348 lines
14 KiB
Python
348 lines
14 KiB
Python
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import pytest
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import numpy as np
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from scipy import sparse
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from scipy.sparse import csgraph
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from scipy.linalg import eigh
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from sklearn.manifold import SpectralEmbedding
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from sklearn.manifold._spectral_embedding import _graph_is_connected
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from sklearn.manifold._spectral_embedding import _graph_connected_component
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from sklearn.manifold import spectral_embedding
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from sklearn.metrics.pairwise import rbf_kernel
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from sklearn.metrics import normalized_mutual_info_score
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from sklearn.neighbors import NearestNeighbors
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from sklearn.cluster import KMeans
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from sklearn.datasets import make_blobs
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from sklearn.utils.extmath import _deterministic_vector_sign_flip
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from sklearn.utils._testing import assert_array_almost_equal
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from sklearn.utils._testing import assert_array_equal
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# non centered, sparse centers to check the
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centers = np.array([
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[0.0, 5.0, 0.0, 0.0, 0.0],
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[0.0, 0.0, 4.0, 0.0, 0.0],
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[1.0, 0.0, 0.0, 5.0, 1.0],
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])
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n_samples = 1000
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n_clusters, n_features = centers.shape
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S, true_labels = make_blobs(n_samples=n_samples, centers=centers,
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cluster_std=1., random_state=42)
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def _assert_equal_with_sign_flipping(A, B, tol=0.0):
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""" Check array A and B are equal with possible sign flipping on
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each columns"""
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tol_squared = tol ** 2
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for A_col, B_col in zip(A.T, B.T):
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assert (np.max((A_col - B_col) ** 2) <= tol_squared or
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np.max((A_col + B_col) ** 2) <= tol_squared)
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def test_sparse_graph_connected_component():
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rng = np.random.RandomState(42)
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n_samples = 300
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boundaries = [0, 42, 121, 200, n_samples]
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p = rng.permutation(n_samples)
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connections = []
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for start, stop in zip(boundaries[:-1], boundaries[1:]):
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group = p[start:stop]
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# Connect all elements within the group at least once via an
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# arbitrary path that spans the group.
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for i in range(len(group) - 1):
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connections.append((group[i], group[i + 1]))
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# Add some more random connections within the group
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min_idx, max_idx = 0, len(group) - 1
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n_random_connections = 1000
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source = rng.randint(min_idx, max_idx, size=n_random_connections)
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target = rng.randint(min_idx, max_idx, size=n_random_connections)
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connections.extend(zip(group[source], group[target]))
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# Build a symmetric affinity matrix
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row_idx, column_idx = tuple(np.array(connections).T)
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data = rng.uniform(.1, 42, size=len(connections))
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affinity = sparse.coo_matrix((data, (row_idx, column_idx)))
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affinity = 0.5 * (affinity + affinity.T)
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for start, stop in zip(boundaries[:-1], boundaries[1:]):
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component_1 = _graph_connected_component(affinity, p[start])
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component_size = stop - start
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assert component_1.sum() == component_size
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# We should retrieve the same component mask by starting by both ends
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# of the group
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component_2 = _graph_connected_component(affinity, p[stop - 1])
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assert component_2.sum() == component_size
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assert_array_equal(component_1, component_2)
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def test_spectral_embedding_two_components(seed=36):
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# Test spectral embedding with two components
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random_state = np.random.RandomState(seed)
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n_sample = 100
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affinity = np.zeros(shape=[n_sample * 2, n_sample * 2])
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# first component
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affinity[0:n_sample,
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0:n_sample] = np.abs(random_state.randn(n_sample, n_sample)) + 2
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# second component
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affinity[n_sample::,
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n_sample::] = np.abs(random_state.randn(n_sample, n_sample)) + 2
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# Test of internal _graph_connected_component before connection
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component = _graph_connected_component(affinity, 0)
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assert component[:n_sample].all()
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assert not component[n_sample:].any()
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component = _graph_connected_component(affinity, -1)
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assert not component[:n_sample].any()
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assert component[n_sample:].all()
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# connection
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affinity[0, n_sample + 1] = 1
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affinity[n_sample + 1, 0] = 1
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affinity.flat[::2 * n_sample + 1] = 0
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affinity = 0.5 * (affinity + affinity.T)
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true_label = np.zeros(shape=2 * n_sample)
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true_label[0:n_sample] = 1
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se_precomp = SpectralEmbedding(n_components=1, affinity="precomputed",
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random_state=np.random.RandomState(seed))
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embedded_coordinate = se_precomp.fit_transform(affinity)
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# Some numpy versions are touchy with types
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embedded_coordinate = \
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se_precomp.fit_transform(affinity.astype(np.float32))
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# thresholding on the first components using 0.
