481 lines
18 KiB
Python
481 lines
18 KiB
Python
import numpy as np
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import scipy.sparse as sp
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import numbers
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from scipy import linalg
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from sklearn.decomposition import NMF, non_negative_factorization
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from sklearn.decomposition import nmf # For testing internals
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from scipy.sparse import csc_matrix
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from sklearn.utils.testing import assert_true
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from sklearn.utils.testing import assert_false
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from sklearn.utils.testing import assert_raise_message, assert_no_warnings
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from sklearn.utils.testing import assert_array_equal
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.utils.testing import assert_almost_equal
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from sklearn.utils.testing import assert_less
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from sklearn.utils.testing import assert_greater
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from sklearn.utils.testing import ignore_warnings
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from sklearn.utils.extmath import squared_norm
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from sklearn.base import clone
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from sklearn.exceptions import ConvergenceWarning
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def test_initialize_nn_output():
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# Test that initialization does not return negative values
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rng = np.random.mtrand.RandomState(42)
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data = np.abs(rng.randn(10, 10))
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for init in ('random', 'nndsvd', 'nndsvda', 'nndsvdar'):
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W, H = nmf._initialize_nmf(data, 10, init=init, random_state=0)
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assert_false((W < 0).any() or (H < 0).any())
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def test_parameter_checking():
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A = np.ones((2, 2))
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name = 'spam'
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msg = "Invalid solver parameter: got 'spam' instead of one of"
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assert_raise_message(ValueError, msg, NMF(solver=name).fit, A)
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msg = "Invalid init parameter: got 'spam' instead of one of"
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assert_raise_message(ValueError, msg, NMF(init=name).fit, A)
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msg = "Invalid beta_loss parameter: got 'spam' instead of one"
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assert_raise_message(ValueError, msg, NMF(solver='mu',
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beta_loss=name).fit, A)
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msg = "Invalid beta_loss parameter: solver 'cd' does not handle "
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msg += "beta_loss = 1.0"
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assert_raise_message(ValueError, msg, NMF(solver='cd',
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beta_loss=1.0).fit, A)
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msg = "Negative values in data passed to"
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assert_raise_message(ValueError, msg, NMF().fit, -A)
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assert_raise_message(ValueError, msg, nmf._initialize_nmf, -A,
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2, 'nndsvd')
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clf = NMF(2, tol=0.1).fit(A)
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assert_raise_message(ValueError, msg, clf.transform, -A)
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def test_initialize_close():
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# Test NNDSVD error
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# Test that _initialize_nmf error is less than the standard deviation of
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# the entries in the matrix.
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rng = np.random.mtrand.RandomState(42)
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A = np.abs(rng.randn(10, 10))
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W, H = nmf._initialize_nmf(A, 10, init='nndsvd')
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error = linalg.norm(np.dot(W, H) - A)
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sdev = linalg.norm(A - A.mean())
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assert_true(error <= sdev)
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def test_initialize_variants():
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# Test NNDSVD variants correctness
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# Test that the variants 'nndsvda' and 'nndsvdar' differ from basic
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# 'nndsvd' only where the basic version has zeros.
