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# Various Agglomerative Clustering on a 2D embedding of digits

An illustration of various linkage option for agglomerative clustering on a 2D embedding of the digits dataset.

The goal of this example is to show intuitively how the metrics behave, and not to find good clusters for the digits. This is why the example works on a 2D embedding.

What this example shows us is the behavior “rich getting richer” of agglomerative clustering that tends to create uneven cluster sizes.

This behavior is pronounced for the average linkage strategy, that ends up with a couple of clusters with few datapoints.

The case of single linkage is even more pathologic with a very large cluster covering most digits, an intermediate size (clean) cluster with most zero digits and all other clusters being drawn from noise points around the fringes.

The other linkage strategies lead to more evenly distributed clusters that are therefore likely to be less sensible to a random resampling of the dataset.

    Computing embedding
    Done.
    ward :  0.05s
    average :       0.03s
    complete :      0.03s
    single :        0.01s

    # Authors: Gael Varoquaux
    # License: BSD 3 clause (C) INRIA 2014

    from time import time

    import numpy as np
    from matplotlib import pyplot as plt

    from sklearn import datasets, manifold

    digits = datasets.load_digits()
    X, y = digits.data, digits.target
    n_samples, n_features = X.shape

    np.random.seed(0)

    # ----------------------------------------------------------------------
    # Visualize the clustering
    def plot_clustering(X_red, labels, title=None):
        x_min, x_max = np.min(X_red, axis=0), np.max(X_red, axis=0)
        X_red = (X_red - x_min) / (x_max - x_min)

        plt.figure(figsize=(6, 4))
        for digit in digits.target_names:
            plt.scatter(
                *X_red[y == digit].T,
                marker=f"${digit}$",
                s=50,
                c=plt.cm.nipy_spectral(labels[y == digit] / 10),
                alpha=0.5,
            )

        plt.xticks([])
        plt.yticks([])
        if title is not None:
            plt.title(title, size=17)
        plt.axis("off")
        plt.tight_layout(rect=[0, 0.03, 1, 0.95])

    # ----------------------------------------------------------------------
    # 2D embedding of the digits dataset
    print("Computing embedding")
    X_red = manifold.SpectralEmbedding(n_components=2).fit_transform(X)
    print("Done.")

    from sklearn.cluster import AgglomerativeClustering

    for linkage in ("ward", "average", "complete", "single"):
        clustering = AgglomerativeClustering(linkage=linkage, n_clusters=10)
        t0 = time()
        clustering.fit(X_red)
        print("%s :\t%.2fs" % (linkage, time() - t0))

        plot_clustering(X_red, clustering.labels_, "%s linkage" % linkage)

    plt.show()

Total running time of the script: (0 minutes 1.611 seconds)

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