160 lines
5.8 KiB
Python
160 lines
5.8 KiB
Python
"""
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===============================================================================
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Selecting the number of clusters with silhouette analysis on KMeans clustering
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===============================================================================
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Silhouette analysis can be used to study the separation distance between the
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resulting clusters. The silhouette plot displays a measure of how close each
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point in one cluster is to points in the neighboring clusters and thus provides
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a way to assess parameters like number of clusters visually. This measure has a
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range of [-1, 1].
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Silhouette coefficients (as these values are referred to as) near +1 indicate
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that the sample is far away from the neighboring clusters. A value of 0
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indicates that the sample is on or very close to the decision boundary between
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two neighboring clusters and negative values indicate that those samples might
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have been assigned to the wrong cluster.
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In this example the silhouette analysis is used to choose an optimal value for
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``n_clusters``. The silhouette plot shows that the ``n_clusters`` value of 3, 5
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and 6 are a bad pick for the given data due to the presence of clusters with
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below average silhouette scores and also due to wide fluctuations in the size
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of the silhouette plots. Silhouette analysis is more ambivalent in deciding
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between 2 and 4.
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Also from the thickness of the silhouette plot the cluster size can be
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visualized. The silhouette plot for cluster 0 when ``n_clusters`` is equal to
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2, is bigger in size owing to the grouping of the 3 sub clusters into one big
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cluster. However when the ``n_clusters`` is equal to 4, all the plots are more
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or less of similar thickness and hence are of similar sizes as can be also
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verified from the labelled scatter plot on the right.
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"""
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import matplotlib.cm as cm
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.cluster import KMeans
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from sklearn.datasets import make_blobs
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from sklearn.metrics import silhouette_samples, silhouette_score
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# Generating the sample data from make_blobs
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# This particular setting has one distinct cluster and 3 clusters placed close
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# together.
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X, y = make_blobs(
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n_samples=500,
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n_features=2,
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centers=4,
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cluster_std=1,
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center_box=(-10.0, 10.0),
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shuffle=True,
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random_state=1,
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) # For reproducibility
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range_n_clusters = [2, 3, 4, 5, 6]
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for n_clusters in range_n_clusters:
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# Create a subplot with 1 row and 2 columns
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fig, (ax1, ax2) = plt.subplots(1, 2)
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fig.set_size_inches(18, 7)
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# The 1st subplot is the silhouette plot
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# The silhouette coefficient can range from -1, 1 but in this example all
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# lie within [-0.1, 1]
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ax1.set_xlim([-0.1, 1])
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# The (n_clusters+1)*10 is for inserting blank space between silhouette
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# plots of individual clusters, to demarcate them clearly.
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ax1.set_ylim([0, len(X) + (n_clusters + 1) * 10])
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# Initialize the clusterer with n_clusters value and a random generator
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# seed of 10 for reproducibility.
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clusterer = KMeans(n_clusters=n_clusters, random_state=10)
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cluster_labels = clusterer.fit_predict(X)
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# The silhouette_score gives the average value for all the samples.
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# This gives a perspective into the density and separation of the formed
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# clusters
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silhouette_avg = silhouette_score(X, cluster_labels)
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print(
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"For n_clusters =",
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n_clusters,
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"The average silhouette_score is :",
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silhouette_avg,
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)
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# Compute the silhouette scores for each sample
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sample_silhouette_values = silhouette_samples(X, cluster_labels)
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y_lower = 10
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for i in range(n_clusters):
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# Aggregate the silhouette scores for samples belonging to
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# cluster i, and sort them
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ith_cluster_silhouette_values = sample_silhouette_values[cluster_labels == i]
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ith_cluster_silhouette_values.sort()
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size_cluster_i = ith_cluster_silhouette_values.shape[0]
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y_upper = y_lower + size_cluster_i
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color = cm.nipy_spectral(float(i) / n_clusters)
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ax1.fill_betweenx(
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np.arange(y_lower, y_upper),
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0,
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ith_cluster_silhouette_values,
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facecolor=color,
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edgecolor=color,
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alpha=0.7,
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)
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# Label the silhouette plots with their cluster numbers at the middle
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ax1.text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))
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# Compute the new y_lower for next plot
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y_lower = y_upper + 10 # 10 for the 0 samples
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ax1.set_title("The silhouette plot for the various clusters.")
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ax1.set_xlabel("The silhouette coefficient values")
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ax1.set_ylabel("Cluster label")
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# The vertical line for average silhouette score of all the values
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ax1.axvline(x=silhouette_avg, color="red", linestyle="--")
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ax1.set_yticks([]) # Clear the yaxis labels / ticks
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ax1.set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])
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# 2nd Plot showing the actual clusters formed
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colors = cm.nipy_spectral(cluster_labels.astype(float) / n_clusters)
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ax2.scatter(
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X[:, 0], X[:, 1], marker=".", s=30, lw=0, alpha=0.7, c=colors, edgecolor="k"
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)
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# Labeling the clusters
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centers = clusterer.cluster_centers_
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# Draw white circles at cluster centers
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ax2.scatter(
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centers[:, 0],
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centers[:, 1],
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marker="o",
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c="white",
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alpha=1,
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s=200,
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edgecolor="k",
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)
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for i, c in enumerate(centers):
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ax2.scatter(c[0], c[1], marker="$%d$" % i, alpha=1, s=50, edgecolor="k")
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ax2.set_title("The visualization of the clustered data.")
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ax2.set_xlabel("Feature space for the 1st feature")
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ax2.set_ylabel("Feature space for the 2nd feature")
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plt.suptitle(
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"Silhouette analysis for KMeans clustering on sample data with n_clusters = %d"
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% n_clusters,
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fontsize=14,
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fontweight="bold",
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)
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plt.show()
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