Note
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Example builds a swiss roll dataset and runs hierarchical clustering on their position.
For more information, see Hierarchical clustering.
In a first step, the hierarchical clustering is performed without connectivity constraints on the structure and is solely based on distance, whereas in a second step the clustering is restricted to the k-Nearest Neighbors graph: it’s a hierarchical clustering with structure prior.
Some of the clusters learned without connectivity constraints do not respect the structure of the swiss roll and extend across different folds of the manifolds. On the opposite, when opposing connectivity constraints, the clusters form a nice parcellation of the swiss roll.
Out:
Compute unstructured hierarchical clustering... Elapsed time: 0.07s Number of points: 1500 Compute structured hierarchical clustering... Elapsed time: 0.13s Number of points: 1500
# Authors : Vincent Michel, 2010 # Alexandre Gramfort, 2010 # Gael Varoquaux, 2010 # License: BSD 3 clause print(__doc__) import time as time import numpy as np import matplotlib.pyplot as plt import mpl_toolkits.mplot3d.axes3d as p3 from sklearn.cluster import AgglomerativeClustering from sklearn.datasets.samples_generator import make_swiss_roll # ############################################################################# # Generate data (swiss roll dataset) n_samples = 1500 noise = 0.05 X, _ = make_swiss_roll(n_samples, noise) # Make it thinner X[:, 1] *= .5 # ############################################################################# # Compute clustering print("Compute unstructured hierarchical clustering...") st = time.time() ward = AgglomerativeClustering(n_clusters=6, linkage='ward').fit(X) elapsed_time = time.time() - st label = ward.labels_ print("Elapsed time: %.2fs" % elapsed_time) print("Number of points: %i" % label.size) # ############################################################################# # Plot result fig = plt.figure() ax = p3.Axes3D(fig) ax.view_init(7, -80) for l in np.unique(label): ax.scatter(X[label == l, 0], X[label == l, 1], X[label == l, 2], color=plt.cm.jet(np.float(l) / np.max(label + 1)), s=20, edgecolor='k') plt.title('Without connectivity constraints (time %.2fs)' % elapsed_time) # ############################################################################# # Define the structure A of the data. Here a 10 nearest neighbors from sklearn.neighbors import kneighbors_graph connectivity = kneighbors_graph(X, n_neighbors=10, include_self=False) # ############################################################################# # Compute clustering print("Compute structured hierarchical clustering...") st = time.time() ward = AgglomerativeClustering(n_clusters=6, connectivity=connectivity, linkage='ward').fit(X) elapsed_time = time.time() - st label = ward.labels_ print("Elapsed time: %.2fs" % elapsed_time) print("Number of points: %i" % label.size) # ############################################################################# # Plot result fig = plt.figure() ax = p3.Axes3D(fig) ax.view_init(7, -80) for l in np.unique(label): ax.scatter(X[label == l, 0], X[label == l, 1], X[label == l, 2], color=plt.cm.jet(float(l) / np.max(label + 1)), s=20, edgecolor='k') plt.title('With connectivity constraints (time %.2fs)' % elapsed_time) plt.show()
Total running time of the script: ( 0 minutes 0.296 seconds)
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http://scikit-learn.org/stable/auto_examples/cluster/plot_ward_structured_vs_unstructured.html