355 lines
14 KiB
Python
355 lines
14 KiB
Python
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from __future__ import division
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import numpy as np
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import scipy.sparse as sp
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from sklearn.metrics import euclidean_distances
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from sklearn.random_projection import johnson_lindenstrauss_min_dim
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from sklearn.random_projection import gaussian_random_matrix
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from sklearn.random_projection import sparse_random_matrix
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from sklearn.random_projection import SparseRandomProjection
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from sklearn.random_projection import GaussianRandomProjection
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from sklearn.utils.testing import assert_less
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from sklearn.utils.testing import assert_raises
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from sklearn.utils.testing import assert_raise_message
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from sklearn.utils.testing import assert_array_equal
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from sklearn.utils.testing import assert_equal
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from sklearn.utils.testing import assert_almost_equal
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from sklearn.utils.testing import assert_in
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.utils.testing import assert_warns
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from sklearn.exceptions import DataDimensionalityWarning
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all_sparse_random_matrix = [sparse_random_matrix]
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all_dense_random_matrix = [gaussian_random_matrix]
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all_random_matrix = set(all_sparse_random_matrix + all_dense_random_matrix)
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all_SparseRandomProjection = [SparseRandomProjection]
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all_DenseRandomProjection = [GaussianRandomProjection]
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all_RandomProjection = set(all_SparseRandomProjection +
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all_DenseRandomProjection)
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# Make some random data with uniformly located non zero entries with
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# Gaussian distributed values
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def make_sparse_random_data(n_samples, n_features, n_nonzeros):
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rng = np.random.RandomState(0)
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data_coo = sp.coo_matrix(
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(rng.randn(n_nonzeros),
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(rng.randint(n_samples, size=n_nonzeros),
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rng.randint(n_features, size=n_nonzeros))),
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shape=(n_samples, n_features))
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return data_coo.toarray(), data_coo.tocsr()
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def densify(matrix):
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if not sp.issparse(matrix):
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return matrix
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else:
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return matrix.toarray()
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n_samples, n_features = (10, 1000)
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n_nonzeros = int(n_samples * n_features / 100.)
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data, data_csr = make_sparse_random_data(n_samples, n_features, n_nonzeros)
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###############################################################################
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# test on JL lemma
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###############################################################################
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def test_invalid_jl_domain():
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assert_raises(ValueError, johnson_lindenstrauss_min_dim, 100, 1.1)
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assert_raises(ValueError, johnson_lindenstrauss_min_dim, 100, 0.0)
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assert_raises(ValueError, johnson_lindenstrauss_min_dim, 100, -0.1)
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assert_raises(ValueError, johnson_lindenstrauss_min_dim, 0, 0.5)
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def test_input_size_jl_min_dim():
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assert_raises(ValueError, johnson_lindenstrauss_min_dim,
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3 * [100], 2 * [0.9])
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assert_raises(ValueError, johnson_lindenstrauss_min_dim, 3 * [100],
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2 * [0.9])
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johnson_lindenstrauss_min_dim(np.random.randint(1, 10, size=(10, 10)),
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0.5 * np.ones((10, 10)))
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###############################################################################
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# tests random matrix generation
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###############################################################################
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def check_input_size_random_matrix(random_matrix):
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assert_raises(ValueError, random_matrix, 0, 0)
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assert_raises(ValueError, random_matrix, -1, 1)
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assert_raises(ValueError, random_matrix, 1, -1)
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assert_raises(ValueError, random_matrix, 1, 0)
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assert_raises(ValueError, random_matrix, -1, 0)
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def check_size_generated(random_matrix):
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assert_equal(random_matrix(1, 5).shape, (1, 5))
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assert_equal(random_matrix(5, 1).shape, (5, 1))
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assert_equal(random_matrix(5, 5).shape, (5, 5))
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assert_equal(random_matrix(1, 1).shape, (1, 1))
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def check_zero_mean_and_unit_norm(random_matrix):
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# All random matrix should produce a transformation matrix
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# with zero mean and unit norm for each columns
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A = densify(random_matrix(10000, 1, random_state=0))
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assert_array_almost_equal(0, np.mean(A), 3)
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assert_array_almost_equal(1.0, np.linalg.norm(A), 1)
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def check_input_with_sparse_random_matrix(random_matrix):
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n_components, n_features = 5, 10
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for density in [-1., 0.0, 1.1]:
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assert_raises(ValueError,
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random_matrix, n_components, n_features, density=density)
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def test_basic_property_of_random_matrix():
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# Check basic properties of random matrix generation
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for random_matrix in all_random_matrix:
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yield check_input_size_random_matrix, random_matrix
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yield check_size_generated, random_matrix
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yield check_zero_mean_and_unit_norm, random_matrix
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for random_matrix in all_sparse_random_matrix:
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yield check_input_with_sparse_random_matrix, random_matrix
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random_matrix_dense = \
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lambda n_components, n_features, random_state: random_matrix(
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n_components, n_features, random_state=random_state,
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density=1.0)
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yield check_zero_mean_and_unit_norm, random_matrix_dense
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def test_gaussian_random_matrix():
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# Check some statical properties of Gaussian random matrix
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# Check that the random matrix follow the proper distribution.
