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# Hashing feature transformation using Totally Random Trees

RandomTreesEmbedding provides a way to map data to a very high-dimensional, sparse representation, which might be beneficial for classification. The mapping is completely unsupervised and very efficient.

This example visualizes the partitions given by several trees and shows how the transformation can also be used for non-linear dimensionality reduction or non-linear classification.

Points that are neighboring often share the same leaf of a tree and therefore share large parts of their hashed representation. This allows to separate two concentric circles simply based on the principal components of the transformed data with truncated SVD.

In high-dimensional spaces, linear classifiers often achieve excellent accuracy. For sparse binary data, BernoulliNB is particularly well-suited. The bottom row compares the decision boundary obtained by BernoulliNB in the transformed space with an ExtraTreesClassifier forests learned on the original data.

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import make_circles
    from sklearn.decomposition import TruncatedSVD
    from sklearn.ensemble import ExtraTreesClassifier, RandomTreesEmbedding
    from sklearn.naive_bayes import BernoulliNB

    # make a synthetic dataset
    X, y = make_circles(factor=0.5, random_state=0, noise=0.05)

    # use RandomTreesEmbedding to transform data
    hasher = RandomTreesEmbedding(n_estimators=10, random_state=0, max_depth=3)
    X_transformed = hasher.fit_transform(X)

    # Visualize result after dimensionality reduction using truncated SVD
    svd = TruncatedSVD(n_components=2)
    X_reduced = svd.fit_transform(X_transformed)

    # Learn a Naive Bayes classifier on the transformed data
    nb = BernoulliNB()
    nb.fit(X_transformed, y)

    # Learn an ExtraTreesClassifier for comparison
    trees = ExtraTreesClassifier(max_depth=3, n_estimators=10, random_state=0)
    trees.fit(X, y)

    # scatter plot of original and reduced data
    fig = plt.figure(figsize=(9, 8))

    ax = plt.subplot(221)
    ax.scatter(X[:, 0], X[:, 1], c=y, s=50, edgecolor="k")
    ax.set_title("Original Data (2d)")
    ax.set_xticks(())
    ax.set_yticks(())

    ax = plt.subplot(222)
    ax.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, s=50, edgecolor="k")
    ax.set_title(
        "Truncated SVD reduction (2d) of transformed data (%dd)" % X_transformed.shape[1]
    )
    ax.set_xticks(())
    ax.set_yticks(())

    # Plot the decision in original space. For that, we will assign a color
    # to each point in the mesh [x_min, x_max]x[y_min, y_max].
    h = 0.01
    x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
    y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))

    # transform grid using RandomTreesEmbedding
    transformed_grid = hasher.transform(np.c_[xx.ravel(), yy.ravel()])
    y_grid_pred = nb.predict_proba(transformed_grid)[:, 1]

    ax = plt.subplot(223)
    ax.set_title("Naive Bayes on Transformed data")
    ax.pcolormesh(xx, yy, y_grid_pred.reshape(xx.shape))
    ax.scatter(X[:, 0], X[:, 1], c=y, s=50, edgecolor="k")
    ax.set_ylim(-1.4, 1.4)
    ax.set_xlim(-1.4, 1.4)
    ax.set_xticks(())
    ax.set_yticks(())

    # transform grid using ExtraTreesClassifier
    y_grid_pred = trees.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]

    ax = plt.subplot(224)
    ax.set_title("ExtraTrees predictions")
    ax.pcolormesh(xx, yy, y_grid_pred.reshape(xx.shape))
    ax.scatter(X[:, 0], X[:, 1], c=y, s=50, edgecolor="k")
    ax.set_ylim(-1.4, 1.4)
    ax.set_xlim(-1.4, 1.4)
    ax.set_xticks(())
    ax.set_yticks(())

    plt.tight_layout()
    plt.show()

Total running time of the script: (0 minutes 0.259 seconds)

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