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)
def test_cooccurrence_expectation_simple():
doc_word_mtx = np.array([
[1, 0, 3, 2],
[4, 1, 5, 0]
])
result_1 = np.array([
[0, 0, 3, 2],
[0, 0, 0, 0],
[3, 0, 6, 6],
[2, 0, 6, 2],
])
result_2 = np.array([
[12, 4, 20, 0],
[4, 0, 5, 0],
[20, 5, 20, 0],
[0, 0, 0, 0],
])
result = (result_1 / float(6 * 5)) + \
(result_2 / float(10 * 9))
result /= 2
e2, ignored_cnt = cooccurrence_expectation(doc_word_mtx, min_words=3)
assert_equal(ignored_cnt, 0)
assert_array_almost_equal(result, e2.toarray())
def test_cooccurrence_expectation():
rng = np.random.RandomState(0)
n_features = 100
n_samples = rng.randint(100, 200)
doc_word_mtx = rng.randint(0, 3, size=(n_samples, n_features)).astype('float')
word_cnts = doc_word_mtx.sum(axis=1).astype('float')
min_count = int(word_cnts.min() + 1)
mask = (word_cnts >= min_count)
result = np.zeros((n_features, n_features))
for i in xrange(n_samples):
cnt = word_cnts[i]
if cnt < min_count:
continue
doc_i = doc_word_mtx[i, :]
result_i = (doc_i * doc_i[:, np.newaxis]) - np.diag(doc_i)
result_i /= cnt * (cnt - 1)
result += result_i
result /= mask.sum()
e2, ignored_cnt = cooccurrence_expectation(
doc_word_mtx, min_words=min_count)
e2_dense = e2.toarray()
assert_greater(ignored_cnt, 0)
assert_equal(mask.sum(), n_samples - ignored_cnt)
assert_array_almost_equal(result, e2_dense)
# cooccurrence should be symmertic
assert_array_almost_equal(result, e2_dense.T)
assert_true(np.all(e2_dense >= 0.))
def test_second_order_moments():
# compare create M2 directly vs create eigen value
# and vectors with optimized method
rng = np.random.RandomState(100)
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_true, m2_vecs_true = sp.linalg.eigsh(m2, k=n_components)
m2_vecs_true, m2_vals_true, m2_vec_t = sp.linalg.svds(
e2, k=n_components, which='LM', return_singular_vectors=True)
assert_array_almost_equal(m2_vecs_true, m2_vec_t.T)
assert_true(np.all(m2_vals_true > 0.))
# create M2 eigen values & vectors with optimized method
m2_vals, m2_vecs = second_order_moments(n_components, e2, m1, alpha0)
# make sure all eigen values are greater than 0.
assert_true(np.all(m2_vals > 0.))
assert_equal(m2_vals.shape[0], n_components)
assert_equal(m2_vecs.shape[0], n_features)
assert_equal(m2_vecs.shape[1], n_components)
m2_reconstruct_true = np.dot(np.dot(m2_vecs_true, np.diag(m2_vals_true)),
m2_vecs_true.T)
m2_reconstruct = np.dot(np.dot(m2_vecs, np.diag(m2_vals)), m2_vecs.T)
# compare reconstructed version
assert_array_almost_equal(m2_reconstruct_true, m2_reconstruct, decimal=4)
# compare original M2 with reconstructed version
assert_array_almost_equal(m2, m2_reconstruct, decimal=4)