def test_random_projection_embedding_quality():
data, _ = make_sparse_random_data(8, 5000, 15000)
eps = 0.2
original_distances = euclidean_distances(data, squared=True)
original_distances = original_distances.ravel()
non_identical = original_distances != 0.0
# remove 0 distances to avoid division by 0
original_distances = original_distances[non_identical]
for RandomProjection in all_RandomProjection:
rp = RandomProjection(n_components='auto', eps=eps, random_state=0)
projected = rp.fit_transform(data)
projected_distances = euclidean_distances(projected, squared=True)
projected_distances = projected_distances.ravel()
# remove 0 distances to avoid division by 0
projected_distances = projected_distances[non_identical]
distances_ratio = projected_distances / original_distances
# check that the automatically tuned values for the density respect the
# contract for eps: pairwise distances are preserved according to the
# Johnson-Lindenstrauss lemma
assert distances_ratio.max() < 1 + eps
assert 1 - eps < distances_ratio.min()
def test_affinity_propagation_equal_mutual_similarities():
X = np.array([[-1, 1], [1, -1]])
S = -euclidean_distances(X, squared=True)
# setting preference > similarity
cluster_center_indices, labels = assert_warns_message(
UserWarning, "mutually equal", affinity_propagation, S, preference=0)
# expect every sample to become an exemplar
assert_array_equal([0, 1], cluster_center_indices)
assert_array_equal([0, 1], labels)
# setting preference < similarity
cluster_center_indices, labels = assert_warns_message(
UserWarning, "mutually equal", affinity_propagation, S, preference=-10)
# expect one cluster, with arbitrary (first) sample as exemplar
assert_array_equal([0], cluster_center_indices)
assert_array_equal([0, 0], labels)
# setting different preferences
cluster_center_indices, labels = assert_no_warnings(
affinity_propagation, S, preference=[-20, -10])
# expect one cluster, with highest-preference sample as exemplar
assert_array_equal([1], cluster_center_indices)
assert_array_equal([0, 0], labels)
def test_equal_similarities_and_preferences():
# Unequal distances
X = np.array([[0, 0], [1, 1], [-2, -2]])
S = -euclidean_distances(X, squared=True)
assert not _equal_similarities_and_preferences(S, np.array(0))
assert not _equal_similarities_and_preferences(S, np.array([0, 0]))
assert not _equal_similarities_and_preferences(S, np.array([0, 1]))
# Equal distances
X = np.array([[0, 0], [1, 1]])
S = -euclidean_distances(X, squared=True)
# Different preferences
assert not _equal_similarities_and_preferences(S, np.array([0, 1]))
# Same preferences
assert _equal_similarities_and_preferences(S, np.array([0, 0]))
assert _equal_similarities_and_preferences(S, np.array(0))
def test_affinity_propagation():
# Affinity Propagation algorithm
# Compute similarities
S = -euclidean_distances(X, squared=True)
preference = np.median(S) * 10
# Compute Affinity Propagation
cluster_centers_indices, labels = affinity_propagation(
S, preference=preference)
n_clusters_ = len(cluster_centers_indices)
assert n_clusters == n_clusters_
af = AffinityPropagation(preference=preference, affinity="precomputed")
labels_precomputed = af.fit(S).labels_
af = AffinityPropagation(preference=preference, verbose=True)
labels = af.fit(X).labels_
assert_array_equal(labels, labels_precomputed)
cluster_centers_indices = af.cluster_centers_indices_
n_clusters_ = len(cluster_centers_indices)
assert np.unique(labels).size == n_clusters_
assert n_clusters == n_clusters_
# Test also with no copy
_, labels_no_copy = affinity_propagation(S, preference=preference,
copy=False)
assert_array_equal(labels, labels_no_copy)
# Test input validation
with pytest.raises(ValueError):
affinity_propagation(S[:, :-1])
with pytest.raises(ValueError):
affinity_propagation(S, damping=0)
af = AffinityPropagation(affinity="unknown")
with pytest.raises(ValueError):
af.fit(X)
af_2 = AffinityPropagation(affinity='precomputed')
with pytest.raises(TypeError):
af_2.fit(csr_matrix((3, 3)))
from matplotlib import pyplot as plt
from matplotlib.collections import LineCollection
from mrex import manifold
from mrex.metrics import euclidean_distances
from mrex.decomposition import PCA
EPSILON = np.finfo(np.float32).eps
n_samples = 20
seed = np.random.RandomState(seed=3)
X_true = seed.randint(0, 20, 2 * n_samples).astype(np.float)
X_true = X_true.reshape((n_samples, 2))
# Center the data
X_true -= X_true.mean()
similarities = euclidean_distances(X_true)
# Add noise to the similarities
noise = np.random.rand(n_samples, n_samples)
noise = noise + noise.T
noise[np.arange(noise.shape[0]), np.arange(noise.shape[0])] = 0
similarities += noise
mds = manifold.MDS(n_components=2,
max_iter=3000,
eps=1e-9,
random_state=seed,
dissimilarity="precomputed",
n_jobs=1)
pos = mds.fit(similarities).embedding_