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label_ = np.array(embedded_coordinate.ravel() < 0, dtype="float")
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assert normalized_mutual_info_score(
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true_label, label_) == pytest.approx(1.0)
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@pytest.mark.parametrize("X", [S, sparse.csr_matrix(S)],
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ids=["dense", "sparse"])
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def test_spectral_embedding_precomputed_affinity(X, seed=36):
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# Test spectral embedding with precomputed kernel
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gamma = 1.0
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se_precomp = SpectralEmbedding(n_components=2, affinity="precomputed",
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random_state=np.random.RandomState(seed))
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se_rbf = SpectralEmbedding(n_components=2, affinity="rbf",
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gamma=gamma,
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random_state=np.random.RandomState(seed))
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embed_precomp = se_precomp.fit_transform(rbf_kernel(X, gamma=gamma))
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embed_rbf = se_rbf.fit_transform(X)
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assert_array_almost_equal(
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se_precomp.affinity_matrix_, se_rbf.affinity_matrix_)
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_assert_equal_with_sign_flipping(embed_precomp, embed_rbf, 0.05)
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def test_precomputed_nearest_neighbors_filtering():
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# Test precomputed graph filtering when containing too many neighbors
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n_neighbors = 2
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results = []
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for additional_neighbors in [0, 10]:
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nn = NearestNeighbors(
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n_neighbors=n_neighbors + additional_neighbors).fit(S)
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graph = nn.kneighbors_graph(S, mode='connectivity')
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embedding = SpectralEmbedding(random_state=0, n_components=2,
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affinity='precomputed_nearest_neighbors',
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n_neighbors=n_neighbors
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).fit(graph).embedding_
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results.append(embedding)
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assert_array_equal(results[0], results[1])
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@pytest.mark.parametrize("X", [S, sparse.csr_matrix(S)],
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ids=["dense", "sparse"])
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def test_spectral_embedding_callable_affinity(X, seed=36):
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# Test spectral embedding with callable affinity
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gamma = 0.9
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kern = rbf_kernel(S, gamma=gamma)
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se_callable = SpectralEmbedding(n_components=2,
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affinity=(
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lambda x: rbf_kernel(x, gamma=gamma)),
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gamma=gamma,
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random_state=np.random.RandomState(seed))
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se_rbf = SpectralEmbedding(n_components=2, affinity="rbf",
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gamma=gamma,
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random_state=np.random.RandomState(seed))
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embed_rbf = se_rbf.fit_transform(X)
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embed_callable = se_callable.fit_transform(X)
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assert_array_almost_equal(
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se_callable.affinity_matrix_, se_rbf.affinity_matrix_)
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assert_array_almost_equal(kern, se_rbf.affinity_matrix_)
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_assert_equal_with_sign_flipping(embed_rbf, embed_callable, 0.05)
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# TODO: Remove when pyamg does replaces sp.rand call with np.random.rand
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# https://github.com/scikit-learn/scikit-learn/issues/15913
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@pytest.mark.filterwarnings(
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"ignore:scipy.rand is deprecated:DeprecationWarning:pyamg.*")
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def test_spectral_embedding_amg_solver(seed=36):
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# Test spectral embedding with amg solver
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pytest.importorskip('pyamg')
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se_amg = SpectralEmbedding(n_components=2, affinity="nearest_neighbors",
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eigen_solver="amg", n_neighbors=5,
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random_state=np.random.RandomState(seed))
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se_arpack = SpectralEmbedding(n_components=2, affinity="nearest_neighbors",
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eigen_solver="arpack", n_neighbors=5,
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random_state=np.random.RandomState(seed))
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embed_amg = se_amg.fit_transform(S)
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embed_arpack = se_arpack.fit_transform(S)
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_assert_equal_with_sign_flipping(embed_amg, embed_arpack, 1e-5)
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# same with special case in which amg is not actually used
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# regression test for #10715
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# affinity between nodes
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row = [0, 0, 1, 2, 3, 3, 4]
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col = [1, 2, 2, 3, 4, 5, 5]
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val = [100, 100, 100, 1, 100, 100, 100]
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affinity = sparse.coo_matrix((val + val, (row + col, col + row)),
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shape=(6, 6)).toarray()
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se_amg.affinity = "precomputed"
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se_arpack.affinity = "precomputed"
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embed_amg = se_amg.fit_transform(affinity)
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embed_arpack = se_arpack.fit_transform(affinity)
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_assert_equal_with_sign_flipping(embed_amg, embed_arpack, 1e-5)
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# TODO: Remove filterwarnings when pyamg does replaces sp.rand call with
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# np.random.rand:
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# https://github.com/scikit-learn/scikit-learn/issues/15913
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@pytest.mark.filterwarnings(
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"ignore:scipy.rand is deprecated:DeprecationWarning:pyamg.*")
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def test_spectral_embedding_amg_solver_failure():
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# Non-regression test for amg solver failure (issue #13393 on github)
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pytest.importorskip('pyamg')
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seed = 36
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num_nodes = 100
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X = sparse.rand(num_nodes, num_nodes, density=0.1, random_state=seed)
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upper = sparse.triu(X) - sparse.diags(X.diagonal())
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sym_matrix = upper + upper.T
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embedding = spectral_embedding(sym_matrix,
