def test_pca_randomized_solver(setup):
# PCA on dense arrays
X = iris
# Loop excluding the 0, invalid for randomized
for n_comp in np.arange(1, X.shape[1]):
pca = PCA(n_components=n_comp, svd_solver='randomized', random_state=0)
X_r = pca.fit(X).transform(X)
np.testing.assert_equal(X_r.shape[1], n_comp)
X_r2 = pca.fit_transform(X)
assert_array_almost_equal(X_r.fetch(), X_r2.fetch())
X_r = pca.transform(X)
assert_array_almost_equal(X_r.fetch(), X_r2.fetch())
# Test get_covariance and get_precision
cov = pca.get_covariance()
precision = pca.get_precision()
assert_array_almost_equal(mt.dot(cov, precision).to_numpy(),
mt.eye(X.shape[1]).to_numpy(), 12)
pca = PCA(n_components=0, svd_solver='randomized', random_state=0)
with pytest.raises(ValueError):
pca.fit(X)
pca = PCA(n_components=0, svd_solver='randomized', random_state=0)
with pytest.raises(ValueError):
pca.fit(X)
# Check internal state
assert pca.n_components == PCA(n_components=0,
svd_solver='randomized', random_state=0).n_components
assert pca.svd_solver == PCA(n_components=0,
svd_solver='randomized', random_state=0).svd_solver
def testPCA(self):
X = self.iris
for n_comp in np.arange(X.shape[1]):
pca = PCA(n_components=n_comp, svd_solver='full')
X_r = pca.fit(X).transform(X).fetch()
np.testing.assert_equal(X_r.shape[1], n_comp)
X_r2 = pca.fit_transform(X).fetch()
assert_array_almost_equal(X_r, X_r2)
X_r = pca.transform(X).fetch()
X_r2 = pca.fit_transform(X).fetch()
assert_array_almost_equal(X_r, X_r2)
# Test get_covariance and get_precision
cov = pca.get_covariance()
precision = pca.get_precision()
assert_array_almost_equal(
mt.dot(cov, precision).to_numpy(), np.eye(X.shape[1]), 12)
# test explained_variance_ratio_ == 1 with all components
pca = PCA(svd_solver='full')
pca.fit(X)
np.testing.assert_allclose(
pca.explained_variance_ratio_.sum().to_numpy(), 1.0, 3)
def test_n_components_none(self):
for solver in self.solver_list:
# Ensures that n_components == None is handled correctly
X = self.iris
# We conduct the same test on X.T so that it is invariant to axis.
for data in [X, X.T]:
pca = PCA(svd_solver=solver)
pca.fit(data)
self.assertEqual(pca.n_components_, min(data.shape))
def test_singular_values(self):
# Check that the PCA output has the correct singular values
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', random_state=rng).fit(X)
rpca = PCA(n_components=2, svd_solver='randomized',
random_state=rng).fit(X)
assert_array_almost_equal(pca.singular_values_.fetch(),
rpca.singular_values_.fetch(), 1)
# Compare to the Frobenius norm
X_pca = pca.transform(X)
X_rpca = rpca.transform(X)
assert_array_almost_equal(
mt.sum(pca.singular_values_**2.0).to_numpy(),
(mt.linalg.norm(X_pca, "fro")**2.0).to_numpy(), 12)
assert_array_almost_equal(
mt.sum(rpca.singular_values_**2.0).to_numpy(),
(mt.linalg.norm(X_rpca, "fro")**2.0).to_numpy(), 0)
# Compare to the 2-norms of the score vectors
assert_array_almost_equal(
pca.singular_values_.fetch(),
mt.sqrt(mt.sum(X_pca**2.0, axis=0)).to_numpy(), 12)
assert_array_almost_equal(
rpca.singular_values_.fetch(),
mt.sqrt(mt.sum(X_rpca**2.0, axis=0)).to_numpy(), 2)
# Set the singular values and see what we get back
rng = np.random.RandomState(0)
n_samples = 100
n_features = 110
X = mt.tensor(rng.randn(n_samples, n_features))
pca = PCA(n_components=3, svd_solver='full', random_state=rng)
