scikit-learn/sklearn/tests/test_kernel_approximation.py

import numpy as np
from scipy.sparse import csr_matrix

from sklearn.utils.testing import assert_array_equal, assert_equal
from sklearn.utils.testing import assert_array_almost_equal, assert_raises

from sklearn.kernel_approximation import RBFSampler
from sklearn.kernel_approximation import AdditiveChi2Sampler
from sklearn.kernel_approximation import SkewedChi2Sampler
from sklearn.kernel_approximation import Nystroem
from sklearn.metrics.pairwise import rbf_kernel

# generate data
rng = np.random.RandomState(0)
X = rng.random_sample(size=(300, 50))
Y = rng.random_sample(size=(300, 50))
X /= X.sum(axis=1)[:, np.newaxis]
Y /= Y.sum(axis=1)[:, np.newaxis]


def test_additive_chi2_sampler():
    """test that AdditiveChi2Sampler approximates kernel on random data"""

    # compute exact kernel
    # appreviations for easier formular
    X_ = X[:, np.newaxis, :]
    Y_ = Y[np.newaxis, :, :]

    large_kernel = 2 * X_ * Y_ / (X_ + Y_)

    # reduce to n_samples_x x n_samples_y by summing over features
    kernel = (large_kernel.sum(axis=2))

    # appoximate kernel mapping
    transform = AdditiveChi2Sampler(sample_steps=3)
    X_trans = transform.fit_transform(X)
    Y_trans = transform.transform(Y)

    kernel_approx = np.dot(X_trans, Y_trans.T)

    assert_array_almost_equal(kernel, kernel_approx, 1)

    X_sp_trans = transform.fit_transform(csr_matrix(X))
    Y_sp_trans = transform.transform(csr_matrix(Y))

    assert_array_equal(X_trans, X_sp_trans.A)
    assert_array_equal(Y_trans, Y_sp_trans.A)

    # test error is raised on negative input
    Y_neg = Y.copy()
    Y_neg[0, 0] = -1
    assert_raises(ValueError, transform.transform, Y_neg)

    # test error on invalid sample_steps
    transform = AdditiveChi2Sampler(sample_steps=4)
    assert_raises(ValueError, transform.fit, X)


def test_skewed_chi2_sampler():
    """test that RBFSampler approximates kernel on random data"""

    # compute exact kernel
    c = 0.03
    # appreviations for easier formular
    X_c = (X + c)[:, np.newaxis, :]
    Y_c = (Y + c)[np.newaxis, :, :]

    # we do it in log-space in the hope that it's more stable
    # this array is n_samples_x x n_samples_y big x n_features
    log_kernel = ((np.log(X_c) / 2.) + (np.log(Y_c) / 2.) + np.log(2.) -
                  np.log(X_c + Y_c))
    # reduce to n_samples_x x n_samples_y by summing over features in log-space
    kernel = np.exp(log_kernel.sum(axis=2))

    # appoximate kernel mapping
    transform = SkewedChi2Sampler(skewedness=c, n_components=1000,
                                  random_state=42)
    X_trans = transform.fit_transform(X)
    Y_trans = transform.transform(Y)

    kernel_approx = np.dot(X_trans, Y_trans.T)
    assert_array_almost_equal(kernel, kernel_approx, 1)

    # test error is raised on negative input
    Y_neg = Y.copy()
    Y_neg[0, 0] = -1
    assert_raises(ValueError, transform.transform, Y_neg)


def test_rbf_sampler():
    """test that RBFSampler approximates kernel on random data"""
    # compute exact kernel
    gamma = 10.
    kernel = rbf_kernel(X, Y, gamma=gamma)

    # appoximate kernel mapping
    rbf_transform = RBFSampler(gamma=gamma, n_components=1000, random_state=42)
    X_trans = rbf_transform.fit_transform(X)
    Y_trans = rbf_transform.transform(Y)
    kernel_approx = np.dot(X_trans, Y_trans.T)

    assert_array_almost_equal(kernel, kernel_approx, 1)


def test_input_validation():
    """Regression test: kernel approx. transformers should work on lists

    No assertions; the old versions would simply crash
    """
    X = [[1, 2], [3, 4], [5, 6]]
    AdditiveChi2Sampler().fit(X).transform(X)
    SkewedChi2Sampler().fit(X).transform(X)
    RBFSampler().fit(X).transform(X)

    X = csr_matrix(X)
    RBFSampler().fit(X).transform(X)


def test_nystrom_approximation():
    # some basic tests
    rnd = np.random.RandomState(0)
    X = rnd.uniform(size=(10, 4))

    # With n_components = n_samples this is exact
    X_transformed = Nystroem(n_components=X.shape[0]).fit_transform(X)
    K = rbf_kernel(X)
    assert_array_almost_equal(np.dot(X_transformed, X_transformed.T), K)

    trans = Nystroem(n_components=2, random_state=rnd)
    X_transformed = trans.fit(X).transform(X)
    assert_equal(X_transformed.shape, (X.shape[0], 2))

    # test callable kernel
    linear_kernel = lambda X, Y: np.dot(X, Y.T)
    trans = Nystroem(n_components=2, kernel=linear_kernel, random_state=rnd)
    X_transformed = trans.fit(X).transform(X)
    assert_equal(X_transformed.shape, (X.shape[0], 2))


if __name__ == "__main__":
    test_additive_chi2_sampler()
    test_input_validation()
    test_skewed_chi2_sampler()
    test_rbf_sampler()