453 lines
15 KiB
Python
453 lines
15 KiB
Python
"""
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Test the fastica algorithm.
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"""
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import itertools
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import os
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import warnings
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import numpy as np
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import pytest
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from scipy import stats
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from sklearn.decomposition import PCA, FastICA, fastica
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from sklearn.decomposition._fastica import _gs_decorrelation
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from sklearn.exceptions import ConvergenceWarning
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from sklearn.utils._testing import assert_allclose
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def center_and_norm(x, axis=-1):
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"""Centers and norms x **in place**
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Parameters
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-----------
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x: ndarray
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Array with an axis of observations (statistical units) measured on
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random variables.
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axis: int, optional
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Axis along which the mean and variance are calculated.
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"""
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x = np.rollaxis(x, axis)
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x -= x.mean(axis=0)
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x /= x.std(axis=0)
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def test_gs():
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# Test gram schmidt orthonormalization
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# generate a random orthogonal matrix
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rng = np.random.RandomState(0)
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W, _, _ = np.linalg.svd(rng.randn(10, 10))
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w = rng.randn(10)
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_gs_decorrelation(w, W, 10)
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assert (w**2).sum() < 1.0e-10
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w = rng.randn(10)
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u = _gs_decorrelation(w, W, 5)
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tmp = np.dot(u, W.T)
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assert (tmp[:5] ** 2).sum() < 1.0e-10
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def test_fastica_attributes_dtypes(global_dtype):
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rng = np.random.RandomState(0)
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X = rng.random_sample((100, 10)).astype(global_dtype, copy=False)
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fica = FastICA(
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n_components=5, max_iter=1000, whiten="unit-variance", random_state=0
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).fit(X)
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assert fica.components_.dtype == global_dtype
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assert fica.mixing_.dtype == global_dtype
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assert fica.mean_.dtype == global_dtype
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assert fica.whitening_.dtype == global_dtype
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def test_fastica_return_dtypes(global_dtype):
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rng = np.random.RandomState(0)
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X = rng.random_sample((100, 10)).astype(global_dtype, copy=False)
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k_, mixing_, s_ = fastica(
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X, max_iter=1000, whiten="unit-variance", random_state=rng
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)
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assert k_.dtype == global_dtype
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assert mixing_.dtype == global_dtype
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assert s_.dtype == global_dtype
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@pytest.mark.parametrize("add_noise", [True, False])
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def test_fastica_simple(add_noise, global_random_seed, global_dtype):
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if (
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global_random_seed == 20
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and global_dtype == np.float32
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and not add_noise
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and os.getenv("DISTRIB") == "ubuntu"
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):
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pytest.xfail(
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"FastICA instability with Ubuntu Atlas build with float32 "
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"global_dtype. For more details, see "
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"https://github.com/scikit-learn/scikit-learn/issues/24131#issuecomment-1208091119" # noqa
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)
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# Test the FastICA algorithm on very simple data.
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rng = np.random.RandomState(global_random_seed)
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n_samples = 1000
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# Generate two sources:
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s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
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s2 = stats.t.rvs(1, size=n_samples, random_state=global_random_seed)
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s = np.c_[s1, s2].T
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center_and_norm(s)
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s = s.astype(global_dtype)
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s1, s2 = s
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# Mixing angle
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phi = 0.6
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mixing = np.array([[np.cos(phi), np.sin(phi)], [np.sin(phi), -np.cos(phi)]])
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mixing = mixing.astype(global_dtype)
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m = np.dot(mixing, s)
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if add_noise:
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m += 0.1 * rng.randn(2, 1000)
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center_and_norm(m)
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# function as fun arg
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def g_test(x):
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return x**3, (3 * x**2).mean(axis=-1)
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algos = ["parallel", "deflation"]
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nls = ["logcosh", "exp", "cube", g_test]
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whitening = ["arbitrary-variance", "unit-variance", False]
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for algo, nl, whiten in itertools.product(algos, nls, whitening):
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if whiten:
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k_, mixing_, s_ = fastica(
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m.T, fun=nl, whiten=whiten, algorithm=algo, random_state=rng
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)
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with pytest.raises(ValueError):
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fastica(m.T, fun=np.tanh, whiten=whiten, algorithm=algo)
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else:
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pca = PCA(n_components=2, whiten=True, random_state=rng)
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X = pca.fit_transform(m.T)
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k_, mixing_, s_ = fastica(
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X, fun=nl, algorithm=algo, whiten=False, random_state=rng
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)
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with pytest.raises(ValueError):
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fastica(X, fun=np.tanh, algorithm=algo)
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s_ = s_.T
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# Check that the mixing model described in the docstring holds:
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if whiten:
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# XXX: exact reconstruction to standard relative tolerance is not
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# possible. This is probably expected when add_noise is True but we
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# also need a non-trivial atol in float32 when add_noise is False.
