def test_barycenter_kneighbors_graph():
X = np.array([[0, 1], [1.01, 1.], [2, 0]])
distance_matrix = squareform(pdist(X))
A = lle.barycenter_graph(distance_matrix, X)
# check that columns sum to one
assert_array_almost_equal(np.sum(A.toarray(), 1), np.ones(3))
pred = np.dot(A.toarray(), X)
assert(np.linalg.norm(pred - X) / X.shape[0] < 1)
def test_ltsa_manifold():
rng = np.random.RandomState(0)
# similar test on a slightly more complex manifold
X = np.array(list(product(np.arange(18), repeat=2)))
X = np.c_[X, X[:, 0] ** 2 / 18]
X = X + 1e-10 * rng.uniform(size=X.shape)
n_components = 2
Geometry = geom.Geometry(X, neighborhood_radius = 3)
distance_matrix = Geometry.get_distance_matrix()
tol = 1.5
N = barycenter_graph(distance_matrix, X).todense()
reconstruction_error = np.linalg.norm(np.dot(N, X) - X)
assert(reconstruction_error < tol)
for eigen_solver in eigen_solvers:
clf = ltsa.LTSA(n_components = n_components, Geometry = Geometry,
eigen_solver = eigen_solver, random_state = rng)
clf.fit(X)
assert(clf.embedding_.shape[1] == n_components)
reconstruction_error = np.linalg.norm(
np.dot(N, clf.embedding_) - clf.embedding_, 'fro') ** 2
assert(reconstruction_error < tol)
def test_lle_simple_grid():
# note: ARPACK is numerically unstable, so this test will fail for
# some random seeds. We choose 20 because the tests pass.
rng = np.random.RandomState(20)
tol = 0.1
# grid of equidistant points in 2D, n_components = n_dim
X = np.array(list(product(range(5), repeat=2)))
X = X + 1e-10 * rng.uniform(size=X.shape)
n_components = 2
Geometry = geom.Geometry(X, neighborhood_radius = 3)
tol = 0.1
distance_matrix = Geometry.get_distance_matrix()
N = lle.barycenter_graph(distance_matrix, X).todense()
reconstruction_error = np.linalg.norm(np.dot(N, X) - X, 'fro')
assert(reconstruction_error < tol)
for eigen_solver in eigen_solvers:
clf = lle.LocallyLinearEmbedding(n_components = n_components, Geometry = Geometry,
eigen_solver = eigen_solver, random_state = rng)
clf.fit(X)
assert(clf.embedding_.shape[1] == n_components)
reconstruction_error = np.linalg.norm(
np.dot(N, clf.embedding_) - clf.embedding_, 'fro') ** 2
assert(reconstruction_error < tol)
