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 testMultiOutputsOp(self):
sess = new_session()
rs = np.random.RandomState(0)
raw = rs.rand(20, 5)
a = mt.tensor(raw, chunk_size=5)
q = mt.abs(mt.linalg.qr(a)[0])
ret = sess.run(q)
np.testing.assert_almost_equal(ret, np.abs(np.linalg.qr(raw)[0]))
self.assertEqual(len(sess._sess.executor.chunk_result),
len(get_tiled(q).chunks))
def test_randomized_pca_check_projection(self):
# Test that the projection by randomized PCA on dense data is correct
rng = np.random.RandomState(0)
n, p = 100, 3
X = mt.tensor(rng.randn(n, p) * .1)
X[:10] += mt.array([3, 4, 5])
Xt = 0.1 * mt.tensor(rng.randn(1, p)) + mt.array([3, 4, 5])
Yt = PCA(n_components=2, svd_solver='randomized',
random_state=0).fit(X).transform(Xt)
Yt /= np.sqrt((Yt**2).sum())
assert_almost_equal(mt.abs(Yt[0][0]).to_numpy(), 1., 1)
def test_pca_check_projection(setup):
# Test that the projection of data is correct
rng = np.random.RandomState(0)
n, p = 100, 3
X = mt.tensor(rng.randn(n, p) * .1)
X[:10] += mt.array([3, 4, 5])
Xt = 0.1 * mt.tensor(rng.randn(1, p)) + mt.array([3, 4, 5])
for solver in solver_list:
Yt = PCA(n_components=2, svd_solver=solver).fit(X).transform(Xt)
Yt /= mt.sqrt((Yt ** 2).sum())
assert_almost_equal(mt.abs(Yt[0][0]).to_numpy(), 1., 1)
