276 lines
10 KiB
Python
276 lines
10 KiB
Python
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"""Tests for Incremental PCA."""
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import numpy as np
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from sklearn.utils.testing import assert_almost_equal
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from sklearn.utils.testing import assert_array_almost_equal
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from sklearn.utils.testing import assert_raises
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from sklearn import datasets
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from sklearn.decomposition import PCA, IncrementalPCA
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iris = datasets.load_iris()
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def test_incremental_pca():
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# Incremental PCA on dense arrays.
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X = iris.data
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batch_size = X.shape[0] // 3
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ipca = IncrementalPCA(n_components=2, batch_size=batch_size)
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pca = PCA(n_components=2)
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pca.fit_transform(X)
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X_transformed = ipca.fit_transform(X)
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np.testing.assert_equal(X_transformed.shape, (X.shape[0], 2))
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assert_almost_equal(ipca.explained_variance_ratio_.sum(),
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pca.explained_variance_ratio_.sum(), 1)
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for n_components in [1, 2, X.shape[1]]:
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ipca = IncrementalPCA(n_components, batch_size=batch_size)
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ipca.fit(X)
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cov = ipca.get_covariance()
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precision = ipca.get_precision()
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assert_array_almost_equal(np.dot(cov, precision),
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np.eye(X.shape[1]))
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def test_incremental_pca_check_projection():
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# Test that the projection of data is correct.
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rng = np.random.RandomState(1999)
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n, p = 100, 3
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X = rng.randn(n, p) * .1
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X[:10] += np.array([3, 4, 5])
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Xt = 0.1 * rng.randn(1, p) + np.array([3, 4, 5])
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# Get the reconstruction of the generated data X
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# Note that Xt has the same "components" as X, just separated
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# This is what we want to ensure is recreated correctly
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Yt = IncrementalPCA(n_components=2).fit(X).transform(Xt)
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# Normalize
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Yt /= np.sqrt((Yt ** 2).sum())
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# Make sure that the first element of Yt is ~1, this means
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# the reconstruction worked as expected
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assert_almost_equal(np.abs(Yt[0][0]), 1., 1)
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def test_incremental_pca_inverse():
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# Test that the projection of data can be inverted.
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rng = np.random.RandomState(1999)
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n, p = 50, 3
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X = rng.randn(n, p) # spherical data
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X[:, 1] *= .00001 # make middle component relatively small
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X += [5, 4, 3] # make a large mean
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# same check that we can find the original data from the transformed
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# signal (since the data is almost of rank n_components)
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ipca = IncrementalPCA(n_components=2, batch_size=10).fit(X)
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Y = ipca.transform(X)
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Y_inverse = ipca.inverse_transform(Y)
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assert_almost_equal(X, Y_inverse, decimal=3)
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def test_incremental_pca_validation():
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# Test that n_components is >=1 and <= n_features.
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X = [[0, 1], [1, 0]]
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for n_components in [-1, 0, .99, 3]:
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assert_raises(ValueError, IncrementalPCA(n_components,
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batch_size=10).fit, X)
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def test_incremental_pca_set_params():
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# Test that components_ sign is stable over batch sizes.
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rng = np.random.RandomState(1999)
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n_samples = 100
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n_features = 20
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X = rng.randn(n_samples, n_features)
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X2 = rng.randn(n_samples, n_features)
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X3 = rng.randn(n_samples, n_features)
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ipca = IncrementalPCA(n_components=20)
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ipca.fit(X)
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# Decreasing number of components
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ipca.set_params(n_components=10)
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assert_raises(ValueError, ipca.partial_fit, X2)
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# Increasing number of components
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ipca.set_params(n_components=15)
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assert_raises(ValueError, ipca.partial_fit, X3)
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# Returning to original setting
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ipca.set_params(n_components=20)
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ipca.partial_fit(X)
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def test_incremental_pca_num_features_change():
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# Test that changing n_components will raise an error.
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rng = np.random.RandomState(1999)
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n_samples = 100
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X = rng.randn(n_samples, 20)
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X2 = rng.randn(n_samples, 50)
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ipca = IncrementalPCA(n_components=None)
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ipca.fit(X)
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assert_raises(ValueError, ipca.partial_fit, X2)
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def test_incremental_pca_batch_signs():
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# Test that components_ sign is stable over batch sizes.
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rng = np.random.RandomState(1999)
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n_samples = 100
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n_features = 3
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X = rng.randn(n_samples, n_features)
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all_components = []
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batch_sizes = np.arange(10, 20)
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for batch_size in batch_sizes:
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ipca = IncrementalPCA(n_components=None, batch_size=batch_size).fit(X)
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all_components.append(ipca.components_)
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for i, j in zip(all_components[:-1], all_components[1:]):
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assert_almost_equal(np.sign(i), np.sign(j), decimal=6)
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def test_incremental_pca_batch_values():
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# Test that components_ values are stable over batch sizes.
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rng = np.random.RandomState(1999)
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n_samples = 100
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n_features = 3
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X = rng.randn(n_samples, n_features)
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all_components = []
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batch_sizes = np.arange(20, 40, 3)
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for batch_size in batch_sizes:
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ipca = IncrementalPCA(n_components=None, batch_size=batch_size).fit(X)
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all_components.append(ipca.components_)
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for i, j in zip(all_components[:-1], all_components[1:]):
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assert_almost_equal(i, j, decimal=1)
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def test_incremental_pca_partial_fit():
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# Test that fit and partial_fit get equivalent results.
