/usr/lib/python3/dist-packages/sklearn/decomposition/tests/test_fastica.py is in python3-sklearn 0.17.0-4.
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Test the fastica algorithm.
"""
import itertools
import warnings
import numpy as np
from scipy import stats
from nose.tools import assert_raises
from sklearn.utils.testing import assert_almost_equal
from sklearn.utils.testing import assert_array_almost_equal
from sklearn.utils.testing import assert_true
from sklearn.utils.testing import assert_less
from sklearn.utils.testing import assert_equal
from sklearn.utils.testing import assert_warns
from sklearn.decomposition import FastICA, fastica, PCA
from sklearn.decomposition.fastica_ import _gs_decorrelation
from sklearn.externals.six import moves
def center_and_norm(x, axis=-1):
""" Centers and norms x **in place**
Parameters
-----------
x: ndarray
Array with an axis of observations (statistical units) measured on
random variables.
axis: int, optional
Axis along which the mean and variance are calculated.
"""
x = np.rollaxis(x, axis)
x -= x.mean(axis=0)
x /= x.std(axis=0)
def test_gs():
# Test gram schmidt orthonormalization
# generate a random orthogonal matrix
rng = np.random.RandomState(0)
W, _, _ = np.linalg.svd(rng.randn(10, 10))
w = rng.randn(10)
_gs_decorrelation(w, W, 10)
assert_less((w ** 2).sum(), 1.e-10)
w = rng.randn(10)
u = _gs_decorrelation(w, W, 5)
tmp = np.dot(u, W.T)
assert_less((tmp[:5] ** 2).sum(), 1.e-10)
def test_fastica_simple(add_noise=False):
# Test the FastICA algorithm on very simple data.
rng = np.random.RandomState(0)
# scipy.stats uses the global RNG:
np.random.seed(0)
n_samples = 1000
# Generate two sources:
s1 = (2 * np.sin(np.linspace(0, 100, n_samples)) > 0) - 1
s2 = stats.t.rvs(1, size=n_samples)
s = np.c_[s1, s2].T
center_and_norm(s)
s1, s2 = s
# Mixing angle
phi = 0.6
mixing = np.array([[np.cos(phi), np.sin(phi)],
[np.sin(phi), -np.cos(phi)]])
m = np.dot(mixing, s)
if add_noise:
m += 0.1 * rng.randn(2, 1000)
center_and_norm(m)
# function as fun arg
def g_test(x):
return x ** 3, (3 * x ** 2).mean(axis=-1)
algos = ['parallel', 'deflation']
nls = ['logcosh', 'exp', 'cube', g_test]
whitening = [True, False]
for algo, nl, whiten in itertools.product(algos, nls, whitening):
if whiten:
k_, mixing_, s_ = fastica(m.T, fun=nl, algorithm=algo)
assert_raises(ValueError, fastica, m.T, fun=np.tanh,
algorithm=algo)
else:
X = PCA(n_components=2, whiten=True).fit_transform(m.T)
k_, mixing_, s_ = fastica(X, fun=nl, algorithm=algo, whiten=False)
assert_raises(ValueError, fastica, X, fun=np.tanh,
algorithm=algo)
s_ = s_.T
# Check that the mixing model described in the docstring holds:
if whiten:
assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
center_and_norm(s_)
s1_, s2_ = s_
# Check to see if the sources have been estimated
# in the wrong order
if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
s2_, s1_ = s_
s1_ *= np.sign(np.dot(s1_, s1))
s2_ *= np.sign(np.dot(s2_, s2))
# Check that we have estimated the original sources
if not add_noise:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=2)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=2)
else:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=1)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=1)
# Test FastICA class
_, _, sources_fun = fastica(m.T, fun=nl, algorithm=algo, random_state=0)
ica = FastICA(fun=nl, algorithm=algo, random_state=0)
sources = ica.fit_transform(m.T)
assert_equal(ica.components_.shape, (2, 2))
assert_equal(sources.shape, (1000, 2))
assert_array_almost_equal(sources_fun, sources)
assert_array_almost_equal(sources, ica.transform(m.T))
assert_equal(ica.mixing_.shape, (2, 2))
for fn in [np.tanh, "exp(-.5(x^2))"]:
ica = FastICA(fun=fn, algorithm=algo, random_state=0)
assert_raises(ValueError, ica.fit, m.T)
assert_raises(TypeError, FastICA(fun=moves.xrange(10)).fit, m.T)
def test_fastica_nowhiten():
m = [[0, 1], [1, 0]]
# test for issue #697
ica = FastICA(n_components=1, whiten=False, random_state=0)
assert_warns(UserWarning, ica.fit, m)
assert_true(hasattr(ica, 'mixing_'))
def test_non_square_fastica(add_noise=False):
