def test_incremental_pca(svd_solver):
# Incremental PCA on dense arrays.
X = iris.data
X = da.from_array(X, chunks=(3, -1))
batch_size = X.shape[0] // 3
ipca = IncrementalPCA(n_components=2, batch_size=batch_size, svd_solver=svd_solver)
pca = PCA(n_components=2, svd_solver=svd_solver)
pca.fit_transform(X)
X_transformed = ipca.fit_transform(X)
assert X_transformed.shape == (X.shape[0], 2)
np.testing.assert_allclose(
ipca.explained_variance_ratio_.sum(),
pca.explained_variance_ratio_.sum(),
rtol=1e-3,
)
for n_components in [1, 2, X.shape[1]]:
ipca = IncrementalPCA(n_components, batch_size=batch_size)
ipca.fit(X)
cov = ipca.get_covariance()
precision = ipca.get_precision()
np.testing.assert_allclose(
np.dot(cov, precision), np.eye(X.shape[1]), atol=1e-13
)
assert isinstance(pca.singular_values_, type(ipca.singular_values_))
assert isinstance(pca.mean_, type(ipca.mean_))
assert isinstance(pca.explained_variance_, type(ipca.explained_variance_))
assert isinstance(
pca.explained_variance_ratio_, type(ipca.explained_variance_ratio_)
)
def test_compare_with_sklearn(svd_solver, batch_number):
X = iris.data
X_da = da.from_array(X, chunks=(3, -1))
batch_size = X.shape[0] // batch_number
ipca = sd.IncrementalPCA(n_components=2, batch_size=batch_size)
ipca.fit(X)
ipca_da = IncrementalPCA(
n_components=2, batch_size=batch_size, svd_solver=svd_solver
)
ipca_da.fit(X_da)
np.testing.assert_allclose(ipca.components_, ipca_da.components_, atol=1e-13)
np.testing.assert_allclose(
ipca.explained_variance_, ipca_da.explained_variance_, atol=1e-13
)
np.testing.assert_allclose(
ipca.explained_variance_, ipca_da.explained_variance_, atol=1e-13
)
np.testing.assert_allclose(
ipca.explained_variance_ratio_, ipca_da.explained_variance_ratio_, atol=1e-13
)
if svd_solver == "randomized":
# noise variance in randomized solver is probabilistic.
assert_almost_equal(ipca.noise_variance_, ipca_da.noise_variance_, decimal=1)
else:
np.testing.assert_allclose(
ipca.noise_variance_, ipca_da.noise_variance_, atol=1e-13
)
def test_incremental_pca_set_params():
# Test that components_ sign is stable over batch sizes.
rng = np.random.RandomState(1999)
n_samples = 100
n_features = 20
X = rng.randn(n_samples, n_features)
X2 = rng.randn(n_samples, n_features)
X3 = rng.randn(n_samples, n_features)
X = da.from_array(X, chunks=[4, -1])
X2 = da.from_array(X2, chunks=[4, -1])
X3 = da.from_array(X3, chunks=[4, -1])
ipca = IncrementalPCA(n_components=20)
ipca.fit(X)
# Decreasing number of components
ipca.set_params(n_components=10)
with pytest.raises(ValueError):
ipca.partial_fit(X2)
# Increasing number of components
ipca.set_params(n_components=15)
with pytest.raises(ValueError):
ipca.partial_fit(X3)
# Returning to original setting
ipca.set_params(n_components=20)
ipca.partial_fit(X)
def test_singular_values(svd_solver):
# 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
)
X = da.from_array(X, chunks=[200, -1])
pca = PCA(n_components=10, svd_solver=svd_solver, random_state=rng).fit(X)
ipca = IncrementalPCA(n_components=10, batch_size=100, svd_solver=svd_solver).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
)
X = da.from_array(X, chunks=[4, -1])
pca = PCA(n_components=3, svd_solver=svd_solver, random_state=rng)
ipca = IncrementalPCA(n_components=3, batch_size=100, svd_solver=svd_solver)
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)
X_hat = da.from_array(X_hat, chunks=(4, -1))
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_incremental_pca_num_features_change():
# Test that changing n_components will raise an error.
rng = np.random.RandomState(1999)
n_samples = 100
X = rng.randn(n_samples, 20)
X2 = rng.randn(n_samples, 50)
X = da.from_array(X, chunks=[4, -1])
X2 = da.from_array(X2, chunks=[4, -1])
ipca = IncrementalPCA(n_components=None)
ipca.fit(X)
with pytest.raises(ValueError):
ipca.partial_fit(X2)