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# Hierarchical clustering: structured vs unstructured wardΒΆ

Example builds a swiss roll dataset and runs hierarchical clustering on their position.

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.

Script output:

Compute unstructured hierarchical clustering...
Elapsed time: 1.89s
Number of points: 1500
Compute structured hierarchical clustering...
Elapsed time: 0.12s
Number of points: 1500

Python source code: plot_ward_structured_vs_unstructured.py

# Authors : Vincent Michel, 2010
#           Alexandre Gramfort, 2010
#           Gael Varoquaux, 2010

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()
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.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,
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.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 example: 2.30 seconds ( 0 minutes 2.30 seconds)