def test_pca_singular_values(svd_solver):
rng = np.random.RandomState(0)
n_samples, n_features = 100, 80
X = rng.randn(n_samples, n_features)
pca = PCA(n_components=2, svd_solver=svd_solver, random_state=rng)
X_trans = pca.fit_transform(X)
# compare to the Frobenius norm
assert_allclose(np.sum(pca.singular_values_**2),
np.linalg.norm(X_trans, "fro")**2)
# Compare to the 2-norms of the score vectors
assert_allclose(pca.singular_values_, np.sqrt(np.sum(X_trans**2, axis=0)))
# set the singular values and see what er get back
n_samples, n_features = 100, 110
X = rng.randn(n_samples, n_features)
pca = PCA(n_components=3, svd_solver=svd_solver, random_state=rng)
X_trans = pca.fit_transform(X)
X_trans /= np.sqrt(np.sum(X_trans**2, axis=0))
X_trans[:, 0] *= 3.142
X_trans[:, 1] *= 2.718
X_hat = np.dot(X_trans, pca.components_)
pca.fit(X_hat)
assert_allclose(pca.singular_values_, [3.142, 2.718, 1.0])
def test_pca_score_consistency_solvers(svd_solver):
# Check the consistency of score between solvers
X, _ = datasets.load_digits(return_X_y=True)
pca_full = PCA(n_components=30, svd_solver='full', random_state=0)
pca_other = PCA(n_components=30, svd_solver=svd_solver, random_state=0)
pca_full.fit(X)
pca_other.fit(X)
assert_allclose(pca_full.score(X), pca_other.score(X), rtol=5e-6)
def test_n_components_mle(svd_solver):
# Ensure that n_components == 'mle' doesn't raise error for auto/full
rng = np.random.RandomState(0)
n_samples, n_features = 600, 10
X = rng.randn(n_samples, n_features)
pca = PCA(n_components='mle', svd_solver=svd_solver)
pca.fit(X)
assert pca.n_components_ == 0
def test_pca_svd_solver_auto(data, n_components, expected_solver):
pca_auto = PCA(n_components=n_components, random_state=0)
pca_test = PCA(n_components=n_components,
svd_solver=expected_solver,
random_state=0)
pca_auto.fit(data)
pca_test.fit(data)
assert_allclose(pca_auto.components_, pca_test.components_)
def test_pca_sparse_input(svd_solver):
X = np.random.RandomState(0).rand(5, 4)
X = sp.sparse.csr_matrix(X)
assert sp.sparse.issparse(X)
pca = PCA(n_components=3, svd_solver=svd_solver)
with pytest.raises(TypeError):
pca.fit(X)
def test_pca_sanity_noise_variance(svd_solver):
# Sanity check for the noise_variance_. For more details see
# https://github.com/scikit-learn/scikit-learn/issues/7568
# https://github.com/scikit-learn/scikit-learn/issues/8541
# https://github.com/scikit-learn/scikit-learn/issues/8544
X, _ = datasets.load_digits(return_X_y=True)
pca = PCA(n_components=30, svd_solver=svd_solver, random_state=0)
pca.fit(X)
assert np.all((pca.explained_variance_ - pca.noise_variance_) >= 0)
def test_no_empty_slice_warning():
# test if we avoid numpy warnings for computing over empty arrays
n_components = 10
n_features = n_components + 2 # anything > n_comps triggered it in 0.16
X = np.random.uniform(-1, 1, size=(n_components, n_features))
pca = PCA(n_components=n_components)
with pytest.warns(None) as record:
pca.fit(X)
assert not record.list
def test_n_components_mle_error(svd_solver):
# Ensure that n_components == 'mle' will raise an error for unsupported
# solvers
rng = np.random.RandomState(0)
n_samples, n_features = 600, 10
X = rng.randn(n_samples, n_features)
pca = PCA(n_components='mle', svd_solver=svd_solver)
err_msg = ("n_components='mle' cannot be a string with svd_solver='{}'".