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rng = np.random.mtrand.RandomState(42)
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data = np.abs(rng.randn(10, 10))
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W0, H0 = nmf._initialize_nmf(data, 10, init='nndsvd')
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Wa, Ha = nmf._initialize_nmf(data, 10, init='nndsvda')
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War, Har = nmf._initialize_nmf(data, 10, init='nndsvdar',
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random_state=0)
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for ref, evl in ((W0, Wa), (W0, War), (H0, Ha), (H0, Har)):
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assert_almost_equal(evl[ref != 0], ref[ref != 0])
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# ignore UserWarning raised when both solver='mu' and init='nndsvd'
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@ignore_warnings(category=UserWarning)
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def test_nmf_fit_nn_output():
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# Test that the decomposition does not contain negative values
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A = np.c_[5 * np.ones(5) - np.arange(1, 6),
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5 * np.ones(5) + np.arange(1, 6)]
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for solver in ('cd', 'mu'):
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for init in (None, 'nndsvd', 'nndsvda', 'nndsvdar', 'random'):
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model = NMF(n_components=2, solver=solver, init=init,
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random_state=0)
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transf = model.fit_transform(A)
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assert_false((model.components_ < 0).any() or
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(transf < 0).any())
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def test_nmf_fit_close():
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rng = np.random.mtrand.RandomState(42)
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# Test that the fit is not too far away
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for solver in ('cd', 'mu'):
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pnmf = NMF(5, solver=solver, init='nndsvdar', random_state=0,
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max_iter=600)
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X = np.abs(rng.randn(6, 5))
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assert_less(pnmf.fit(X).reconstruction_err_, 0.1)
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def test_nmf_transform():
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# Test that NMF.transform returns close values
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rng = np.random.mtrand.RandomState(42)
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A = np.abs(rng.randn(6, 5))
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for solver in ['cd', 'mu']:
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m = NMF(solver=solver, n_components=3, init='random',
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random_state=0, tol=1e-5)
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ft = m.fit_transform(A)
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t = m.transform(A)
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assert_array_almost_equal(ft, t, decimal=2)
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def test_nmf_transform_custom_init():
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# Smoke test that checks if NMF.transform works with custom initialization
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random_state = np.random.RandomState(0)
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A = np.abs(random_state.randn(6, 5))
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n_components = 4
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avg = np.sqrt(A.mean() / n_components)
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H_init = np.abs(avg * random_state.randn(n_components, 5))
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W_init = np.abs(avg * random_state.randn(6, n_components))
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m = NMF(solver='cd', n_components=n_components, init='custom',
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random_state=0)
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m.fit_transform(A, W=W_init, H=H_init)
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m.transform(A)
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def test_nmf_inverse_transform():
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# Test that NMF.inverse_transform returns close values
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random_state = np.random.RandomState(0)
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A = np.abs(random_state.randn(6, 4))
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for solver in ('cd', 'mu'):
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m = NMF(solver=solver, n_components=4, init='random', random_state=0,
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max_iter=1000)
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ft = m.fit_transform(A)
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A_new = m.inverse_transform(ft)
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assert_array_almost_equal(A, A_new, decimal=2)
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def test_n_components_greater_n_features():
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# Smoke test for the case of more components than features.
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rng = np.random.mtrand.RandomState(42)
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A = np.abs(rng.randn(30, 10))
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NMF(n_components=15, random_state=0, tol=1e-2).fit(A)
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def test_nmf_sparse_input():
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# Test that sparse matrices are accepted as input
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from scipy.sparse import csc_matrix
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rng = np.random.mtrand.RandomState(42)
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A = np.abs(rng.randn(10, 10))
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A[:, 2 * np.arange(5)] = 0
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A_sparse = csc_matrix(A)
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for solver in ('cd', 'mu'):
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est1 = NMF(solver=solver, n_components=5, init='random',
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random_state=0, tol=1e-2)
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est2 = clone(est1)
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W1 = est1.fit_transform(A)
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W2 = est2.fit_transform(A_sparse)
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H1 = est1.components_
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H2 = est2.components_
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assert_array_almost_equal(W1, W2)
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assert_array_almost_equal(H1, H2)
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def test_nmf_sparse_transform():
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# Test that transform works on sparse data. Issue #2124
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rng = np.random.mtrand.RandomState(42)
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A = np.abs(rng.randn(3, 2))
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A[1, 1] = 0
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A = csc_matrix(A)
