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.
# 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)
Out:
Compute unstructured hierarchical clustering... Elapsed time: 0.07s Number of points: 1500
Plot result
fig = plt.figure() ax = p3.Axes3D(fig) ax.view_init(7, -80) for l in np.unique(label): ax.plot3D(X[label == l, 0], X[label == l, 1], X[label == l, 2], 'o', color=plt.cm.jet(np.float(l) / np.max(label + 1))) 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)
Out:
Compute structured hierarchical clustering... Elapsed time: 0.14s Number of points: 1500
Plot result
fig = plt.figure() ax = p3.Axes3D(fig) ax.view_init(7, -80) for l in np.unique(label): ax.plot3D(X[label == l, 0], X[label == l, 1], X[label == l, 2], 'o', color=plt.cm.jet(float(l) / np.max(label + 1))) plt.title('With connectivity constraints (time %.2fs)' % elapsed_time) plt.show()
Total running time of the script: (0 minutes 0.299 seconds)
plot_ward_structured_vs_unstructured.py
plot_ward_structured_vs_unstructured.ipynb
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