def test_randomized_pca_inverse(self):
# Test that randomized PCA is inversible on dense data
rng = np.random.RandomState(0)
n, p = 50, 3
X = mt.tensor(rng.randn(n, p)) # spherical data
X[:, 1] *= .00001 # make middle component relatively small
X += [5, 4, 3] # make a large mean
# same check that we can find the original data from the transformed signal
# (since the data is almost of rank n_components)
pca = PCA(n_components=2, svd_solver='randomized',
random_state=0).fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_almost_equal(X.to_numpy(), Y_inverse.to_numpy(), decimal=2)
# same as above with whitening (approximate reconstruction)
pca = PCA(n_components=2,
whiten=True,
svd_solver='randomized',
random_state=0).fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
relative_max_delta = (mt.abs(X - Y_inverse) / mt.abs(X).mean()).max()
self.assertLess(relative_max_delta.to_numpy(), 1e-5)
def test_pca_inverse(self):
# Test that the projection of data can be inverted
rng = np.random.RandomState(0)
n, p = 50, 3
X = mt.tensor(rng.randn(n, p)) # spherical data
X[:, 1] *= .00001 # make middle component relatively small
X += [5, 4, 3] # make a large mean
# same check that we can find the original data from the transformed
# signal (since the data is almost of rank n_components)
pca = PCA(n_components=2, svd_solver='full').fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_almost_equal(X.to_numpy(), Y_inverse.to_numpy(), decimal=3)
# same as above with whitening (approximate reconstruction)
for solver in self.solver_list:
pca = PCA(n_components=2, whiten=True, svd_solver=solver)
pca.fit(X)
Y = pca.transform(X)
Y_inverse = pca.inverse_transform(Y)
assert_almost_equal(X.to_numpy(), Y_inverse.to_numpy(), decimal=3)
