.. _sphx_glr_auto_examples_cluster_plot_kmeans_digits.py: =========================================================== A demo of K-Means clustering on the handwritten digits data =========================================================== In this example we compare the various initialization strategies for K-means in terms of runtime and quality of the results. As the ground truth is known here, we also apply different cluster quality metrics to judge the goodness of fit of the cluster labels to the ground truth. Cluster quality metrics evaluated (see :ref:`clustering_evaluation` for definitions and discussions of the metrics): =========== ======================================================== Shorthand full name =========== ======================================================== homo homogeneity score compl completeness score v-meas V measure ARI adjusted Rand index AMI adjusted mutual information silhouette silhouette coefficient =========== ======================================================== .. code-block:: python print(__doc__) from time import time import numpy as np import matplotlib.pyplot as plt from sklearn import metrics from sklearn.cluster import KMeans from sklearn.datasets import load_digits from sklearn.decomposition import PCA from sklearn.preprocessing import scale np.random.seed(42) digits = load_digits() data = scale(digits.data) n_samples, n_features = data.shape n_digits = len(np.unique(digits.target)) labels = digits.target sample_size = 300 print("n_digits: %d, \t n_samples %d, \t n_features %d" % (n_digits, n_samples, n_features)) print(79 * '_') print('% 9s' % 'init' ' time inertia homo compl v-meas ARI AMI silhouette') def bench_k_means(estimator, name, data): t0 = time() estimator.fit(data) print('% 9s %.2fs %i %.3f %.3f %.3f %.3f %.3f %.3f' % (name, (time() - t0), estimator.inertia_, metrics.homogeneity_score(labels, estimator.labels_), metrics.completeness_score(labels, estimator.labels_), metrics.v_measure_score(labels, estimator.labels_), metrics.adjusted_rand_score(labels, estimator.labels_), metrics.adjusted_mutual_info_score(labels, estimator.labels_), metrics.silhouette_score(data, estimator.labels_, metric='euclidean', sample_size=sample_size))) bench_k_means(KMeans(init='k-means++', n_clusters=n_digits, n_init=10), name="k-means++", data=data) bench_k_means(KMeans(init='random', n_clusters=n_digits, n_init=10), name="random", data=data) # in this case the seeding of the centers is deterministic, hence we run the # kmeans algorithm only once with n_init=1 pca = PCA(n_components=n_digits).fit(data) bench_k_means(KMeans(init=pca.components_, n_clusters=n_digits, n_init=1), name="PCA-based", data=data) print(79 * '_') .. rst-class:: sphx-glr-script-out Out:: n_digits: 10, n_samples 1797, n_features 64 _______________________________________________________________________________ init time inertia homo compl v-meas ARI AMI silhouette k-means++ 0.32s 69432 0.602 0.650 0.625 0.465 0.598 0.146 random 0.26s 69694 0.669 0.710 0.689 0.553 0.666 0.147 PCA-based 0.05s 70804 0.671 0.698 0.684 0.561 0.668 0.118 _______________________________________________________________________________ Visualize the results on PCA-reduced data .. code-block:: python reduced_data = PCA(n_components=2).fit_transform(data) kmeans = KMeans(init='k-means++', n_clusters=n_digits, n_init=10) kmeans.fit(reduced_data) # Step size of the mesh. Decrease to increase the quality of the VQ. h = .02 # point in the mesh [x_min, x_max]x[y_min, y_max]. # Plot the decision boundary. For that, we will assign a color to each x_min, x_max = reduced_data[:, 0].min() - 1, reduced_data[:, 0].max() + 1 y_min, y_max = reduced_data[:, 1].min() - 1, reduced_data[:, 1].max() + 1 xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) # Obtain labels for each point in mesh. Use last trained model. Z = kmeans.predict(np.c_[xx.ravel(), yy.ravel()]) # Put the result into a color plot Z = Z.reshape(xx.shape) plt.figure(1) plt.clf() plt.imshow(Z, interpolation='nearest', extent=(xx.min(), xx.max(), yy.min(), yy.max()), cmap=plt.cm.Paired, aspect='auto', origin='lower') plt.plot(reduced_data[:, 0], reduced_data[:, 1], 'k.', markersize=2) # Plot the centroids as a white X centroids = kmeans.cluster_centers_ plt.scatter(centroids[:, 0], centroids[:, 1], marker='x', s=169, linewidths=3, color='w', zorder=10) plt.title('K-means clustering on the digits dataset (PCA-reduced data)\n' 'Centroids are marked with white cross') plt.xlim(x_min, x_max) plt.ylim(y_min, y_max) plt.xticks(()) plt.yticks(()) plt.show() .. image:: /auto_examples/cluster/images/sphx_glr_plot_kmeans_digits_001.png :align: center **Total running time of the script:** (0 minutes 1.879 seconds) .. container:: sphx-glr-download **Download Python source code:** :download:`plot_kmeans_digits.py ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_kmeans_digits.ipynb `