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#
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# Note that the 2 sources are non-Gaussian in this test.
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atol = 1e-5 if global_dtype == np.float32 else 0
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assert_allclose(np.dot(np.dot(mixing_, k_), m), s_, atol=atol)
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center_and_norm(s_)
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s1_, s2_ = s_
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# Check to see if the sources have been estimated
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# in the wrong order
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if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
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s2_, s1_ = s_
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s1_ *= np.sign(np.dot(s1_, s1))
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s2_ *= np.sign(np.dot(s2_, s2))
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# Check that we have estimated the original sources
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if not add_noise:
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assert_allclose(np.dot(s1_, s1) / n_samples, 1, atol=1e-2)
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assert_allclose(np.dot(s2_, s2) / n_samples, 1, atol=1e-2)
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else:
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assert_allclose(np.dot(s1_, s1) / n_samples, 1, atol=1e-1)
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assert_allclose(np.dot(s2_, s2) / n_samples, 1, atol=1e-1)
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# Test FastICA class
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_, _, sources_fun = fastica(
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m.T, fun=nl, algorithm=algo, random_state=global_random_seed
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)
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ica = FastICA(fun=nl, algorithm=algo, random_state=global_random_seed)
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sources = ica.fit_transform(m.T)
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assert ica.components_.shape == (2, 2)
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assert sources.shape == (1000, 2)
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assert_allclose(sources_fun, sources)
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# Set atol to account for the different magnitudes of the elements in sources
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# (from 1e-4 to 1e1).
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atol = np.max(np.abs(sources)) * (1e-5 if global_dtype == np.float32 else 1e-7)
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assert_allclose(sources, ica.transform(m.T), atol=atol)
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assert ica.mixing_.shape == (2, 2)
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ica = FastICA(fun=np.tanh, algorithm=algo)
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with pytest.raises(ValueError):
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ica.fit(m.T)
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def test_fastica_nowhiten():
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m = [[0, 1], [1, 0]]
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# test for issue #697
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ica = FastICA(n_components=1, whiten=False, random_state=0)
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warn_msg = "Ignoring n_components with whiten=False."
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with pytest.warns(UserWarning, match=warn_msg):
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ica.fit(m)
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assert hasattr(ica, "mixing_")
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def test_fastica_convergence_fail():
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# Test the FastICA algorithm on very simple data
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# (see test_non_square_fastica).
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# Ensure a ConvergenceWarning raised if the tolerance is sufficiently low.
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rng = np.random.RandomState(0)
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n_samples = 1000
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# Generate two sources:
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t = np.linspace(0, 100, n_samples)
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s1 = np.sin(t)
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s2 = np.ceil(np.sin(np.pi * t))
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s = np.c_[s1, s2].T
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center_and_norm(s)
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# Mixing matrix
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mixing = rng.randn(6, 2)
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m = np.dot(mixing, s)
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# Do fastICA with tolerance 0. to ensure failing convergence
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warn_msg = (
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"FastICA did not converge. Consider increasing tolerance "
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"or the maximum number of iterations."
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)
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with pytest.warns(ConvergenceWarning, match=warn_msg):
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ica = FastICA(
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algorithm="parallel", n_components=2, random_state=rng, max_iter=2, tol=0.0
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)
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ica.fit(m.T)
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@pytest.mark.parametrize("add_noise", [True, False])
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def test_non_square_fastica(add_noise):
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# Test the FastICA algorithm on very simple data.
