test_random_projection.py

from __future__ import division

import numpy as np
import scipy.sparse as sp

from sklearn.metrics import euclidean_distances

from sklearn.random_projection import johnson_lindenstrauss_min_dim
from sklearn.random_projection import gaussian_random_matrix
from sklearn.random_projection import sparse_random_matrix
from sklearn.random_projection import SparseRandomProjection
from sklearn.random_projection import GaussianRandomProjection

from sklearn.utils.testing import assert_less
from sklearn.utils.testing import assert_raises
from sklearn.utils.testing import assert_raise_message
from sklearn.utils.testing import assert_array_equal
from sklearn.utils.testing import assert_equal
from sklearn.utils.testing import assert_almost_equal
from sklearn.utils.testing import assert_in
from sklearn.utils.testing import assert_array_almost_equal
from sklearn.utils.testing import assert_warns
from sklearn.exceptions import DataDimensionalityWarning

all_sparse_random_matrix = [sparse_random_matrix]
all_dense_random_matrix = [gaussian_random_matrix]
all_random_matrix = set(all_sparse_random_matrix + all_dense_random_matrix)

all_SparseRandomProjection = [SparseRandomProjection]
all_DenseRandomProjection = [GaussianRandomProjection]
all_RandomProjection = set(all_SparseRandomProjection +
                           all_DenseRandomProjection)


# Make some random data with uniformly located non zero entries with
# Gaussian distributed values
def make_sparse_random_data(n_samples, n_features, n_nonzeros):
    rng = np.random.RandomState(0)
    data_coo = sp.coo_matrix(
        (rng.randn(n_nonzeros),
         (rng.randint(n_samples, size=n_nonzeros),
          rng.randint(n_features, size=n_nonzeros))),
        shape=(n_samples, n_features))
    return data_coo.toarray(), data_coo.tocsr()


def densify(matrix):
    if not sp.issparse(matrix):
        return matrix
    else:
        return matrix.toarray()


n_samples, n_features = (10, 1000)
n_nonzeros = int(n_samples * n_features / 100.)
data, data_csr = make_sparse_random_data(n_samples, n_features, n_nonzeros)


###############################################################################
# test on JL lemma
###############################################################################
def test_invalid_jl_domain():
    assert_raises(ValueError, johnson_lindenstrauss_min_dim, 100, 1.1)
    assert_raises(ValueError, johnson_lindenstrauss_min_dim, 100, 0.0)
    assert_raises(ValueError, johnson_lindenstrauss_min_dim, 100, -0.1)
    assert_raises(ValueError, johnson_lindenstrauss_min_dim, 0, 0.5)


def test_input_size_jl_min_dim():
    assert_raises(ValueError, johnson_lindenstrauss_min_dim,
                  3 * [100], 2 * [0.9])

    assert_raises(ValueError, johnson_lindenstrauss_min_dim, 3 * [100],
                  2 * [0.9])

    johnson_lindenstrauss_min_dim(np.random.randint(1, 10, size=(10, 10)),
                                  0.5 * np.ones((10, 10)))


###############################################################################
# tests random matrix generation
###############################################################################
def check_input_size_random_matrix(random_matrix):
    assert_raises(ValueError, random_matrix, 0, 0)
    assert_raises(ValueError, random_matrix, -1, 1)
    assert_raises(ValueError, random_matrix, 1, -1)
    assert_raises(ValueError, random_matrix, 1, 0)
    assert_raises(ValueError, random_matrix, -1, 0)


def check_size_generated(random_matrix):
    assert_equal(random_matrix(1, 5).shape, (1, 5))
    assert_equal(random_matrix(5, 1).shape, (5, 1))
    assert_equal(random_matrix(5, 5).shape, (5, 5))
    assert_equal(random_matrix(1, 1).shape, (1, 1))


def check_zero_mean_and_unit_norm(random_matrix):
    # All random matrix should produce a transformation matrix
    # with zero mean and unit norm for each columns

