mg12nRiC1Nkj9TeSeSPip7Lbddlsfv/CyEZGL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\n8cUXe+v3EUcc4U477TRfnvgmCvJfNKQLAUZoOfbZZx+/krMEBHM8ioN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BlPGVXFNuuVZD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\nQmCC\n",
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {
"image/png": {
"width": 500
}
},
"output_type": "execute_result"
}
],
"source": [
"Image(filename='./images/11_11.png', width=500) "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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0t1uw6s2pVywWbSp1roW8hYHl+k6lzq1b3/pu2oPPufhCD0zLBVGAkhhrNMms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\nIiISSQpQIiISSQpQIiISSQpQIiISSf8f4bHRuu7FZLUAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.datasets import make_moons\n",
"\n",
"X, y = make_moons(n_samples=200, noise=0.05, random_state=0)\n",
"plt.scatter(X[:,0], X[:,1])\n",
"plt.tight_layout()\n",
"#plt.savefig('./figures/moons.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"K-means and hierarchical clustering:"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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v4LMxQ5k+8nXWzv2KiGe1woAGg4GNiRuoXi2QVV9NZ+u6b6jZ4HFO/LKfUqV9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\ngg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f, (ax1, ax2) = plt.subplots(1, 2, figsize=(8,3))\n",
"\n",
"km = KMeans(n_clusters=2, random_state=0)\n",
"y_km = km.fit_predict(X)\n",
"ax1.scatter(X[y_km==0,0], X[y_km==0,1], c='lightblue', marker='o', s=40, label='cluster 1')\n",
"ax1.scatter(X[y_km==1,0], X[y_km==1,1], c='red', marker='s', s=40, label='cluster 2')\n",
"ax1.set_title('K-means clustering')\n",
"\n",
"ac = AgglomerativeClustering(n_clusters=2, affinity='euclidean', linkage='complete')\n",
"y_ac = ac.fit_predict(X)\n",
"ax2.scatter(X[y_ac==0,0], X[y_ac==0,1], c='lightblue', marker='o', s=40, label='cluster 1')\n",
"ax2.scatter(X[y_ac==1,0], X[y_ac==1,1], c='red', marker='s', s=40, label='cluster 2')\n",
"ax2.set_title('Agglomerative clustering')\n",
"\n",
"plt.legend()\n",
"plt.tight_layout()\n",
"#plt.savefig('./figures/kmeans_and_ac.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Density-based clustering:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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zGDpsGIMUaQr7oHzE3rIHzi6JYDAY8Pzzz+PNufNwS7fu6HZ/X3RM6I3qqspa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\nRK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from sklearn.cluster import DBSCAN\n",
"\n",
"db = DBSCAN(eps=0.2, min_samples=5, metric='euclidean')\n",
"y_db = db.fit_predict(X)\n",
"plt.scatter(X[y_db==0,0], X[y_db==0,1], c='lightblue', marker='o', s=40, label='cluster 1')\n",
"plt.scatter(X[y_db==1,0], X[y_db==1,1], c='red', marker='s', s=40, label='cluster 2')\n",
"plt.legend()\n",
"plt.tight_layout()\n",
"#plt.savefig('./figures/moons_dbscan.png', dpi=300)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Summary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"..."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
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