format(svd_solver))
with pytest.raises(ValueError, match=err_msg):
pca.fit(X)
def test_infer_dim_3():
n, p = 100, 5
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1
X[:10] += np.array([3, 4, 5, 1, 2])
X[10:20] += np.array([6, 0, 7, 2, -1])
X[30:40] += 2 * np.array([-1, 1, -1, 1, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
assert _infer_dimension_(spect, n, p) > 2
def test_infer_dim_2():
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1
X[:10] += np.array([3, 4, 5, 1, 2])
X[10:20] += np.array([6, 0, 7, 2, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
assert _infer_dimension_(spect, n, p) > 1
def test_infer_dim_1():
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = (rng.randn(n, p) * .1 + rng.randn(n, 1) * np.array([3, 4, 5, 1, 2]) +
np.array([1, 0, 7, 4, 6]))
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_
ll = np.array([_assess_dimension_(spect, k, n, p) for k in range(p)])
assert ll[1] > ll.max() - .01 * n
def test_pca_zero_noise_variance_edge_cases(svd_solver):
# ensure that noise_variance_ is 0 in edge cases
# when n_components == min(n_samples, n_features)
n, p = 100, 3
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1 + np.array([3, 4, 5])
pca = PCA(n_components=p, svd_solver=svd_solver)
pca.fit(X)
assert pca.noise_variance_ == 0
pca.fit(X.T)
assert pca.noise_variance_ == 0
def test_pca_singular_values_consistency(svd_solver):
rng = np.random.RandomState(0)
n_samples, n_features = 100, 80
X = rng.randn(n_samples, n_features)
pca_full = PCA(n_components=2, svd_solver='full', random_state=rng)
pca_other = PCA(n_components=2, svd_solver=svd_solver, random_state=rng)
pca_full.fit(X)
pca_other.fit(X)
assert_allclose(pca_full.singular_values_,
pca_other.singular_values_,
rtol=5e-3)
def test_singular_values():
# Check that the IncrementalPCA output has the correct singular values
rng = np.random.RandomState(0)
n_samples = 1000
n_features = 100
X = datasets.make_low_rank_matrix(n_samples, n_features, tail_strength=0.0,
effective_rank=10, random_state=rng)
pca = PCA(n_components=10, svd_solver='full', random_state=rng).fit(X)
ipca = IncrementalPCA(n_components=10, batch_size=100).fit(X)
assert_array_almost_equal(pca.singular_values_, ipca.singular_values_, 2)
# Compare to the Frobenius norm
X_pca = pca.transform(X)
X_ipca = ipca.transform(X)
assert_array_almost_equal(np.sum(pca.singular_values_**2.0),
np.linalg.norm(X_pca, "fro")**2.0, 12)
assert_array_almost_equal(np.sum(ipca.singular_values_**2.0),
np.linalg.norm(X_ipca, "fro")**2.0, 2)
# Compare to the 2-norms of the score vectors
assert_array_almost_equal(pca.singular_values_,
np.sqrt(np.sum(X_pca**2.0, axis=0)), 12)
assert_array_almost_equal(ipca.singular_values_,
np.sqrt(np.sum(X_ipca**2.0, axis=0)), 2)
# Set the singular values and see what we get back
rng = np.random.RandomState(0)
n_samples = 100
n_features = 110
X = datasets.make_low_rank_matrix(n_samples, n_features, tail_strength=0.0,
effective_rank=3, random_state=rng)
pca = PCA(n_components=3, svd_solver='full', random_state=rng)
ipca = IncrementalPCA(n_components=3, batch_size=100)
X_pca = pca.fit_transform(X)
X_pca /= np.sqrt(np.sum(X_pca**2.0, axis=0))
X_pca[:, 0] *= 3.142
X_pca[:, 1] *= 2.718
X_hat = np.dot(X_pca, pca.components_)
pca.fit(X_hat)
ipca.fit(X_hat)
assert_array_almost_equal(pca.singular_values_, [3.142, 2.718, 1.0], 14)
assert_array_almost_equal(ipca.singular_values_, [3.142, 2.718, 1.0], 14)
def test_pca_score3():
# Check that probabilistic PCA selects the right model
n, p = 200, 3
rng = np.random.RandomState(0)
Xl = (rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
np.array([1, 0, 7]))
Xt = (rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
np.array([1, 0, 7]))
ll = np.zeros(p)
for k in range(p):