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rng = np.random.RandomState(0)
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n_samples = 1000
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# Generate two sources:
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t = np.linspace(0, 100, n_samples)
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s1 = np.sin(t)
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s2 = np.ceil(np.sin(np.pi * t))
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s = np.c_[s1, s2].T
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center_and_norm(s)
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s1, s2 = s
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# Mixing matrix
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mixing = rng.randn(6, 2)
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m = np.dot(mixing, s)
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if add_noise:
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m += 0.1 * rng.randn(6, n_samples)
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center_and_norm(m)
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k_, mixing_, s_ = fastica(
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m.T, n_components=2, whiten="unit-variance", random_state=rng
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)
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s_ = s_.T
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# Check that the mixing model described in the docstring holds:
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assert_allclose(s_, np.dot(np.dot(mixing_, k_), m))
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center_and_norm(s_)
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s1_, s2_ = s_
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# Check to see if the sources have been estimated
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# in the wrong order
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if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
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s2_, s1_ = s_
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s1_ *= np.sign(np.dot(s1_, s1))
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s2_ *= np.sign(np.dot(s2_, s2))
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# Check that we have estimated the original sources
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if not add_noise:
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assert_allclose(np.dot(s1_, s1) / n_samples, 1, atol=1e-3)
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assert_allclose(np.dot(s2_, s2) / n_samples, 1, atol=1e-3)
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def test_fit_transform(global_random_seed, global_dtype):
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"""Test unit variance of transformed data using FastICA algorithm.
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Check that `fit_transform` gives the same result as applying
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`fit` and then `transform`.
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Bug #13056
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"""
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# multivariate uniform data in [0, 1]
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rng = np.random.RandomState(global_random_seed)
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X = rng.random_sample((100, 10)).astype(global_dtype)
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max_iter = 300
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for whiten, n_components in [["unit-variance", 5], [False, None]]:
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n_components_ = n_components if n_components is not None else X.shape[1]
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ica = FastICA(
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n_components=n_components, max_iter=max_iter, whiten=whiten, random_state=0
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)
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with warnings.catch_warnings():
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# make sure that numerical errors do not cause sqrt of negative
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# values
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warnings.simplefilter("error", RuntimeWarning)
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# XXX: for some seeds, the model does not converge.
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# However this is not what we test here.
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warnings.simplefilter("ignore", ConvergenceWarning)
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Xt = ica.fit_transform(X)
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assert ica.components_.shape == (n_components_, 10)
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assert Xt.shape == (X.shape[0], n_components_)
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ica2 = FastICA(
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n_components=n_components, max_iter=max_iter, whiten=whiten, random_state=0
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)
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with warnings.catch_warnings():
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# make sure that numerical errors do not cause sqrt of negative
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# values
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warnings.simplefilter("error", RuntimeWarning)
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warnings.simplefilter("ignore", ConvergenceWarning)
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ica2.fit(X)
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assert ica2.components_.shape == (n_components_, 10)
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Xt2 = ica2.transform(X)
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# XXX: we have to set atol for this test to pass for all seeds when
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# fitting with float32 data. Is this revealing a bug?
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if global_dtype:
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atol = np.abs(Xt2).mean() / 1e6
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else:
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atol = 0.0 # the default rtol is enough for float64 data
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assert_allclose(Xt, Xt2, atol=atol)
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@pytest.mark.filterwarnings("ignore:Ignoring n_components with whiten=False.")
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@pytest.mark.parametrize(
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"whiten, n_components, expected_mixing_shape",
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[
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("arbitrary-variance", 5, (10, 5)),
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("arbitrary-variance", 10, (10, 10)),
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("unit-variance", 5, (10, 5)),
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("unit-variance", 10, (10, 10)),
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(False, 5, (10, 10)),
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(False, 10, (10, 10)),
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],
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)
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def test_inverse_transform(
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whiten, n_components, expected_mixing_shape, global_random_seed, global_dtype
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):
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# Test FastICA.inverse_transform
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n_samples = 100
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rng = np.random.RandomState(global_random_seed)
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X = rng.random_sample((n_samples, 10)).astype(global_dtype)
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ica = FastICA(n_components=n_components, random_state=rng, whiten=whiten)
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with warnings.catch_warnings():
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# For some dataset (depending on the value of global_dtype) the model
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# can fail to converge but this should not impact the definition of
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# a valid inverse transform.