rpca = PCA(n_components=3, svd_solver='randomized', random_state=rng)
X_pca = pca.fit_transform(X)
X_pca /= mt.sqrt(mt.sum(X_pca**2.0, axis=0))
X_pca[:, 0] *= 3.142
X_pca[:, 1] *= 2.718
X_hat = mt.dot(X_pca, pca.components_)
pca.fit(X_hat)
rpca.fit(X_hat)
assert_array_almost_equal(pca.singular_values_.fetch(),
[3.142, 2.718, 1.0], 14)
assert_array_almost_equal(rpca.singular_values_.fetch(),
[3.142, 2.718, 1.0], 14)
def test_infer_dim_3(self):
n, p = 100, 5
rng = np.random.RandomState(0)
X = mt.tensor(rng.randn(n, p) * .1)
X[:10] += mt.array([3, 4, 5, 1, 2])
X[10:20] += mt.array([6, 0, 7, 2, -1])
X[30:40] += 2 * mt.array([-1, 1, -1, 1, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_.fetch()
self.assertGreater(_infer_dimension(spect, n), 2)
def test_pca_score(self):
# Test that probabilistic PCA scoring yields a reasonable score
n, p = 1000, 3
rng = np.random.RandomState(0)
X = mt.tensor(rng.randn(n, p) * .1) + mt.array([3, 4, 5])
for solver in self.solver_list:
pca = PCA(n_components=2, svd_solver=solver)
pca.fit(X)
ll1 = pca.score(X)
h = -0.5 * mt.log(2 * mt.pi * mt.exp(1) * 0.1**2) * p
np.testing.assert_almost_equal((ll1 / h).to_numpy(), 1, 0)
def test_infer_dim_2(self):
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = mt.tensor(rng.randn(n, p) * .1)
X[:10] += mt.array([3, 4, 5, 1, 2])
X[10:20] += mt.array([6, 0, 7, 2, -1])
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_.fetch()
self.assertGreater(_infer_dimension(spect, n), 1)
def test_infer_dim_1(setup):
# TODO: explain what this is testing
# Or at least use explicit variable names...
n, p = 1000, 5
rng = np.random.RandomState(0)
X = (mt.tensor(rng.randn(n, p)) * .1 + mt.tensor(rng.randn(n, 1)) * mt.array([3, 4, 5, 1, 2]) +
mt.array([1, 0, 7, 4, 6]))
pca = PCA(n_components=p, svd_solver='full')
pca.fit(X)
spect = pca.explained_variance_.to_numpy()
ll = np.array([_assess_dimension(spect, k, n) for k in range(1, p)])
assert ll[1] > ll.max() - .01 * n
def test_pca_score3(setup):
# Check that probabilistic PCA selects the right model
n, p = 200, 3
rng = np.random.RandomState(0)
Xl = mt.tensor(rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
np.array([1, 0, 7]))
Xt = mt.tensor(rng.randn(n, p) + rng.randn(n, 1) * np.array([3, 4, 5]) +
np.array([1, 0, 7]))
ll = mt.zeros(p)
for k in range(p):
pca = PCA(n_components=k, svd_solver='full')
pca.fit(Xl)
ll[k] = pca.score(Xt)
assert ll.argmax().to_numpy() == 1
def test_pca_score2(setup):
# Test that probabilistic PCA correctly separated different datasets
n, p = 100, 3
rng = np.random.RandomState(0)
X = mt.tensor(rng.randn(n, p) * .1) + mt.array([3, 4, 5])
for solver in solver_list:
pca = PCA(n_components=2, svd_solver=solver)
pca.fit(X)
ll1 = pca.score(X)
ll2 = pca.score(mt.tensor(rng.randn(n, p) * .2) + mt.array([3, 4, 5]))
assert ll1.fetch() > ll2.fetch()
# Test that it gives different scores if whiten=True
pca = PCA(n_components=2, whiten=True, svd_solver=solver)
pca.fit(X)
ll2 = pca.score(X)
assert ll1.fetch() > ll2.fetch()
def test_infer_dim_by_explained_variance(self):
X = self.iris
pca = PCA(n_components=0.95, svd_solver='full')
pca.fit(X)
self.assertEqual(pca.n_components, 0.95)
self.assertEqual(pca.n_components_, 2)
pca = PCA(n_components=0.01, svd_solver='full')
pca.fit(X)
self.assertEqual(pca.n_components, 0.01)
self.assertEqual(pca.n_components_, 1)
rng = np.random.RandomState(0)
