def test_whitening_tensor_e2_m1():
rng = np.random.RandomState(12)
n_features = 300
n_components = 25
min_count = 3
alpha0 = 10.
n_samples = rng.randint(100, 150)
doc_word_mtx = rng.randint(0, 3, size=(n_samples, n_features)).astype('float')
doc_word_mtx = sp.csr_matrix(doc_word_mtx)
m1, _ = first_order_moments(doc_word_mtx, min_words=min_count)
e2, _ = cooccurrence_expectation(doc_word_mtx, min_words=min_count)
# create M2 directly
m2 = (alpha0 + 1.) * e2.toarray()
m2 -= (alpha0 * m1) * m1[:, np.newaxis]
m2_vals, m2_vecs = sp.linalg.eigsh(m2, k=n_components)
# create whitening matrix
W = whitening(m2_vals, m2_vecs)
# optimized method
wt_m1 = np.dot(W.T, m1)
u1_2_3 = whitening_tensor_e2_m1(wt_m1, alpha0)
# compute directly
u1_2_3_true = _compute_e2_m1_directly(doc_word_mtx, W, wt_m1)
assert_array_almost_equal(u1_2_3_true, u1_2_3)
def test_whitening():
rng = np.random.RandomState(1)
n_features = 500
n_components = 50
min_count = 3
alpha0 = 10.
n_samples = rng.randint(100, 150)
doc_word_mtx = rng.randint(0, 3, size=(n_samples, n_features)).astype('float')
doc_word_mtx = sp.csr_matrix(doc_word_mtx)
m1, _ = first_order_moments(doc_word_mtx, min_words=min_count)
e2, _ = cooccurrence_expectation(doc_word_mtx, min_words=min_count)
# create M2 directly
m2 = (alpha0 + 1.) * e2.toarray()
m2 -= (alpha0 * m1) * m1[:, np.newaxis]
m2_vals, m2_vecs = sp.linalg.eigsh(m2, k=n_components)
# create whitening matrix
W = whitening(m2_vals, m2_vecs)
# check whitening matrix shape
assert_equal(n_features, W.shape[0])
assert_equal(n_components, W.shape[1])
# M2(W, W) should be identity matrix
identity = np.dot(np.dot(W.T, m2), W)
assert_array_almost_equal(np.eye(n_components, n_components), identity)