This example is meant to illustrate situations where k-means will produce unintuitive and possibly unexpected clusters. In the first three plots, the input data does not conform to some implicit assumption that k-means makes and undesirable clusters are produced as a result. In the last plot, k-means returns intuitive clusters despite unevenly sized blobs.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | print(__doc__)# Author: Phil Roth <mr.phil.roth@gmail.com># License: BSD 3 clauseimport numpy as npimport matplotlib.pyplot as pltfrom sklearn.cluster import KMeansfrom sklearn.datasets import make_blobsplt.figure(figsize=(12, 12))n_samples = 1500random_state = 170X, y = make_blobs(n_samples=n_samples, random_state=random_state)# Incorrect number of clustersy_pred = KMeans(n_clusters=2, random_state=random_state).fit_predict(X)plt.subplot(221)plt.scatter(X[:, 0], X[:, 1], c=y_pred)plt.title("Incorrect Number of Blobs")# Anisotropicly distributed datatransformation = [[ 0.60834549, -0.63667341], [-0.40887718, 0.85253229]]X_aniso = np.dot(X, transformation)y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_aniso)plt.subplot(222)plt.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred)plt.title("Anisotropicly Distributed Blobs")# Different varianceX_varied, y_varied = make_blobs(n_samples=n_samples, cluster_std=[1.0, 2.5, 0.5], random_state=random_state)y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)plt.subplot(223)plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred)plt.title("Unequal Variance")# Unevenly sized blobsX_filtered = np.vstack((X[y == 0][:500], X[y == 1][:100], X[y == 2][:10]))y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_filtered)plt.subplot(224)plt.scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred)plt.title("Unevenly Sized Blobs")plt.show() |
Total running time of the script: (0 minutes 0.353 seconds)
Download Python source code:
plot_kmeans_assumptions.py
Download IPython notebook:
plot_kmeans_assumptions.ipynb
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