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import numpy as np
import scipy.sparse as sp
import pytest
from scipy.sparse import csr_matrix
from sklearn import datasets
from sklearn.utils.testing import assert_false
from sklearn.utils.testing import assert_array_equal
from sklearn.utils.testing import assert_equal
from sklearn.utils.testing import assert_raises_regexp
from sklearn.utils.testing import assert_raise_message
from sklearn.utils.testing import assert_greater
from sklearn.metrics.cluster import silhouette_score
from sklearn.metrics.cluster import silhouette_samples
from sklearn.metrics import pairwise_distances
from sklearn.metrics.cluster import calinski_harabaz_score
from sklearn.metrics.cluster import davies_bouldin_score
def test_silhouette():
# Tests the Silhouette Coefficient.
dataset = datasets.load_iris()
X_dense = dataset.data
X_csr = csr_matrix(X_dense)
X_dok = sp.dok_matrix(X_dense)
X_lil = sp.lil_matrix(X_dense)
y = dataset.target
for X in [X_dense, X_csr, X_dok, X_lil]:
D = pairwise_distances(X, metric='euclidean')
# Given that the actual labels are used, we can assume that S would be
# positive.
score_precomputed = silhouette_score(D, y, metric='precomputed')
assert_greater(score_precomputed, 0)
# Test without calculating D
score_euclidean = silhouette_score(X, y, metric='euclidean')
pytest.approx(score_precomputed, score_euclidean)
if X is X_dense:
score_dense_without_sampling = score_precomputed
else:
pytest.approx(score_euclidean,
score_dense_without_sampling)
# Test with sampling
score_precomputed = silhouette_score(D, y, metric='precomputed',
sample_size=int(X.shape[0] / 2),
random_state=0)
score_euclidean = silhouette_score(X, y, metric='euclidean',
sample_size=int(X.shape[0] / 2),
random_state=0)
assert_greater(score_precomputed, 0)
assert_greater(score_euclidean, 0)
pytest.approx(score_euclidean, score_precomputed)
if X is X_dense:
score_dense_with_sampling = score_precomputed
else:
pytest.approx(score_euclidean, score_dense_with_sampling)
def test_cluster_size_1():
# Assert Silhouette Coefficient == 0 when there is 1 sample in a cluster
# (cluster 0). We also test the case where there are identical samples
# as the only members of a cluster (cluster 2). To our knowledge, this case
# is not discussed in reference material, and we choose for it a sample
# score of 1.
X = [[0.], [1.], [1.], [2.], [3.], [3.]]
labels = np.array([0, 1, 1, 1, 2, 2])
# Cluster 0: 1 sample -> score of 0 by Rousseeuw's convention
# Cluster 1: intra-cluster = [.5, .5, 1]
# inter-cluster = [1, 1, 1]
# silhouette = [.5, .5, 0]
# Cluster 2: intra-cluster = [0, 0]
# inter-cluster = [arbitrary, arbitrary]
# silhouette = [1., 1.]
silhouette = silhouette_score(X, labels)
assert_false(np.isnan(silhouette))
ss = silhouette_samples(X, labels)
assert_array_equal(ss, [0, .5, .5, 0, 1, 1])
def test_silhouette_paper_example():
# Explicitly check per-sample results against Rousseeuw (1987)
# Data from Table 1
lower = [5.58,
7.00, 6.50,
7.08, 7.00, 3.83,
4.83, 5.08, 8.17, 5.83,
2.17, 5.75, 6.67, 6.92, 4.92,
6.42, 5.00, 5.58, 6.00, 4.67, 6.42,
3.42, 5.50, 6.42, 6.42, 5.00, 3.92, 6.17,
2.50, 4.92, 6.25, 7.33, 4.50, 2.25, 6.33, 2.75,
6.08, 6.67, 4.25, 2.67, 6.00, 6.17, 6.17, 6.92, 6.17,
5.25, 6.83, 4.50, 3.75, 5.75, 5.42, 6.08, 5.83, 6.67, 3.67,
4.75, 3.00, 6.08, 6.67, 5.00, 5.58, 4.83, 6.17, 5.67, 6.50, 6.92]
D = np.zeros((12, 12))
D[np.tril_indices(12, -1)] = lower
D += D.T
names = ['BEL', 'BRA', 'CHI', 'CUB', 'EGY', 'FRA', 'IND', 'ISR', 'USA',
'USS', 'YUG', 'ZAI']
# Data from Figure 2
labels1 = [1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1]
expected1 = {'USA': .43, 'BEL': .39, 'FRA': .35, 'ISR': .30, 'BRA': .22,
'EGY': .20, 'ZAI': .19, 'CUB': .40, 'USS': .34, 'CHI': .33,
