def testExplainedVariance(self): # Check that PCA output has unit-variance rng = np.random.RandomState(0) n_samples = 100 n_features = 80 X = mt.tensor(rng.randn(n_samples, n_features)) pca = PCA(n_components=2, svd_solver='full').fit(X) rpca = PCA(n_components=2, svd_solver='randomized', random_state=42).fit(X) assert_array_almost_equal(pca.explained_variance_.to_numpy(), rpca.explained_variance_.to_numpy(), 1) assert_array_almost_equal(pca.explained_variance_ratio_.to_numpy(), rpca.explained_variance_ratio_.to_numpy(), 1) # compare to empirical variances expected_result = np.linalg.eig(np.cov(X.to_numpy(), rowvar=False))[0] expected_result = sorted(expected_result, reverse=True)[:2] X_pca = pca.transform(X) assert_array_almost_equal(pca.explained_variance_.to_numpy(), mt.var(X_pca, ddof=1, axis=0).to_numpy()) assert_array_almost_equal(pca.explained_variance_.to_numpy(), expected_result) X_rpca = rpca.transform(X) assert_array_almost_equal(rpca.explained_variance_.to_numpy(), mt.var(X_rpca, ddof=1, axis=0).to_numpy(), decimal=1) assert_array_almost_equal(rpca.explained_variance_.to_numpy(), expected_result, decimal=1) # Same with correlated data X = datasets.make_classification(n_samples, n_features, n_informative=n_features - 2, random_state=rng)[0] X = mt.tensor(X) pca = PCA(n_components=2).fit(X) rpca = PCA(n_components=2, svd_solver='randomized', random_state=rng).fit(X) assert_array_almost_equal(pca.explained_variance_ratio_.to_numpy(), rpca.explained_variance_ratio_.to_numpy(), 5)
def test_explained_variance(setup): # Test sparse data svd_r_10_sp = TruncatedSVD(10, algorithm="randomized", random_state=42) svd_r_20_sp = TruncatedSVD(20, algorithm="randomized", random_state=42) X_trans_r_10_sp = svd_r_10_sp.fit_transform(X) X_trans_r_20_sp = svd_r_20_sp.fit_transform(X) # Test dense data svd_r_10_de = TruncatedSVD(10, algorithm="randomized", random_state=42) svd_r_20_de = TruncatedSVD(20, algorithm="randomized", random_state=42) X_trans_r_10_de = svd_r_10_de.fit_transform(X.toarray()) X_trans_r_20_de = svd_r_20_de.fit_transform(X.toarray()) # helper arrays for tests below svds = (svd_r_10_sp, svd_r_20_sp, svd_r_10_de, svd_r_20_de) svds_trans = ( (svd_r_10_sp, X_trans_r_10_sp), (svd_r_20_sp, X_trans_r_20_sp), (svd_r_10_de, X_trans_r_10_de), (svd_r_20_de, X_trans_r_20_de), ) svds_10_v_20 = ( (svd_r_10_sp, svd_r_20_sp), (svd_r_10_de, svd_r_20_de), ) svds_sparse_v_dense = ( (svd_r_10_sp, svd_r_10_de), (svd_r_20_sp, svd_r_20_de), ) # Assert the 1st component is equal for svd_10, svd_20 in svds_10_v_20: assert_array_almost_equal( svd_10.explained_variance_ratio_.to_numpy(), svd_20.explained_variance_ratio_[:10].to_numpy(), decimal=4, ) # Assert that 20 components has higher explained variance than 10 for svd_10, svd_20 in svds_10_v_20: assert svd_20.explained_variance_ratio_.sum().to_numpy( ) > svd_10.explained_variance_ratio_.sum().to_numpy() # Assert that all the values are greater than 0 for svd in svds: assert_array_less(0.0, svd.explained_variance_ratio_.to_numpy()) # Assert that total explained variance is less than 1 for svd in svds: assert_array_less(svd.explained_variance_ratio_.sum().to_numpy(), 1.0) # Compare sparse vs. dense for svd_sparse, svd_dense in svds_sparse_v_dense: assert_array_almost_equal( svd_sparse.explained_variance_ratio_.to_numpy(), svd_dense.explained_variance_ratio_.to_numpy()) # Test that explained_variance is correct for svd, transformed in svds_trans: total_variance = mt.var(X.toarray(), axis=0).sum().to_numpy() variances = mt.var(transformed, axis=0) true_explained_variance_ratio = variances / total_variance assert_array_almost_equal( svd.explained_variance_ratio_.to_numpy(), true_explained_variance_ratio.to_numpy(), )