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for solver in ('cd', 'mu'):
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model = NMF(solver=solver, random_state=0, n_components=2,
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max_iter=400)
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A_fit_tr = model.fit_transform(A)
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A_tr = model.transform(A)
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assert_array_almost_equal(A_fit_tr, A_tr, decimal=1)
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def test_non_negative_factorization_consistency():
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# Test that the function is called in the same way, either directly
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# or through the NMF class
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rng = np.random.mtrand.RandomState(42)
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A = np.abs(rng.randn(10, 10))
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A[:, 2 * np.arange(5)] = 0
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for solver in ('cd', 'mu'):
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W_nmf, H, _ = non_negative_factorization(
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A, solver=solver, random_state=1, tol=1e-2)
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W_nmf_2, _, _ = non_negative_factorization(
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A, H=H, update_H=False, solver=solver, random_state=1, tol=1e-2)
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model_class = NMF(solver=solver, random_state=1, tol=1e-2)
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W_cls = model_class.fit_transform(A)
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W_cls_2 = model_class.transform(A)
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assert_array_almost_equal(W_nmf, W_cls, decimal=10)
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assert_array_almost_equal(W_nmf_2, W_cls_2, decimal=10)
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def test_non_negative_factorization_checking():
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A = np.ones((2, 2))
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# Test parameters checking is public function
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nnmf = non_negative_factorization
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assert_no_warnings(nnmf, A, A, A, np.int64(1))
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msg = ("Number of components must be a positive integer; "
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"got (n_components=1.5)")
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assert_raise_message(ValueError, msg, nnmf, A, A, A, 1.5)
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msg = ("Number of components must be a positive integer; "
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"got (n_components='2')")
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assert_raise_message(ValueError, msg, nnmf, A, A, A, '2')
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msg = "Negative values in data passed to NMF (input H)"
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assert_raise_message(ValueError, msg, nnmf, A, A, -A, 2, 'custom')
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msg = "Negative values in data passed to NMF (input W)"
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assert_raise_message(ValueError, msg, nnmf, A, -A, A, 2, 'custom')
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msg = "Array passed to NMF (input H) is full of zeros"
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assert_raise_message(ValueError, msg, nnmf, A, A, 0 * A, 2, 'custom')
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msg = "Invalid regularization parameter: got 'spam' instead of one of"
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assert_raise_message(ValueError, msg, nnmf, A, A, 0 * A, 2, 'custom', True,
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'cd', 2., 1e-4, 200, 0., 0., 'spam')
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def _beta_divergence_dense(X, W, H, beta):
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"""Compute the beta-divergence of X and W.H for dense array only.
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Used as a reference for testing nmf._beta_divergence.
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"""
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if isinstance(X, numbers.Number):
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W = np.array([[W]])
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H = np.array([[H]])
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X = np.array([[X]])
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WH = np.dot(W, H)
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if beta == 2:
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return squared_norm(X - WH) / 2
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WH_Xnonzero = WH[X != 0]
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X_nonzero = X[X != 0]
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np.maximum(WH_Xnonzero, 1e-9, out=WH_Xnonzero)
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if beta == 1:
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res = np.sum(X_nonzero * np.log(X_nonzero / WH_Xnonzero))
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res += WH.sum() - X.sum()
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elif beta == 0:
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div = X_nonzero / WH_Xnonzero
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res = np.sum(div) - X.size - np.sum(np.log(div))
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else:
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res = (X_nonzero ** beta).sum()
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res += (beta - 1) * (WH ** beta).sum()
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res -= beta * (X_nonzero * (WH_Xnonzero ** (beta - 1))).sum()
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res /= beta * (beta - 1)
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return res
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def test_beta_divergence():
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# Compare _beta_divergence with the reference _beta_divergence_dense
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n_samples = 20
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n_features = 10
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n_components = 5
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beta_losses = [0., 0.5, 1., 1.5, 2.]
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# initialization
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rng = np.random.mtrand.RandomState(42)
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X = rng.randn(n_samples, n_features)
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X[X < 0] = 0.
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X_csr = sp.csr_matrix(X)
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W, H = nmf._initialize_nmf(X, n_components, init='random', random_state=42)
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for beta in beta_losses:
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ref = _beta_divergence_dense(X, W, H, beta)
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loss = nmf._beta_divergence(X, W, H, beta)
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loss_csr = nmf._beta_divergence(X_csr, W, H, beta)
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assert_almost_equal(ref, loss, decimal=7)
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assert_almost_equal(ref, loss_csr, decimal=7)
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def test_special_sparse_dot():
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# Test the function that computes np.dot(W, H), only where X is non zero.