# Test the FastICA algorithm on very simple data.
rng = np.random.RandomState(0)
n_samples = 1000
# Generate two sources:
t = np.linspace(0, 100, n_samples)
s1 = np.sin(t)
s2 = np.ceil(np.sin(np.pi * t))
s = np.c_[s1, s2].T
center_and_norm(s)
s1, s2 = s
# Mixing matrix
mixing = rng.randn(6, 2)
m = np.dot(mixing, s)
if add_noise:
m += 0.1 * rng.randn(6, n_samples)
center_and_norm(m)
k_, mixing_, s_ = fastica(m.T, n_components=2, random_state=rng)
s_ = s_.T
# Check that the mixing model described in the docstring holds:
assert_almost_equal(s_, np.dot(np.dot(mixing_, k_), m))
center_and_norm(s_)
s1_, s2_ = s_
# Check to see if the sources have been estimated
# in the wrong order
if abs(np.dot(s1_, s2)) > abs(np.dot(s1_, s1)):
s2_, s1_ = s_
s1_ *= np.sign(np.dot(s1_, s1))
s2_ *= np.sign(np.dot(s2_, s2))
# Check that we have estimated the original sources
if not add_noise:
assert_almost_equal(np.dot(s1_, s1) / n_samples, 1, decimal=3)
assert_almost_equal(np.dot(s2_, s2) / n_samples, 1, decimal=3)
def test_fit_transform():
# Test FastICA.fit_transform
rng = np.random.RandomState(0)
X = rng.random_sample((100, 10))
for whiten, n_components in [[True, 5], [False, None]]:
n_components_ = (n_components if n_components is not None else
X.shape[1])
ica = FastICA(n_components=n_components, whiten=whiten, random_state=0)
Xt = ica.fit_transform(X)
assert_equal(ica.components_.shape, (n_components_, 10))
assert_equal(Xt.shape, (100, n_components_))
ica = FastICA(n_components=n_components, whiten=whiten, random_state=0)
ica.fit(X)
assert_equal(ica.components_.shape, (n_components_, 10))
Xt2 = ica.transform(X)
assert_array_almost_equal(Xt, Xt2)
def test_inverse_transform():
# Test FastICA.inverse_transform
n_features = 10
n_samples = 100
n1, n2 = 5, 10
rng = np.random.RandomState(0)
X = rng.random_sample((n_samples, n_features))
expected = {(True, n1): (n_features, n1),
(True, n2): (n_features, n2),
(False, n1): (n_features, n2),
(False, n2): (n_features, n2)}
for whiten in [True, False]:
for n_components in [n1, n2]:
n_components_ = (n_components if n_components is not None else
X.shape[1])
ica = FastICA(n_components=n_components, random_state=rng,
whiten=whiten)
with warnings.catch_warnings(record=True):
# catch "n_components ignored" warning
Xt = ica.fit_transform(X)
expected_shape = expected[(whiten, n_components_)]
assert_equal(ica.mixing_.shape, expected_shape)
X2 = ica.inverse_transform(Xt)
assert_equal(X.shape, X2.shape)
# reversibility test in non-reduction case
if n_components == X.shape[1]:
assert_array_almost_equal(X, X2)
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