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warnings.simplefilter("ignore", ConvergenceWarning)
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Xt = ica.fit_transform(X)
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assert ica.mixing_.shape == expected_mixing_shape
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X2 = ica.inverse_transform(Xt)
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assert X.shape == X2.shape
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# reversibility test in non-reduction case
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if n_components == X.shape[1]:
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# XXX: we have to set atol for this test to pass for all seeds when
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# fitting with float32 data. Is this revealing a bug?
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if global_dtype:
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# XXX: dividing by a smaller number makes
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# tests fail for some seeds.
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atol = np.abs(X2).mean() / 1e5
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else:
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atol = 0.0 # the default rtol is enough for float64 data
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assert_allclose(X, X2, atol=atol)
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def test_fastica_errors():
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n_features = 3
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n_samples = 10
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rng = np.random.RandomState(0)
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X = rng.random_sample((n_samples, n_features))
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w_init = rng.randn(n_features + 1, n_features + 1)
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with pytest.raises(ValueError, match=r"alpha must be in \[1,2\]"):
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fastica(X, fun_args={"alpha": 0})
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with pytest.raises(
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ValueError, match="w_init has invalid shape.+" r"should be \(3L?, 3L?\)"
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):
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fastica(X, w_init=w_init)
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def test_fastica_whiten_unit_variance():
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"""Test unit variance of transformed data using FastICA algorithm.
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Bug #13056
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"""
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rng = np.random.RandomState(0)
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X = rng.random_sample((100, 10))
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n_components = X.shape[1]
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ica = FastICA(n_components=n_components, whiten="unit-variance", random_state=0)
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Xt = ica.fit_transform(X)
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assert np.var(Xt) == pytest.approx(1.0)
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@pytest.mark.parametrize("whiten", ["arbitrary-variance", "unit-variance", False])
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@pytest.mark.parametrize("return_X_mean", [True, False])
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@pytest.mark.parametrize("return_n_iter", [True, False])
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def test_fastica_output_shape(whiten, return_X_mean, return_n_iter):
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n_features = 3
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n_samples = 10
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rng = np.random.RandomState(0)
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X = rng.random_sample((n_samples, n_features))
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expected_len = 3 + return_X_mean + return_n_iter
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out = fastica(
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X, whiten=whiten, return_n_iter=return_n_iter, return_X_mean=return_X_mean
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)
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assert len(out) == expected_len
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if not whiten:
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assert out[0] is None
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@pytest.mark.parametrize("add_noise", [True, False])
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def test_fastica_simple_different_solvers(add_noise, global_random_seed):
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"""Test FastICA is consistent between whiten_solvers."""
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rng = np.random.RandomState(global_random_seed)
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n_samples = 1000
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# Generate two sources:
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s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
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s2 = stats.t.rvs(1, size=n_samples, random_state=rng)
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s = np.c_[s1, s2].T
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center_and_norm(s)
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s1, s2 = s
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# Mixing angle
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phi = rng.rand() * 2 * np.pi
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mixing = np.array([[np.cos(phi), np.sin(phi)], [np.sin(phi), -np.cos(phi)]])
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m = np.dot(mixing, s)
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if add_noise:
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m += 0.1 * rng.randn(2, 1000)
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center_and_norm(m)
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outs = {}
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for solver in ("svd", "eigh"):
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ica = FastICA(random_state=0, whiten="unit-variance", whiten_solver=solver)
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sources = ica.fit_transform(m.T)
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outs[solver] = sources
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assert ica.components_.shape == (2, 2)
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assert sources.shape == (1000, 2)
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# compared numbers are not all on the same magnitude. Using a small atol to
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# make the test less brittle
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assert_allclose(outs["eigh"], outs["svd"], atol=1e-12)
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def test_fastica_eigh_low_rank_warning(global_random_seed):
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"""Test FastICA eigh solver raises warning for low-rank data."""
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rng = np.random.RandomState(global_random_seed)
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A = rng.randn(10, 2)
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X = A @ A.T
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ica = FastICA(random_state=0, whiten="unit-variance", whiten_solver="eigh")
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msg = "There are some small singular values"
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with pytest.warns(UserWarning, match=msg):
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ica.fit(X)
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