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n_samples = 10
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n_features = 5
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n_components = 3
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rng = np.random.mtrand.RandomState(42)
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X = rng.randn(n_samples, n_features)
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X[X < 0] = 0.
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X_csr = sp.csr_matrix(X)
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W = np.abs(rng.randn(n_samples, n_components))
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H = np.abs(rng.randn(n_components, n_features))
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WH_safe = nmf._special_sparse_dot(W, H, X_csr)
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WH = nmf._special_sparse_dot(W, H, X)
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# test that both results have same values, in X_csr nonzero elements
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ii, jj = X_csr.nonzero()
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WH_safe_data = np.asarray(WH_safe[ii, jj]).ravel()
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assert_array_almost_equal(WH_safe_data, WH[ii, jj], decimal=10)
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# test that WH_safe and X_csr have the same sparse structure
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assert_array_equal(WH_safe.indices, X_csr.indices)
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assert_array_equal(WH_safe.indptr, X_csr.indptr)
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assert_array_equal(WH_safe.shape, X_csr.shape)
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@ignore_warnings(category=ConvergenceWarning)
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def test_nmf_multiplicative_update_sparse():
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# Compare sparse and dense input in multiplicative update NMF
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# Also test continuity of the results with respect to beta_loss parameter
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n_samples = 20
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n_features = 10
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n_components = 5
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alpha = 0.1
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l1_ratio = 0.5
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n_iter = 20
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# initialization
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rng = np.random.mtrand.RandomState(1337)
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X = rng.randn(n_samples, n_features)
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X = np.abs(X)
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X_csr = sp.csr_matrix(X)
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W0, H0 = nmf._initialize_nmf(X, n_components, init='random',
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random_state=42)
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for beta_loss in (-1.2, 0, 0.2, 1., 2., 2.5):
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# Reference with dense array X
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W, H = W0.copy(), H0.copy()
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W1, H1, _ = non_negative_factorization(
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X, W, H, n_components, init='custom', update_H=True,
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solver='mu', beta_loss=beta_loss, max_iter=n_iter, alpha=alpha,
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l1_ratio=l1_ratio, regularization='both', random_state=42)
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# Compare with sparse X
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W, H = W0.copy(), H0.copy()
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W2, H2, _ = non_negative_factorization(
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X_csr, W, H, n_components, init='custom', update_H=True,
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solver='mu', beta_loss=beta_loss, max_iter=n_iter, alpha=alpha,
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l1_ratio=l1_ratio, regularization='both', random_state=42)
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assert_array_almost_equal(W1, W2, decimal=7)
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assert_array_almost_equal(H1, H2, decimal=7)
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# Compare with almost same beta_loss, since some values have a specific
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# behavior, but the results should be continuous w.r.t beta_loss
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beta_loss -= 1.e-5
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W, H = W0.copy(), H0.copy()
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W3, H3, _ = non_negative_factorization(
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X_csr, W, H, n_components, init='custom', update_H=True,
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solver='mu', beta_loss=beta_loss, max_iter=n_iter, alpha=alpha,
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l1_ratio=l1_ratio, regularization='both', random_state=42)
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assert_array_almost_equal(W1, W3, decimal=4)
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assert_array_almost_equal(H1, H3, decimal=4)
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def test_nmf_negative_beta_loss():
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# Test that an error is raised if beta_loss < 0 and X contains zeros.
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# Test that the output has not NaN values when the input contains zeros.
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n_samples = 6
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n_features = 5
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n_components = 3
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rng = np.random.mtrand.RandomState(42)
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X = rng.randn(n_samples, n_features)
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X[X < 0] = 0
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X_csr = sp.csr_matrix(X)
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def _assert_nmf_no_nan(X, beta_loss):
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W, H, _ = non_negative_factorization(
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X, n_components=n_components, solver='mu', beta_loss=beta_loss,
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random_state=0, max_iter=1000)
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assert_false(np.any(np.isnan(W)))
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assert_false(np.any(np.isnan(H)))
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msg = "When beta_loss <= 0 and X contains zeros, the solver may diverge."