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rng = np.random.RandomState(1999)
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n, p = 50, 3
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X = rng.randn(n, p) # spherical data
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X[:, 1] *= .00001 # make middle component relatively small
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X += [5, 4, 3] # make a large mean
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# same check that we can find the original data from the transformed
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# signal (since the data is almost of rank n_components)
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batch_size = 10
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ipca = IncrementalPCA(n_components=2, batch_size=batch_size).fit(X)
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pipca = IncrementalPCA(n_components=2, batch_size=batch_size)
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# Add one to make sure endpoint is included
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batch_itr = np.arange(0, n + 1, batch_size)
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for i, j in zip(batch_itr[:-1], batch_itr[1:]):
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pipca.partial_fit(X[i:j, :])
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assert_almost_equal(ipca.components_, pipca.components_, decimal=3)
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def test_incremental_pca_against_pca_iris():
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# Test that IncrementalPCA and PCA are approximate (to a sign flip).
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X = iris.data
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Y_pca = PCA(n_components=2).fit_transform(X)
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Y_ipca = IncrementalPCA(n_components=2, batch_size=25).fit_transform(X)
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assert_almost_equal(np.abs(Y_pca), np.abs(Y_ipca), 1)
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def test_incremental_pca_against_pca_random_data():
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# Test that IncrementalPCA and PCA are approximate (to a sign flip).
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rng = np.random.RandomState(1999)
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n_samples = 100
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n_features = 3
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X = rng.randn(n_samples, n_features) + 5 * rng.rand(1, n_features)
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Y_pca = PCA(n_components=3).fit_transform(X)
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Y_ipca = IncrementalPCA(n_components=3, batch_size=25).fit_transform(X)
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assert_almost_equal(np.abs(Y_pca), np.abs(Y_ipca), 1)
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def test_explained_variances():
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# Test that PCA and IncrementalPCA calculations match
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X = datasets.make_low_rank_matrix(1000, 100, tail_strength=0.,
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effective_rank=10, random_state=1999)
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prec = 3
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n_samples, n_features = X.shape
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for nc in [None, 99]:
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pca = PCA(n_components=nc).fit(X)
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ipca = IncrementalPCA(n_components=nc, batch_size=100).fit(X)
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assert_almost_equal(pca.explained_variance_, ipca.explained_variance_,
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decimal=prec)
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assert_almost_equal(pca.explained_variance_ratio_,
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ipca.explained_variance_ratio_, decimal=prec)
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assert_almost_equal(pca.noise_variance_, ipca.noise_variance_,
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decimal=prec)
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def test_singular_values():
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# Check that the IncrementalPCA output has the correct singular values
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rng = np.random.RandomState(0)
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n_samples = 1000
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n_features = 100
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X = datasets.make_low_rank_matrix(n_samples, n_features, tail_strength=0.0,
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effective_rank=10, random_state=rng)
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pca = PCA(n_components=10, svd_solver='full', random_state=rng).fit(X)
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ipca = IncrementalPCA(n_components=10, batch_size=100).fit(X)
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assert_array_almost_equal(pca.singular_values_, ipca.singular_values_, 2)
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# Compare to the Frobenius norm
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X_pca = pca.transform(X)
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X_ipca = ipca.transform(X)
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assert_array_almost_equal(np.sum(pca.singular_values_**2.0),
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np.linalg.norm(X_pca, "fro")**2.0, 12)
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assert_array_almost_equal(np.sum(ipca.singular_values_**2.0),
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np.linalg.norm(X_ipca, "fro")**2.0, 2)
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# Compare to the 2-norms of the score vectors
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assert_array_almost_equal(pca.singular_values_,
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np.sqrt(np.sum(X_pca**2.0, axis=0)), 12)
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assert_array_almost_equal(ipca.singular_values_,
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np.sqrt(np.sum(X_ipca**2.0, axis=0)), 2)
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# Set the singular values and see what we get back
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rng = np.random.RandomState(0)
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n_samples = 100
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n_features = 110
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X = datasets.make_low_rank_matrix(n_samples, n_features, tail_strength=0.0,
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effective_rank=3, random_state=rng)
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pca = PCA(n_components=3, svd_solver='full', random_state=rng)
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ipca = IncrementalPCA(n_components=3, batch_size=100)
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X_pca = pca.fit_transform(X)
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X_pca /= np.sqrt(np.sum(X_pca**2.0, axis=0))
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X_pca[:, 0] *= 3.142
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X_pca[:, 1] *= 2.718
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X_hat = np.dot(X_pca, pca.components_)
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pca.fit(X_hat)
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ipca.fit(X_hat)
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assert_array_almost_equal(pca.singular_values_, [3.142, 2.718, 1.0], 14)
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assert_array_almost_equal(ipca.singular_values_, [3.142, 2.718, 1.0], 14)
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def test_whitening():
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# Test that PCA and IncrementalPCA transforms match to sign flip.
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X = datasets.make_low_rank_matrix(1000, 10, tail_strength=0.,
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effective_rank=2, random_state=1999)
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prec = 3
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n_samples, n_features = X.shape
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for nc in [None, 9]:
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pca = PCA(whiten=True, n_components=nc).fit(X)
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ipca = IncrementalPCA(whiten=True, n_components=nc,
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batch_size=250).fit(X)
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Xt_pca = pca.transform(X)
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Xt_ipca = ipca.transform(X)
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assert_almost_equal(np.abs(Xt_pca), np.abs(Xt_ipca), decimal=prec)
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Xinv_ipca = ipca.inverse_transform(Xt_ipca)
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Xinv_pca = pca.inverse_transform(Xt_pca)
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assert_almost_equal(X, Xinv_ipca, decimal=prec)
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assert_almost_equal(X, Xinv_pca, decimal=prec)
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assert_almost_equal(Xinv_pca, Xinv_ipca, decimal=prec)
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