import itertools import numpy as np import matplotlib.pyplot as plt from sklearn.cluster import KMeans np.random.seed(1) # Set the number of samples, the means and # variances of each of the three simulated clusters samples = 100 mu = [(7, 5), (8, 12), (1, 10)] cov = [ [[0.5, 0], [0, 1.0]], [[2.0, 0], [0, 3.5]], [[3, 0], [0, 5]], ] # Generate a list of the 2D cluster points norm_dists = [ np.random.multivariate_normal(m, c, samples) for m, c in zip(mu, cov) ] X = np.array(list(itertools.chain(*norm_dists))) # Apply the K-Means Algorithm for k=3, which is # equal to the number of true Gaussian clusters km3 = KMeans(n_clusters=3) km3.fit(X) km3_labels = km3.labels_ # Apply the K-Means Algorithm for k=4, which is # larger than the number of true Gaussian clusters km4 = KMeans(n_clusters=4) km4.fit(X) km4_labels = km4.labels_ # Create a subplot comparing k=3 and k=4 # for the K-Means Algorithm fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14,6)) ax1.scatter(X[:, 0], X[:, 1], c=km3_labels.astype(np.float)) ax1.set_xlabel("$x_1$") ax1.set_ylabel("$x_2$") ax1.set_title("K-Means with $k=3$") ax2.scatter(X[:, 0], X[:, 1], c=km4_labels.astype(np.float)) ax2.set_xlabel("$x_1$") ax2.set_ylabel("$x_2$") ax2.set_title("K-Means with $k=4$") plt.show()
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