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n_components=10,
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eigen_solver='amg',
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random_state=0)
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# Check that the learned embedding is stable w.r.t. random solver init:
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for i in range(3):
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new_embedding = spectral_embedding(sym_matrix,
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n_components=10,
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eigen_solver='amg',
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random_state=i + 1)
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_assert_equal_with_sign_flipping(embedding, new_embedding, tol=0.05)
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@pytest.mark.filterwarnings("ignore:the behavior of nmi will "
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"change in version 0.22")
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def test_pipeline_spectral_clustering(seed=36):
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# Test using pipeline to do spectral clustering
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random_state = np.random.RandomState(seed)
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se_rbf = SpectralEmbedding(n_components=n_clusters,
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affinity="rbf",
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random_state=random_state)
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se_knn = SpectralEmbedding(n_components=n_clusters,
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affinity="nearest_neighbors",
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n_neighbors=5,
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random_state=random_state)
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for se in [se_rbf, se_knn]:
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km = KMeans(n_clusters=n_clusters, random_state=random_state)
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km.fit(se.fit_transform(S))
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assert_array_almost_equal(
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normalized_mutual_info_score(
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km.labels_,
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true_labels), 1.0, 2)
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def test_spectral_embedding_unknown_eigensolver(seed=36):
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# Test that SpectralClustering fails with an unknown eigensolver
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se = SpectralEmbedding(n_components=1, affinity="precomputed",
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random_state=np.random.RandomState(seed),
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eigen_solver="<unknown>")
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with pytest.raises(ValueError):
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se.fit(S)
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def test_spectral_embedding_unknown_affinity(seed=36):
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# Test that SpectralClustering fails with an unknown affinity type
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se = SpectralEmbedding(n_components=1, affinity="<unknown>",
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random_state=np.random.RandomState(seed))
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with pytest.raises(ValueError):
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se.fit(S)
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def test_connectivity(seed=36):
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# Test that graph connectivity test works as expected
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graph = np.array([[1, 0, 0, 0, 0],
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[0, 1, 1, 0, 0],
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[0, 1, 1, 1, 0],
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[0, 0, 1, 1, 1],
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[0, 0, 0, 1, 1]])
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assert not _graph_is_connected(graph)
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assert not _graph_is_connected(sparse.csr_matrix(graph))
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assert not _graph_is_connected(sparse.csc_matrix(graph))
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graph = np.array([[1, 1, 0, 0, 0],
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[1, 1, 1, 0, 0],
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[0, 1, 1, 1, 0],
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[0, 0, 1, 1, 1],
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[0, 0, 0, 1, 1]])
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assert _graph_is_connected(graph)
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assert _graph_is_connected(sparse.csr_matrix(graph))
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assert _graph_is_connected(sparse.csc_matrix(graph))
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def test_spectral_embedding_deterministic():
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# Test that Spectral Embedding is deterministic
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random_state = np.random.RandomState(36)
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data = random_state.randn(10, 30)
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sims = rbf_kernel(data)
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embedding_1 = spectral_embedding(sims)
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embedding_2 = spectral_embedding(sims)
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assert_array_almost_equal(embedding_1, embedding_2)
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def test_spectral_embedding_unnormalized():
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# Test that spectral_embedding is also processing unnormalized laplacian
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# correctly
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random_state = np.random.RandomState(36)
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data = random_state.randn(10, 30)
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sims = rbf_kernel(data)
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n_components = 8
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embedding_1 = spectral_embedding(sims,
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norm_laplacian=False,
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n_components=n_components,
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drop_first=False)
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# Verify using manual computation with dense eigh
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laplacian, dd = csgraph.laplacian(sims, normed=False,
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return_diag=True)
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_, diffusion_map = eigh(laplacian)
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embedding_2 = diffusion_map.T[:n_components]
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embedding_2 = _deterministic_vector_sign_flip(embedding_2).T
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assert_array_almost_equal(embedding_1, embedding_2)
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def test_spectral_embedding_first_eigen_vector():
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# Test that the first eigenvector of spectral_embedding
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# is constant and that the second is not (for a connected graph)
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random_state = np.random.RandomState(36)
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data = random_state.randn(10, 30)
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sims = rbf_kernel(data)
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n_components = 2
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for seed in range(10):
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embedding = spectral_embedding(sims,
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norm_laplacian=False,
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|
n_components=n_components,
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|
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drop_first=False,
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random_state=seed)
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|
|
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assert np.std(embedding[:, 0]) == pytest.approx(0)
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assert np.std(embedding[:, 1]) > 1e-3
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