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# Hierarchical clustering: structured vs unstructured ward

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

    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}")

    Compute unstructured hierarchical clustering...
    Elapsed time: 0.02s
    Number of points: 1500

## 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}")

    Compute structured hierarchical clustering...
    Elapsed time: 0.04s
    Number of points: 1500

## 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()

Total running time of the script: (0 minutes 0.242 seconds)

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