pca = PCA(n_components=k, svd_solver='full')
pca.fit(Xl)
ll[k] = pca.score(Xt)
assert ll.argmax() == 1
def test_pca_vs_spca():
rng = np.random.RandomState(0)
Y, _, _ = generate_toy_data(3, 1000, (8, 8), random_state=rng)
Z, _, _ = generate_toy_data(3, 10, (8, 8), random_state=rng)
spca = SparsePCA(alpha=0, ridge_alpha=0, n_components=2)
pca = PCA(n_components=2)
pca.fit(Y)
spca.fit(Y)
results_test_pca = pca.transform(Z)
results_test_spca = spca.transform(Z)
assert_allclose(np.abs(spca.components_.dot(pca.components_.T)),
np.eye(2),
atol=1e-5)
results_test_pca *= np.sign(results_test_pca[0, :])
results_test_spca *= np.sign(results_test_spca[0, :])
assert_allclose(results_test_pca, results_test_spca)
def test_pca_explained_variance_equivalence_solver(svd_solver):
rng = np.random.RandomState(0)
n_samples, n_features = 100, 80
X = rng.randn(n_samples, n_features)
pca_full = PCA(n_components=2, svd_solver='full')
pca_other = PCA(n_components=2, svd_solver=svd_solver, random_state=0)
pca_full.fit(X)
pca_other.fit(X)
assert_allclose(pca_full.explained_variance_,
pca_other.explained_variance_,
rtol=5e-2)
assert_allclose(pca_full.explained_variance_ratio_,
pca_other.explained_variance_ratio_,
rtol=5e-2)
def test_pca_score(svd_solver):
# Test that probabilistic PCA scoring yields a reasonable score
n, p = 1000, 3
rng = np.random.RandomState(0)
X = rng.randn(n, p) * .1 + np.array([3, 4, 5])
pca = PCA(n_components=2, svd_solver=svd_solver)
pca.fit(X)
ll1 = pca.score(X)
h = -0.5 * np.log(2 * np.pi * np.exp(1) * 0.1**2) * p
assert_allclose(ll1 / h, 1, rtol=5e-2)
ll2 = pca.score(rng.randn(n, p) * .2 + np.array([3, 4, 5]))
assert ll1 > ll2
pca = PCA(n_components=2, whiten=True, svd_solver=svd_solver)
pca.fit(X)
ll2 = pca.score(X)
assert ll1 > ll2
def test_pca_validation(svd_solver, data, n_components, err_msg):
# Ensures that solver-specific extreme inputs for the n_components
# parameter raise errors
smallest_d = 2 # The smallest dimension
lower_limit = {'randomized': 1, 'arpack': 1, 'full': 0, 'auto': 0}
pca_fitted = PCA(n_components, svd_solver=svd_solver)
solver_reported = 'full' if svd_solver == 'auto' else svd_solver
err_msg = err_msg.format(n_components, lower_limit[svd_solver], smallest_d,
solver_reported)
with pytest.raises(ValueError, match=err_msg):
pca_fitted.fit(data)
# Additional case for arpack
if svd_solver == 'arpack':
n_components = smallest_d
err_msg = ("n_components={}L? must be strictly less than "
r"min\(n_samples, n_features\)={}L? with "
"svd_solver=\'arpack\'".format(n_components, smallest_d))
with pytest.raises(ValueError, match=err_msg):
PCA(n_components, svd_solver=svd_solver).fit(data)
def test_pca(svd_solver, n_components):
X = iris.data
pca = PCA(n_components=n_components, svd_solver=svd_solver)
# check the shape of fit.transform
X_r = pca.fit(X).transform(X)
assert X_r.shape[1] == n_components
# check the equivalence of fit.transform and fit_transform
X_r2 = pca.fit_transform(X)
assert_allclose(X_r, X_r2)
X_r = pca.transform(X)
assert_allclose(X_r, X_r2)
# Test get_covariance and get_precision
cov = pca.get_covariance()
precision = pca.get_precision()
assert_allclose(np.dot(cov, precision), np.eye(X.shape[1]), atol=1e-12)
def test_pca_bad_solver():
X = np.random.RandomState(0).rand(5, 4)
pca = PCA(n_components=3, svd_solver='bad_argument')
with pytest.raises(ValueError):
pca.fit(X)
def test_n_components_none(data, solver, n_components_):
pca = PCA(svd_solver=solver)
pca.fit(data)
assert pca.n_components_ == n_components_
def test_infer_dim_by_explained_variance(X, n_components,
n_components_validated):
pca = PCA(n_components=n_components, svd_solver='full')
pca.fit(X)
assert pca.n_components == pytest.approx(n_components)
assert pca.n_components_ == n_components_validated