'YUG': .26, 'IND': -.04}
score1 = .28
# Data from Figure 3
labels2 = [1, 2, 3, 3, 1, 1, 2, 1, 1, 3, 3, 2]
expected2 = {'USA': .47, 'FRA': .44, 'BEL': .42, 'ISR': .37, 'EGY': .02,
'ZAI': .28, 'BRA': .25, 'IND': .17, 'CUB': .48, 'USS': .44,
'YUG': .31, 'CHI': .31}
score2 = .33
for labels, expected, score in [(labels1, expected1, score1),
(labels2, expected2, score2)]:
expected = [expected[name] for name in names]
# we check to 2dp because that's what's in the paper
pytest.approx(expected,
silhouette_samples(D, np.array(labels),
metric='precomputed'),
abs=1e-2)
pytest.approx(score,
silhouette_score(D, np.array(labels),
metric='precomputed'),
abs=1e-2)
def test_correct_labelsize():
# Assert 1 < n_labels < n_samples
dataset = datasets.load_iris()
X = dataset.data
# n_labels = n_samples
y = np.arange(X.shape[0])
assert_raises_regexp(ValueError,
r'Number of labels is %d\. Valid values are 2 '
r'to n_samples - 1 \(inclusive\)' % len(np.unique(y)),
silhouette_score, X, y)
# n_labels = 1
y = np.zeros(X.shape[0])
assert_raises_regexp(ValueError,
r'Number of labels is %d\. Valid values are 2 '
r'to n_samples - 1 \(inclusive\)' % len(np.unique(y)),
silhouette_score, X, y)
def test_non_encoded_labels():
dataset = datasets.load_iris()
X = dataset.data
labels = dataset.target
assert_equal(
silhouette_score(X, labels * 2 + 10), silhouette_score(X, labels))
assert_array_equal(
silhouette_samples(X, labels * 2 + 10), silhouette_samples(X, labels))
def test_non_numpy_labels():
dataset = datasets.load_iris()
X = dataset.data
y = dataset.target
assert_equal(
silhouette_score(list(X), list(y)), silhouette_score(X, y))
def assert_raises_on_only_one_label(func):
"""Assert message when there is only one label"""
rng = np.random.RandomState(seed=0)
assert_raise_message(ValueError, "Number of labels is",
func,
rng.rand(10, 2), np.zeros(10))
def assert_raises_on_all_points_same_cluster(func):
"""Assert message when all point are in different clusters"""
rng = np.random.RandomState(seed=0)
assert_raise_message(ValueError, "Number of labels is",
func,
rng.rand(10, 2), np.arange(10))
def test_calinski_harabaz_score():
assert_raises_on_only_one_label(calinski_harabaz_score)
assert_raises_on_all_points_same_cluster(calinski_harabaz_score)
# Assert the value is 1. when all samples are equals
assert_equal(1., calinski_harabaz_score(np.ones((10, 2)),
[0] * 5 + [1] * 5))
# Assert the value is 0. when all the mean cluster are equal
assert_equal(0., calinski_harabaz_score([[-1, -1], [1, 1]] * 10,
[0] * 10 + [1] * 10))
# General case (with non numpy arrays)
X = ([[0, 0], [1, 1]] * 5 + [[3, 3], [4, 4]] * 5 +
[[0, 4], [1, 3]] * 5 + [[3, 1], [4, 0]] * 5)
labels = [0] * 10 + [1] * 10 + [2] * 10 + [3] * 10
pytest.approx(calinski_harabaz_score(X, labels),
45 * (40 - 4) / (5 * (4 - 1)))
def test_davies_bouldin_score():
assert_raises_on_only_one_label(davies_bouldin_score)
assert_raises_on_all_points_same_cluster(davies_bouldin_score)
# Assert the value is 0. when all samples are equals
assert davies_bouldin_score(np.ones((10, 2)),
[0] * 5 + [1] * 5) == pytest.approx(0.0)
# Assert the value is 0. when all the mean cluster are equal
assert davies_bouldin_score([[-1, -1], [1, 1]] * 10,
[0] * 10 + [1] * 10) == pytest.approx(0.0)
# General case (with non numpy arrays)
X = ([[0, 0], [1, 1]] * 5 + [[3, 3], [4, 4]] * 5 +
[[0, 4], [1, 3]] * 5 + [[3, 1], [4, 0]] * 5)
labels = [0] * 10 + [1] * 10 + [2] * 10 + [3] * 10
pytest.approx(davies_bouldin_score(X, labels), 2 * np.sqrt(0.5) / 3)
# General case - cluster have one sample
X = ([[0, 0], [2, 2], [3, 3], [5, 5]])
labels = [0, 0, 1, 2]
pytest.approx(davies_bouldin_score(X, labels), (5. / 4) / 3)
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