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(),
)
