def test_lle_init_parameters():
X = np.random.rand(5, 3)
clf = manifold.LocallyLinearEmbedding(eigen_solver="error")
msg = "unrecognized eigen_solver 'error'"
assert_raise_message(ValueError, msg, clf.fit, X)
clf = manifold.LocallyLinearEmbedding(method="error")
msg = "unrecognized method 'error'"
assert_raise_message(ValueError, msg, clf.fit, X)
def test_lle_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
for method in ["standard", "hessian", "modified", "ltsa"]:
clf = manifold.LocallyLinearEmbedding(n_neighbors=6,
n_components=n_components,
method=method, random_state=0)
tol = 1.5 if method == "standard" else 3
N = barycenter_kneighbors_graph(X, clf.n_neighbors).toarray()
reconstruction_error = linalg.norm(np.dot(N, X) - X)
assert reconstruction_error < tol
for solver in eigen_solvers:
clf.set_params(eigen_solver=solver)
clf.fit(X)
assert clf.embedding_.shape[1] == n_components
reconstruction_error = linalg.norm(
np.dot(N, clf.embedding_) - clf.embedding_, 'fro') ** 2
details = ("solver: %s, method: %s" % (solver, method))
assert reconstruction_error < tol, details
assert (np.abs(clf.reconstruction_error_ -
reconstruction_error) <
tol * reconstruction_error), details
def test_lle_simple_grid():
# note: ARPACK is numerically unstable, so this test will fail for
# some random seeds. We choose 2 because the tests pass.
rng = np.random.RandomState(2)
# 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
clf = manifold.LocallyLinearEmbedding(n_neighbors=5,
n_components=n_components,
random_state=rng)
tol = 0.1
N = barycenter_kneighbors_graph(X, clf.n_neighbors).toarray()
reconstruction_error = linalg.norm(np.dot(N, X) - X, 'fro')
assert reconstruction_error < tol
for solver in eigen_solvers:
clf.set_params(eigen_solver=solver)
clf.fit(X)
assert clf.embedding_.shape[1] == n_components
reconstruction_error = linalg.norm(
np.dot(N, clf.embedding_) - clf.embedding_, 'fro') ** 2
assert reconstruction_error < tol
assert_almost_equal(clf.reconstruction_error_,
reconstruction_error, decimal=1)
# re-embed a noisy version of X using the transform method
noise = rng.randn(*X.shape) / 100
X_reembedded = clf.transform(X + noise)
assert linalg.norm(X_reembedded - clf.embedding_) < tol
def test_integer_input():
rand = np.random.RandomState(0)
X = rand.randint(0, 100, size=(20, 3))
for method in ["standard", "hessian", "modified", "ltsa"]:
clf = manifold.LocallyLinearEmbedding(method=method, n_neighbors=10)
clf.fit(X) # this previously raised a TypeError
def test_pipeline():
# check that LocallyLinearEmbedding works fine as a Pipeline
# only checks that no error is raised.
# TODO check that it actually does something useful
from mrex import pipeline, datasets
X, y = datasets.make_blobs(random_state=0)
clf = pipeline.Pipeline(
[('filter', manifold.LocallyLinearEmbedding(random_state=0)),
('clf', neighbors.KNeighborsClassifier())])
clf.fit(X, y)
assert .9 < clf.score(X, y)
fig = plt.figure(figsize=(15, 8))
plt.suptitle("Manifold Learning with %i points, %i neighbors" %
(1000, n_neighbors),
fontsize=14)
ax = fig.add_subplot(251, projection='3d')
ax.scatter(X[:, 0], X[:, 1], X[:, 2], c=color, cmap=plt.cm.Spectral)
ax.view_init(4, -72)
methods = ['standard', 'ltsa', 'hessian', 'modified']
labels = ['LLE', 'LTSA', 'Hessian LLE', 'Modified LLE']
for i, method in enumerate(methods):
t0 = time()
Y = manifold.LocallyLinearEmbedding(n_neighbors,
n_components,
eigen_solver='auto',
method=method).fit_transform(X)
t1 = time()
print("%s: %.2g sec" % (methods[i], t1 - t0))
ax = fig.add_subplot(252 + i)
plt.scatter(Y[:, 0], Y[:, 1], c=color, cmap=plt.cm.Spectral)
plt.title("%s (%.2g sec)" % (labels[i], t1 - t0))
ax.xaxis.set_major_formatter(NullFormatter())
ax.yaxis.set_major_formatter(NullFormatter())
plt.axis('tight')
t0 = time()
Y = manifold.Isomap(n_neighbors, n_components).fit_transform(X)
t1 = time()
print("Isomap: %.2g sec" % (t1 - t0))
# Cluster using affinity propagation
_, labels = cluster.affinity_propagation(edge_model.covariance_)
n_labels = labels.max()
for i in range(n_labels + 1):
print('Cluster %i: %s' % ((i + 1), ', '.join(names[labels == i])))
# #############################################################################
# Find a low-dimension embedding for visualization: find the best position of
# the nodes (the stocks) on a 2D plane
# We use a dense eigen_solver to achieve reproducibility (arpack is
# initiated with random vectors that we don't control). In addition, we
# use a large number of neighbors to capture the large-scale structure.
node_position_model = manifold.LocallyLinearEmbedding(
n_components=2, eigen_solver='dense', n_neighbors=6)
embedding = node_position_model.fit_transform(X.T).T
# #############################################################################
# Visualization
plt.figure(1, facecolor='w', figsize=(10, 8))
plt.clf()
ax = plt.axes([0., 0., 1., 1.])
plt.axis('off')
# Display a graph of the partial correlations
partial_correlations = edge_model.precision_.copy()
d = 1 / np.sqrt(np.diag(partial_correlations))
partial_correlations *= d
partial_correlations *= d[:, np.newaxis]
# ----------------------------------------------------------------------
# Isomap projection of the digits dataset
print("Computing Isomap projection")
t0 = time()
X_iso = manifold.Isomap(n_neighbors, n_components=2).fit_transform(X)
print("Done.")
plot_embedding(X_iso,
"Isomap projection of the digits (time %.2fs)" %
(time() - t0))
# ----------------------------------------------------------------------
# Locally linear embedding of the digits dataset
print("Computing LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='standard')
t0 = time()
X_lle = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_lle,
"Locally Linear Embedding of the digits (time %.2fs)" %
(time() - t0))
# ----------------------------------------------------------------------
# Modified Locally linear embedding of the digits dataset
print("Computing modified LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors, n_components=2,
method='modified')
t0 = time()
X_mlle = clf.fit_transform(X)