# more features than samples
X = mt.tensor(rng.rand(5, 20))
pca = PCA(n_components=.5, svd_solver='full').fit(X)
self.assertEqual(pca.n_components, 0.5)
self.assertEqual(pca.n_components_, 2)
def test_infer_dim_by_explained_variance(setup):
X = iris
pca = PCA(n_components=0.95, svd_solver='full')
pca.fit(X)
assert pca.n_components == 0.95
assert pca.n_components_ == 2
pca = PCA(n_components=0.01, svd_solver='full')
pca.fit(X)
assert pca.n_components == 0.01
assert pca.n_components_ == 1
rng = np.random.RandomState(0)
# more features than samples
X = mt.tensor(rng.rand(5, 20))
pca = PCA(n_components=.5, svd_solver='full').fit(X)
assert pca.n_components == 0.5
assert pca.n_components_ == 2
def test_n_components_mle(self):
# Ensure that n_components == 'mle' doesn't raise error for auto/full
# svd_solver and raises error for arpack/randomized svd_solver
rng = np.random.RandomState(0)
n_samples = 600
n_features = 10
X = mt.tensor(rng.randn(n_samples, n_features))
n_components_dict = {}
for solver in self.solver_list:
pca = PCA(n_components='mle', svd_solver=solver)
if solver in ['auto', 'full']:
pca.fit(X)
n_components_dict[solver] = pca.n_components_
else: # arpack/randomized solver
error_message = ("n_components='mle' cannot be a string with "
"svd_solver='{}'".format(solver))
assert_raise_message(ValueError, error_message, pca.fit, X)
self.assertEqual(n_components_dict['auto'], n_components_dict['full'])
def test_pca_zero_noise_variance_edge_cases(self):
# ensure that noise_variance_ is 0 in edge cases
# when n_components == min(n_samples, n_features)
n, p = 100, 3
rng = np.random.RandomState(0)
X = mt.tensor(rng.randn(n, p) * .1) + mt.array([3, 4, 5])
# arpack raises ValueError for n_components == min(n_samples,
# n_features)
svd_solvers = ['full', 'randomized']
for svd_solver in svd_solvers:
pca = PCA(svd_solver=svd_solver, n_components=p)
pca.fit(X)
self.assertEqual(pca.noise_variance_, 0)
pca.fit(X.T)
self.assertEqual(pca.noise_variance_, 0)
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)
def test_pca_bad_solver(self):
X = mt.tensor(np.random.RandomState(0).rand(5, 4))
pca = PCA(n_components=3, svd_solver='bad_argument')
with self.assertRaises(ValueError):
pca.fit(X)
def test_svd_solver_auto(self):
rng = np.random.RandomState(0)
X = mt.tensor(rng.uniform(size=(1000, 50)))
# case: n_components in (0,1) => 'full'
pca = PCA(n_components=.5)
pca.fit(X)
pca_test = PCA(n_components=.5, svd_solver='full')
pca_test.fit(X)
assert_array_almost_equal(pca.components_.to_numpy(),
pca_test.components_.to_numpy())
# case: max(X.shape) <= 500 => 'full'
pca = PCA(n_components=5, random_state=0)
Y = X[:10, :]
pca.fit(Y)
pca_test = PCA(n_components=5, svd_solver='full', random_state=0)
pca_test.fit(Y)
assert_array_almost_equal(pca.components_.to_numpy(),
pca_test.components_.to_numpy())
# case: n_components >= .8 * min(X.shape) => 'full'
pca = PCA(n_components=50)
pca.fit(X)
pca_test = PCA(n_components=50, svd_solver='full')
pca_test.fit(X)
assert_array_almost_equal(pca.components_.to_numpy(),
pca_test.components_.to_numpy())
# n_components >= 1 and n_components < .8 * min(X.shape) => 'randomized'
pca = PCA(n_components=10, random_state=0)
pca.fit(X)
pca_test = PCA(n_components=10,
svd_solver='randomized',
random_state=0)
pca_test.fit(X)
assert_array_almost_equal(pca.components_.to_numpy(),
pca_test.components_.to_numpy())
