{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# K-Means Clustering\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "//anaconda/lib/python3.5/site-packages/sklearn/utils/fixes.py:313: FutureWarning: numpy not_equal will not check object identity in the future. The comparison did not return the same result as suggested by the identity (`is`)) and will change.\n", " _nan_object_mask = _nan_object_array != _nan_object_array\n" ] }, { "data": { "image/png": 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9g1FsKTl7LMYbdzKcH02gKve0GFURfG9ymdl0kYFIsKcm5NupIroquH+d9LVZ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\njHFE5MPAjwAb+Kox5vk1s0xRXiFUs/Mt5545NTLLixdnufv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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets.samples_generator import make_blobs\n", "X,y = make_blobs(n_samples=300, centers=4, cluster_std=0.8, random_state=0)\n", "plt.scatter(X[:, 0], X[:, 1], s=50, alpha=0.5);" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "KMeans(algorithm='auto', copy_x=True, init='random', max_iter=300,\n", " n_clusters=4, n_init=10, n_jobs=None, precompute_distances='auto',\n", " random_state=None, tol=0.0001, verbose=0)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.cluster import KMeans\n", "kmeans = KMeans(init='random', n_clusters=4)\n", "kmeans.fit(X)\n", "y_pred = kmeans.predict(X)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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iu+azaPVehvrC2J1WHG4Hnnw34YEIbr/LiLfPipWuS3pP9FE6tZh3fvK+0Xyj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EcvXl5k+yd29mDbkng6h1tXK900li3xujSyeYN1TTVkcoXSqsR5xJJZOhsiN6QBfzUevXc9dVUB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\n/wcKSkG41ZVO1gAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(X[:, 0], X[:, 1], c=y_pred, s=50, alpha=0.5)\n", "centers = kmeans.cluster_centers_\n", "plt.scatter(centers[:, 0], centers[:, 1], c='black', s=200, alpha=0.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Kmeans will produce as many clusters as you ask for:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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KJxfyzs/fM4ZvlOSjKIKOU108+9cv8Pj/fGhYAPNkbSOR/uGthEMd/TjcDqID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\nz85dQ/SX6yw/5gJcvAZVZffu3YyMjLBy5Uquu+461q07fBSA5jusRtR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Gjnw6TIUKA1D8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gp7/TkOPZx8wOrVXdCbxCeECqU2O2NtNIN1x+piJg43ne7ldMITqreo6tmqevaSJR2M/x1ngaOV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\n0ye4oDuO4/QJ/w+emujbR75q+QAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.cluster import KMeans\n", "kmeans = KMeans(n_clusters=2)\n", "kmeans.fit(X)\n", "y_pred = kmeans.predict(X)\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y_pred, s=50, alpha=0.5)\n", "centers = kmeans.cluster_centers_\n", "plt.scatter(centers[:, 0], centers[:, 1], c='black', s=200, alpha=0.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we'll demonstrate where things can go wrong when applying k-means." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3qVjW5HpC0nFd4iThcuuQruchheTyYYuW6+LHEb/c3mRr2OflpWVsXWepUmUQ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RM0q9iThX/iUa2itR9bRt9o8NIq1F8nI8WtM+ovq3/ki9UCOJTEtPTFr+Yce44cjxBPdGrlon1Q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\nIMQfoW6gOVZPswXj8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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_samples = 1000\n", "random_state = 170\n", "X, y = make_blobs(n_samples=n_samples, random_state=random_state)\n", "y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X)\n", "plt.scatter(X[:, 0], X[:, 1], c=y_pred, s=50, alpha=0.3)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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k+5pataRlzcyDpyH5HiJ19VIny/zTGQifxwb7SalC/W/0GFbr7bfKrTZYZYqc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\nB6d/eZ6h7QM3dLleOXWVrv4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N0swyrYYuSPZt6aNarpG0YlaWqgRhQNRMdOEVmBmdpn9L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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Anisotropicly distributed data\n", "transformation = [[0.60834549, -0.63667341], [-0.40887718, 0.85253229]]\n", "X_aniso = np.dot(X, transformation)\n", "y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_aniso)\n", "plt.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred, s=50, alpha=0.3)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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RqrfRTb1b2E6RSMeCCCrPw7oznHYbEArD5xYXlIOQ94qaiNy374JSnSB4XDxG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\n93SpbvJF01teTPp5C6OaVZgL6AW+xyCBnvLtmM5RyCY0eNg6lH9X51v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51TrkFwCn15kx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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_varied, y_varied = make_blobs(n_samples=n_samples,\n", " cluster_std=[1.0, 2.5, 0.5],\n", " random_state=25)\n", "y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)\n", "plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred, s=50, alpha=0.3)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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jG0XM35HyCtD0A653u6UBKCk5oBwYAzBTqfKdJ07z2vKiaYIiwlRY4WunzuzSzulGEbnI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Efd1qCnwDUjLeE0mV213WIkIPLfBqaBWFBNjBGjc0+YnXn+T+cWfzxAIHoKcbYBNioOlM6jfskM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\nax92kqxO0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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_varied, y_varied = make_blobs(n_samples=n_samples,\n", " cluster_std=[1.0, 2.5, 0.5],\n", " random_state=124)\n", "y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)\n", "plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred, s=50, alpha=0.3)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.5" } }, "nbformat": 4, "nbformat_minor": 1 }