scikit-learn/examples/cluster/plot_ward_structured_vs_unstructured.py

"""
===========================================================
Hierarchical clustering: structured vs unstructured ward
===========================================================

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

For more information, see :ref:`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

import time as time

# The following import is required
# for 3D projection to work with matplotlib < 3.2
import mpl_toolkits.mplot3d  # noqa: F401
import numpy as np

# %%
# Generate data
# -------------
#
# We start by generating the Swiss Roll dataset.
from sklearn.datasets import make_swiss_roll

n_samples = 1500
noise = 0.05
X, _ = make_swiss_roll(n_samples, noise=noise)
# Make it thinner
X[:, 1] *= 0.5

# %%
# Compute clustering
# ------------------
#
# We perform AgglomerativeClustering which comes under Hierarchical Clustering
# without any connectivity constraints.

from sklearn.cluster import AgglomerativeClustering

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(f"Elapsed time: {elapsed_time:.2f}s")
print(f"Number of points: {label.size}")

# %%
# Plot result
# -----------
# Plotting the unstructured hierarchical clusters.

import matplotlib.pyplot as plt

fig1 = plt.figure()
ax1 = fig1.add_subplot(111, projection="3d", elev=7, azim=-80)
ax1.set_position([0, 0, 0.95, 1])
for l in np.unique(label):
    ax1.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",
    )
_ = fig1.suptitle(f"Without connectivity constraints (time {elapsed_time:.2f}s)")

# %%
# We are defining k-Nearest Neighbors with 10 neighbors
# -----------------------------------------------------

from sklearn.neighbors import kneighbors_graph

connectivity = kneighbors_graph(X, n_neighbors=10, include_self=False)

# %%
# Compute clustering
# ------------------
#
# We perform AgglomerativeClustering again with connectivity constraints.

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(f"Elapsed time: {elapsed_time:.2f}s")
print(f"Number of points: {label.size}")

# %%
# Plot result
# -----------
#
# Plotting the structured hierarchical clusters.

fig2 = plt.figure()
ax2 = fig2.add_subplot(121, projection="3d", elev=7, azim=-80)
ax2.set_position([0, 0, 0.95, 1])
for l in np.unique(label):
    ax2.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",
    )
fig2.suptitle(f"With connectivity constraints (time {elapsed_time:.2f}s)")

plt.show()