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# Let's say that each element of a_{ij} of A is taken from
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# a_ij ~ N(0.0, 1 / n_components).
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#
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n_components = 100
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n_features = 1000
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A = gaussian_random_matrix(n_components, n_features, random_state=0)
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assert_array_almost_equal(0.0, np.mean(A), 2)
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assert_array_almost_equal(np.var(A, ddof=1), 1 / n_components, 1)
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def test_sparse_random_matrix():
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# Check some statical properties of sparse random matrix
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n_components = 100
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n_features = 500
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for density in [0.3, 1.]:
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s = 1 / density
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A = sparse_random_matrix(n_components,
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n_features,
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density=density,
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random_state=0)
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A = densify(A)
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# Check possible values
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values = np.unique(A)
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assert_in(np.sqrt(s) / np.sqrt(n_components), values)
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assert_in(- np.sqrt(s) / np.sqrt(n_components), values)
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if density == 1.0:
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assert_equal(np.size(values), 2)
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else:
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assert_in(0., values)
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assert_equal(np.size(values), 3)
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# Check that the random matrix follow the proper distribution.
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# Let's say that each element of a_{ij} of A is taken from
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#
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# - -sqrt(s) / sqrt(n_components) with probability 1 / 2s
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# - 0 with probability 1 - 1 / s
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# - +sqrt(s) / sqrt(n_components) with probability 1 / 2s
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#
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assert_almost_equal(np.mean(A == 0.0),
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1 - 1 / s, decimal=2)
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assert_almost_equal(np.mean(A == np.sqrt(s) / np.sqrt(n_components)),
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1 / (2 * s), decimal=2)
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assert_almost_equal(np.mean(A == - np.sqrt(s) / np.sqrt(n_components)),
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1 / (2 * s), decimal=2)
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assert_almost_equal(np.var(A == 0.0, ddof=1),
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(1 - 1 / s) * 1 / s, decimal=2)
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assert_almost_equal(np.var(A == np.sqrt(s) / np.sqrt(n_components),
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ddof=1),
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(1 - 1 / (2 * s)) * 1 / (2 * s), decimal=2)
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assert_almost_equal(np.var(A == - np.sqrt(s) / np.sqrt(n_components),
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ddof=1),
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(1 - 1 / (2 * s)) * 1 / (2 * s), decimal=2)
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###############################################################################
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# tests on random projection transformer
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###############################################################################
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def test_sparse_random_projection_transformer_invalid_density():
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for RandomProjection in all_SparseRandomProjection:
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assert_raises(ValueError,
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RandomProjection(density=1.1).fit, data)
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assert_raises(ValueError,
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RandomProjection(density=0).fit, data)
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assert_raises(ValueError,
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RandomProjection(density=-0.1).fit, data)
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def test_random_projection_transformer_invalid_input():
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for RandomProjection in all_RandomProjection:
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assert_raises(ValueError,
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RandomProjection(n_components='auto').fit, [[0, 1, 2]])
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assert_raises(ValueError,
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RandomProjection(n_components=-10).fit, data)
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def test_try_to_transform_before_fit():
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for RandomProjection in all_RandomProjection:
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assert_raises(ValueError,
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RandomProjection(n_components='auto').transform, data)
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def test_too_many_samples_to_find_a_safe_embedding():
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data, _ = make_sparse_random_data(1000, 100, 1000)
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for RandomProjection in all_RandomProjection:
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rp = RandomProjection(n_components='auto', eps=0.1)
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expected_msg = (
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'eps=0.100000 and n_samples=1000 lead to a target dimension'
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' of 5920 which is larger than the original space with'
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' n_features=100')
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assert_raise_message(ValueError, expected_msg, rp.fit, data)
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def test_random_projection_embedding_quality():
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data, _ = make_sparse_random_data(8, 5000, 15000)
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eps = 0.2
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original_distances = euclidean_distances(data, squared=True)
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original_distances = original_distances.ravel()