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for beta_loss in (-0.6, 0.):
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assert_raise_message(ValueError, msg, _assert_nmf_no_nan, X, beta_loss)
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_assert_nmf_no_nan(X + 1e-9, beta_loss)
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for beta_loss in (0.2, 1., 1.2, 2., 2.5):
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_assert_nmf_no_nan(X, beta_loss)
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_assert_nmf_no_nan(X_csr, beta_loss)
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def test_nmf_regularization():
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# Test the effect of L1 and L2 regularizations
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n_samples = 6
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n_features = 5
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n_components = 3
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rng = np.random.mtrand.RandomState(42)
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X = np.abs(rng.randn(n_samples, n_features))
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# L1 regularization should increase the number of zeros
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l1_ratio = 1.
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for solver in ['cd', 'mu']:
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regul = nmf.NMF(n_components=n_components, solver=solver,
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alpha=0.5, l1_ratio=l1_ratio, random_state=42)
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model = nmf.NMF(n_components=n_components, solver=solver,
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alpha=0., l1_ratio=l1_ratio, random_state=42)
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W_regul = regul.fit_transform(X)
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W_model = model.fit_transform(X)
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H_regul = regul.components_
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H_model = model.components_
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W_regul_n_zeros = W_regul[W_regul == 0].size
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W_model_n_zeros = W_model[W_model == 0].size
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H_regul_n_zeros = H_regul[H_regul == 0].size
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H_model_n_zeros = H_model[H_model == 0].size
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|
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assert_greater(W_regul_n_zeros, W_model_n_zeros)
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assert_greater(H_regul_n_zeros, H_model_n_zeros)
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|
|
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# L2 regularization should decrease the mean of the coefficients
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l1_ratio = 0.
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for solver in ['cd', 'mu']:
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regul = nmf.NMF(n_components=n_components, solver=solver,
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alpha=0.5, l1_ratio=l1_ratio, random_state=42)
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model = nmf.NMF(n_components=n_components, solver=solver,
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alpha=0., l1_ratio=l1_ratio, random_state=42)
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|
|
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W_regul = regul.fit_transform(X)
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|
W_model = model.fit_transform(X)
|
|
|
|
H_regul = regul.components_
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|
H_model = model.components_
|
|
|
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assert_greater(W_model.mean(), W_regul.mean())
|
|
assert_greater(H_model.mean(), H_regul.mean())
|
|
|
|
|
|
@ignore_warnings(category=ConvergenceWarning)
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|
def test_nmf_decreasing():
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# test that the objective function is decreasing at each iteration
|
|
n_samples = 20
|
|
n_features = 15
|
|
n_components = 10
|
|
alpha = 0.1
|
|
l1_ratio = 0.5
|
|
tol = 0.
|
|
|
|
# initialization
|
|
rng = np.random.mtrand.RandomState(42)
|
|
X = rng.randn(n_samples, n_features)
|
|
np.abs(X, X)
|
|
W0, H0 = nmf._initialize_nmf(X, n_components, init='random',
|
|
random_state=42)
|
|
|
|
for beta_loss in (-1.2, 0, 0.2, 1., 2., 2.5):
|
|
for solver in ('cd', 'mu'):
|
|
if solver != 'mu' and beta_loss != 2:
|
|
# not implemented
|
|
continue
|
|
W, H = W0.copy(), H0.copy()
|
|
previous_loss = None
|
|
for _ in range(30):
|
|
# one more iteration starting from the previous results
|
|
W, H, _ = non_negative_factorization(
|
|
X, W, H, beta_loss=beta_loss, init='custom',
|
|
n_components=n_components, max_iter=1, alpha=alpha,
|
|
solver=solver, tol=tol, l1_ratio=l1_ratio, verbose=0,
|
|
regularization='both', random_state=0, update_H=True)
|
|
|
|
loss = nmf._beta_divergence(X, W, H, beta_loss)
|
|
if previous_loss is not None:
|
|
assert_greater(previous_loss, loss)
|
|
previous_loss = loss
|