    A = densify(random_matrix(10000, 1, random_state=0))

    assert_array_almost_equal(0, np.mean(A), 3)
    assert_array_almost_equal(1.0, np.linalg.norm(A),  1)


def check_input_with_sparse_random_matrix(random_matrix):
    n_components, n_features = 5, 10

    for density in [-1., 0.0, 1.1]:
        assert_raises(ValueError,
                      random_matrix, n_components, n_features, density=density)


def test_basic_property_of_random_matrix():
    # Check basic properties of random matrix generation
    for random_matrix in all_random_matrix:
        yield check_input_size_random_matrix, random_matrix
        yield check_size_generated, random_matrix
        yield check_zero_mean_and_unit_norm, random_matrix

    for random_matrix in all_sparse_random_matrix:
        yield check_input_with_sparse_random_matrix, random_matrix

        random_matrix_dense = \
            lambda n_components, n_features, random_state: random_matrix(
                n_components, n_features, random_state=random_state,
                density=1.0)
        yield check_zero_mean_and_unit_norm, random_matrix_dense


def test_gaussian_random_matrix():
    # Check some statical properties of Gaussian random matrix
    # Check that the random matrix follow the proper distribution.
    # Let's say that each element of a_{ij} of A is taken from
    #   a_ij ~ N(0.0, 1 / n_components).
    #
    n_components = 100
    n_features = 1000
    A = gaussian_random_matrix(n_components, n_features, random_state=0)

    assert_array_almost_equal(0.0, np.mean(A), 2)
    assert_array_almost_equal(np.var(A, ddof=1), 1 / n_components, 1)


def test_sparse_random_matrix():
    # Check some statical properties of sparse random matrix
    n_components = 100
    n_features = 500

    for density in [0.3, 1.]:
        s = 1 / density

        A = sparse_random_matrix(n_components,
                                 n_features,
                                 density=density,
                                 random_state=0)
        A = densify(A)

        # Check possible values
        values = np.unique(A)
        assert_in(np.sqrt(s) / np.sqrt(n_components), values)
        assert_in(- np.sqrt(s) / np.sqrt(n_components), values)

        if density == 1.0:
            assert_equal(np.size(values), 2)
        else:
            assert_in(0., values)
            assert_equal(np.size(values), 3)

        # Check that the random matrix follow the proper distribution.
        # Let's say that each element of a_{ij} of A is taken from
        #
        # - -sqrt(s) / sqrt(n_components)   with probability 1 / 2s
        # -  0                              with probability 1 - 1 / s
        # - +sqrt(s) / sqrt(n_components)   with probability 1 / 2s
        #
        assert_almost_equal(np.mean(A == 0.0),
                            1 - 1 / s, decimal=2)
        assert_almost_equal(np.mean(A == np.sqrt(s) / np.sqrt(n_components)),
                            1 / (2 * s), decimal=2)
        assert_almost_equal(np.mean(A == - np.sqrt(s) / np.sqrt(n_components)),
                            1 / (2 * s), decimal=2)

        assert_almost_equal(np.var(A == 0.0, ddof=1),
                            (1 - 1 / s) * 1 / s, decimal=2)
        assert_almost_equal(np.var(A == np.sqrt(s) / np.sqrt(n_components),
                                   ddof=1),
                            (1 - 1 / (2 * s)) * 1 / (2 * s), decimal=2)
        assert_almost_equal(np.var(A == - np.sqrt(s) / np.sqrt(n_components),
                                   ddof=1),
                            (1 - 1 / (2 * s)) * 1 / (2 * s), decimal=2)


###############################################################################
# tests on random projection transformer
###############################################################################
def test_sparse_random_projection_transformer_invalid_density():
    for RandomProjection in all_SparseRandomProjection:
        assert_raises(ValueError,
                      RandomProjection(density=1.1).fit, data)

        assert_raises(ValueError,
                      RandomProjection(density=0).fit, data)

        assert_raises(ValueError,
                      RandomProjection(density=-0.1).fit, data)


def test_random_projection_transformer_invalid_input():
    for RandomProjection in all_RandomProjection:
        assert_raises(ValueError,
                      RandomProjection(n_components='auto').fit, [[0, 1, 2]])

        assert_raises(ValueError,
                      RandomProjection(n_components=-10).fit, data)


def test_try_to_transform_before_fit():
    for RandomProjection in all_RandomProjection:
        assert_raises(ValueError,
                      RandomProjection(n_components='auto').transform, data)


def test_too_many_samples_to_find_a_safe_embedding():
    data, _ = make_sparse_random_data(1000, 100, 1000)

    for RandomProjection in all_RandomProjection:
        rp = RandomProjection(n_components='auto', eps=0.1)
        expected_msg = (
            'eps=0.100000 and n_samples=1000 lead to a target dimension'
            ' of 5920 which is larger than the original space with'
            ' n_features=100')
        assert_raise_message(ValueError, expected_msg, rp.fit, data)


def test_random_projection_embedding_quality():
    data, _ = make_sparse_random_data(8, 5000, 15000)
    eps = 0.2

    original_distances = euclidean_distances(data, squared=True)
    original_distances = original_distances.ravel()
    non_identical = original_distances != 0.0