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non_identical = original_distances != 0.0
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# remove 0 distances to avoid division by 0
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original_distances = original_distances[non_identical]
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for RandomProjection in all_RandomProjection:
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rp = RandomProjection(n_components='auto', eps=eps, random_state=0)
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projected = rp.fit_transform(data)
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projected_distances = euclidean_distances(projected, squared=True)
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projected_distances = projected_distances.ravel()
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# remove 0 distances to avoid division by 0
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projected_distances = projected_distances[non_identical]
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distances_ratio = projected_distances / original_distances
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# check that the automatically tuned values for the density respect the
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# contract for eps: pairwise distances are preserved according to the
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# Johnson-Lindenstrauss lemma
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assert_less(distances_ratio.max(), 1 + eps)
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assert_less(1 - eps, distances_ratio.min())
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def test_SparseRandomProjection_output_representation():
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for SparseRandomProjection in all_SparseRandomProjection:
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# when using sparse input, the projected data can be forced to be a
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# dense numpy array
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rp = SparseRandomProjection(n_components=10, dense_output=True,
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random_state=0)
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rp.fit(data)
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assert isinstance(rp.transform(data), np.ndarray)
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sparse_data = sp.csr_matrix(data)
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assert isinstance(rp.transform(sparse_data), np.ndarray)
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# the output can be left to a sparse matrix instead
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rp = SparseRandomProjection(n_components=10, dense_output=False,
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random_state=0)
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rp = rp.fit(data)
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# output for dense input will stay dense:
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assert isinstance(rp.transform(data), np.ndarray)
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# output for sparse output will be sparse:
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assert sp.issparse(rp.transform(sparse_data))
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def test_correct_RandomProjection_dimensions_embedding():
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for RandomProjection in all_RandomProjection:
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rp = RandomProjection(n_components='auto',
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random_state=0,
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eps=0.5).fit(data)
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# the number of components is adjusted from the shape of the training
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# set
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assert_equal(rp.n_components, 'auto')
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assert_equal(rp.n_components_, 110)
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if RandomProjection in all_SparseRandomProjection:
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assert_equal(rp.density, 'auto')
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assert_almost_equal(rp.density_, 0.03, 2)
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assert_equal(rp.components_.shape, (110, n_features))
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projected_1 = rp.transform(data)
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assert_equal(projected_1.shape, (n_samples, 110))
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# once the RP is 'fitted' the projection is always the same
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projected_2 = rp.transform(data)
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assert_array_equal(projected_1, projected_2)
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# fit transform with same random seed will lead to the same results
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rp2 = RandomProjection(random_state=0, eps=0.5)
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projected_3 = rp2.fit_transform(data)
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assert_array_equal(projected_1, projected_3)
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# Try to transform with an input X of size different from fitted.
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assert_raises(ValueError, rp.transform, data[:, 1:5])
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# it is also possible to fix the number of components and the density
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# level
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if RandomProjection in all_SparseRandomProjection:
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rp = RandomProjection(n_components=100, density=0.001,
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random_state=0)
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projected = rp.fit_transform(data)
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assert_equal(projected.shape, (n_samples, 100))
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assert_equal(rp.components_.shape, (100, n_features))
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assert_less(rp.components_.nnz, 115) # close to 1% density
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assert_less(85, rp.components_.nnz) # close to 1% density
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def test_warning_n_components_greater_than_n_features():
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n_features = 20
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data, _ = make_sparse_random_data(5, n_features, int(n_features / 4))
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for RandomProjection in all_RandomProjection:
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assert_warns(DataDimensionalityWarning,
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RandomProjection(n_components=n_features + 1).fit, data)
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def test_works_with_sparse_data():
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n_features = 20
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data, _ = make_sparse_random_data(5, n_features, int(n_features / 4))
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for RandomProjection in all_RandomProjection:
|
||
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|
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_))
|