DOC Add silhouette analysis plot for KMeans

Author: raghavrv

examples/cluster/plot_kmeans_silhouette_analysis.py

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+"""
+===============================================================================
+Silhouette analysis for sample data clustered using KMeans clustering algorithm
+===============================================================================
+
+Silhouette analysis can be used to study the separation distance between the
+resulting clusters. The silhouette plot displays a measure of how close each
+point in one cluster is to points in the neighboring clusters. This measure has
+a range of [-1, 1]. Silhoette coefficients (as these values are referred to as)
+near +1 indicate that the sample is far away from the neighboring clusters.
+A value of 0 indicates that the sample is on or very close to the decision 
+boundary between two neighboring clusters and negative values (upto -1) 
+indicate that those samples might have been assigned to the wrong cluster.
+"""
+
+from __future__ import print_function
+
+from sklearn.datasets import make_blobs
+from sklearn.cluster import KMeans
+from sklearn.metrics import silhouette_samples, silhouette_score
+
+import matplotlib.pyplot as plt
+import matplotlib.cm as cm
+import numpy as np
+
+print(__doc__)
+
+# Generating the sample data from make_blobs
+# This particular setting has one distict cluster and 3 clusters placed close 
+# together.
+X, y = make_blobs(n_samples=500,
+                  n_features=2,
+                  centers=4,
+                  cluster_std=1.0,
+                  center_box=(-10.0, 10.0),
+                  shuffle=True,
+                  random_state=1) # For reproducibility
+
+range_n_clusters = [ 2, 4, 6 ]
+
+for n_clusters in range_n_clusters:
+    # Create a subplot with 1 row and 2 columns
+    fig, (ax1, ax2) = plt.subplots(1, 2)
+    fig.set_size_inches(18, 7)
+    
+    # The 1st subplot is the silhouette plot
+    # The silhouette coefficient can range from -1, 1 but in this example all
+    # lie within [-0.1, 1]
+    ax1.set_xlim([-0.1, 1])
+    # The n_clusters*10 are the additional samples to demarcate the space 
+    # between silhouette plots of individual clusters.
+    ax1.set_ylim([0, len(X) + n_clusters*10])
+
+    # Initialize the clusterer with n_clusters value and a random generator 
+    # seed of 10 for reproducibility.
+    clusterer = KMeans(n_clusters=n_clusters, random_state=10)
+    cluster_labels = clusterer.fit_predict(X)
+    
+    # The silhouette_score gives the average value for all the samples.
+    # This gives a perspective into the density and separation of the formed 
+    # clusters
+    print("For n_clusters = %d," % n_clusters,
+          "The average silhouette_score is :", 
+          silhouette_score(X, cluster_labels))
+    
+    # Compute the silhouette scores for each sample
+    sample_silhouette_values = silhouette_samples(X, cluster_labels)
+
+    # This will hold the silhouette coefficient of all the clusters separated
+    # by 0 samples.
+    sorted_clustered_sample_silhouette_values = []
+
+    for i in np.unique(cluster_labels):
+        ith_cluster_silhouette_values = \
+                sample_silhouette_values[cluster_labels == i]
+
+        # Add the ith_cluster_silhouette_values after sorting them
+        ith_cluster_silhouette_values.sort()
+
+        # The introduced 0 samples are to differentiate clearly between the 
+        # different clusters
+        sorted_clustered_sample_silhouette_values += \
+                ith_cluster_silhouette_values.tolist() + [0]*10
+
+    # Plot and fill all the sihouette plot polygons
+    ax1.plot(sorted_clustered_sample_silhouette_values, 
+             range(len(X) + 10*n_clusters))
+    ax1.fill_between(sorted_clustered_sample_silhouette_values, 
+                     range(len(X)  + 10*n_clusters))
+    ax1.set_title("The silhouette plot for the various clusters.")
+    ax1.set_xlabel("The silhouette coefficient values")
+    ax1.set_ylabel("Cluster label")
+    # A vertical line at x = 0.
+    ax1.axvline()
+    
+    ax1.set_yticks([]) # Clear the yaxis labels / ticks
+    ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])
+    
+    # Computing custom label coordinates for labeling the clusters
+    
+    offset = 0
+    for i in range(n_clusters):
+        size_cluster_i = sum(cluster_labels == i)
+        
+        x = -0.05
+        # Label them at the middle
+        y = offset + (size_cluster_i / 2.0)        
+        ax1.text(x, y, str(i))
+        
+        # Compute the base offset for next plot
+        offset += size_cluster_i + 10 # 10 for the 0 samples
+        
+    # 2nd Plot showing the actual clusters formed
+    for k in range(len(X)):
+        color = cm.spectral(float(cluster_labels[k]) / n_clusters, 1)
+        ax2.scatter(X[k, 0], X[k, 1], marker='.', color=color)
+        
+    # Label the cluster centers with the cluster number for identification and 
+    # study of the corresponding silhouette plot.
+    for c in clusterer.cluster_centers_:
+        # Use the clusterer to know to which cluster number the current center 
+        # c belongs to
+        i = clusterer.predict(c)[0]
+        ax2.scatter(c[0], c[1], marker='o', c="white", alpha = 1, s = 200)
+        ax2.scatter(c[0], c[1], marker="$%d$" % i, alpha = 1, s = 50)
+    
+    ax2.set_title("The visualization of the clustered data.")
+    plt.suptitle(("Silhouette analysis for KMeans clustering on sample data "
+                  "with n_clusters = %d" % n_clusters), 
+                 fontsize = 14, fontweight = 'bold')
+    ax2.set_xlabel("Feature space for the 1st feature")
+    ax2.set_ylabel("Feature space for the 2nd feature")
+    plt.show()