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_array_equal 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_harabasz_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 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 score_precomputed > 0 assert 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 not 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]) err_msg = (r'Number of labels is %d\. Valid values are 2 ' r'to n_samples - 1 \(inclusive\)' % len(np.unique(y))) with pytest.raises(ValueError, match=err_msg): silhouette_score(X, y) # n_labels = 1 y = np.zeros(X.shape[0]) err_msg = (r'Number of labels is %d\. Valid values are 2 ' r'to n_samples - 1 \(inclusive\)' % len(np.unique(y))) with pytest.raises(ValueError, match=err_msg): silhouette_score(X, y) def test_non_encoded_labels(): dataset = datasets.load_iris() X = dataset.data labels = dataset.target assert ( 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 ( silhouette_score(list(X), list(y)) == silhouette_score(X, y)) @pytest.mark.parametrize('dtype', (np.float32, np.float64)) def test_silhouette_nonzero_diag(dtype): # Make sure silhouette_samples requires diagonal to be zero. # Non-regression test for #12178 # Construct a zero-diagonal matrix dists = pairwise_distances( np.array([[0.2, 0.1, 0.12, 1.34, 1.11, 1.6]], dtype=dtype).T) labels = [0, 0, 0, 1, 1, 1] # small values on the diagonal are OK dists[2][2] = np.finfo(dists.dtype).eps * 10 silhouette_samples(dists, labels, metric='precomputed') # values bigger than eps * 100 are not dists[2][2] = np.finfo(dists.dtype).eps * 1000 with pytest.raises(ValueError, match='contains non-zero'): silhouette_samples(dists, labels, metric='precomputed') def assert_raises_on_only_one_label(func): """Assert message when there is only one label""" rng = np.random.RandomState(seed=0) with pytest.raises(ValueError, match="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) with pytest.raises(ValueError, match="Number of labels is"): func(rng.rand(10, 2), np.arange(10)) def test_calinski_harabasz_score(): assert_raises_on_only_one_label(calinski_harabasz_score) assert_raises_on_all_points_same_cluster(calinski_harabasz_score) # Assert the value is 1. when all samples are equals assert 1. == calinski_harabasz_score(np.ones((10, 2)), [0] * 5 + [1] * 5) # Assert the value is 0. when all the mean cluster are equal assert 0. == calinski_harabasz_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_harabasz_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) # Ensure divide by zero warning is not raised in general case with pytest.warns(None) as record: davies_bouldin_score(X, labels) div_zero_warnings = [ warning for warning in record if "divide by zero encountered" in warning.message.args[0] ] assert len(div_zero_warnings) == 0 # 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)