    # remove 0 distances to avoid division by 0
    original_distances = original_distances[non_identical]

    for RandomProjection in all_RandomProjection:
        rp = RandomProjection(n_components='auto', eps=eps, random_state=0)
        projected = rp.fit_transform(data)

        projected_distances = euclidean_distances(projected, squared=True)
        projected_distances = projected_distances.ravel()

        # remove 0 distances to avoid division by 0
        projected_distances = projected_distances[non_identical]

        distances_ratio = projected_distances / original_distances

        # check that the automatically tuned values for the density respect the
        # contract for eps: pairwise distances are preserved according to the
        # Johnson-Lindenstrauss lemma
        assert_less(distances_ratio.max(), 1 + eps)
        assert_less(1 - eps, distances_ratio.min())


def test_SparseRandomProjection_output_representation():
    for SparseRandomProjection in all_SparseRandomProjection:
        # when using sparse input, the projected data can be forced to be a
        # dense numpy array
        rp = SparseRandomProjection(n_components=10, dense_output=True,
                                    random_state=0)
        rp.fit(data)
        assert isinstance(rp.transform(data), np.ndarray)

        sparse_data = sp.csr_matrix(data)
        assert isinstance(rp.transform(sparse_data), np.ndarray)

        # the output can be left to a sparse matrix instead
        rp = SparseRandomProjection(n_components=10, dense_output=False,
                                    random_state=0)
        rp = rp.fit(data)
        # output for dense input will stay dense:
        assert isinstance(rp.transform(data), np.ndarray)

        # output for sparse output will be sparse:
        assert sp.issparse(rp.transform(sparse_data))


def test_correct_RandomProjection_dimensions_embedding():
    for RandomProjection in all_RandomProjection:
        rp = RandomProjection(n_components='auto',
                              random_state=0,
                              eps=0.5).fit(data)

        # the number of components is adjusted from the shape of the training
        # set
        assert_equal(rp.n_components, 'auto')
        assert_equal(rp.n_components_, 110)

        if RandomProjection in all_SparseRandomProjection:
            assert_equal(rp.density, 'auto')
            assert_almost_equal(rp.density_, 0.03, 2)

        assert_equal(rp.components_.shape, (110, n_features))

        projected_1 = rp.transform(data)
        assert_equal(projected_1.shape, (n_samples, 110))

        # once the RP is 'fitted' the projection is always the same
        projected_2 = rp.transform(data)
        assert_array_equal(projected_1, projected_2)

        # fit transform with same random seed will lead to the same results
        rp2 = RandomProjection(random_state=0, eps=0.5)
        projected_3 = rp2.fit_transform(data)
        assert_array_equal(projected_1, projected_3)

        # Try to transform with an input X of size different from fitted.
        assert_raises(ValueError, rp.transform, data[:, 1:5])

        # it is also possible to fix the number of components and the density
        # level
        if RandomProjection in all_SparseRandomProjection:
            rp = RandomProjection(n_components=100, density=0.001,
                                  random_state=0)
            projected = rp.fit_transform(data)
            assert_equal(projected.shape, (n_samples, 100))
            assert_equal(rp.components_.shape, (100, n_features))
            assert_less(rp.components_.nnz, 115)  # close to 1% density
            assert_less(85, rp.components_.nnz)  # close to 1% density


def test_warning_n_components_greater_than_n_features():
    n_features = 20
    data, _ = make_sparse_random_data(5, n_features, int(n_features / 4))

    for RandomProjection in all_RandomProjection:
        assert_warns(DataDimensionalityWarning,
                     RandomProjection(n_components=n_features + 1).fit, data)


def test_works_with_sparse_data():
    n_features = 20
    data, _ = make_sparse_random_data(5, n_features, int(n_features / 4))

    for RandomProjection in all_RandomProjection:
        rp_dense = RandomProjection(n_components=3,
                                    random_state=1).fit(data)
        rp_sparse = RandomProjection(n_components=3,
                                     random_state=1).fit(sp.csr_matrix(data))
        assert_array_almost_equal(densify(rp_dense.components_),
                                  densify(rp_sparse.components_))