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Carla Floricel
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"""
The :mod:`sklearn.metrics.cluster` submodule contains evaluation metrics for
cluster analysis results. There are two forms of evaluation:
- supervised, which uses a ground truth class values for each sample.
- unsupervised, which does not and measures the 'quality' of the model itself.
"""
from ._supervised import adjusted_mutual_info_score
from ._supervised import normalized_mutual_info_score
from ._supervised import adjusted_rand_score
from ._supervised import rand_score
from ._supervised import completeness_score
from ._supervised import contingency_matrix
from ._supervised import pair_confusion_matrix
from ._supervised import expected_mutual_information
from ._supervised import homogeneity_completeness_v_measure
from ._supervised import homogeneity_score
from ._supervised import mutual_info_score
from ._supervised import v_measure_score
from ._supervised import fowlkes_mallows_score
from ._supervised import entropy
from ._unsupervised import silhouette_samples
from ._unsupervised import silhouette_score
from ._unsupervised import calinski_harabasz_score
from ._unsupervised import davies_bouldin_score
from ._bicluster import consensus_score
__all__ = [
"adjusted_mutual_info_score",
"normalized_mutual_info_score",
"adjusted_rand_score",
"rand_score",
"completeness_score",
"pair_confusion_matrix",
"contingency_matrix",
"expected_mutual_information",
"homogeneity_completeness_v_measure",
"homogeneity_score",
"mutual_info_score",
"v_measure_score",
"fowlkes_mallows_score",
"entropy",
"silhouette_samples",
"silhouette_score",
"calinski_harabasz_score",
"davies_bouldin_score",
"consensus_score",
]

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import numpy as np
from scipy.optimize import linear_sum_assignment
from ...utils.validation import check_consistent_length, check_array
__all__ = ["consensus_score"]
def _check_rows_and_columns(a, b):
"""Unpacks the row and column arrays and checks their shape."""
check_consistent_length(*a)
check_consistent_length(*b)
checks = lambda x: check_array(x, ensure_2d=False)
a_rows, a_cols = map(checks, a)
b_rows, b_cols = map(checks, b)
return a_rows, a_cols, b_rows, b_cols
def _jaccard(a_rows, a_cols, b_rows, b_cols):
"""Jaccard coefficient on the elements of the two biclusters."""
intersection = (a_rows * b_rows).sum() * (a_cols * b_cols).sum()
a_size = a_rows.sum() * a_cols.sum()
b_size = b_rows.sum() * b_cols.sum()
return intersection / (a_size + b_size - intersection)
def _pairwise_similarity(a, b, similarity):
"""Computes pairwise similarity matrix.
result[i, j] is the Jaccard coefficient of a's bicluster i and b's
bicluster j.
"""
a_rows, a_cols, b_rows, b_cols = _check_rows_and_columns(a, b)
n_a = a_rows.shape[0]
n_b = b_rows.shape[0]
result = np.array(
list(
list(
similarity(a_rows[i], a_cols[i], b_rows[j], b_cols[j])
for j in range(n_b)
)
for i in range(n_a)
)
)
return result
def consensus_score(a, b, *, similarity="jaccard"):
"""The similarity of two sets of biclusters.
Similarity between individual biclusters is computed. Then the
best matching between sets is found using the Hungarian algorithm.
The final score is the sum of similarities divided by the size of
the larger set.
Read more in the :ref:`User Guide <biclustering>`.
Parameters
----------
a : (rows, columns)
Tuple of row and column indicators for a set of biclusters.
b : (rows, columns)
Another set of biclusters like ``a``.
similarity : 'jaccard' or callable, default='jaccard'
May be the string "jaccard" to use the Jaccard coefficient, or
any function that takes four arguments, each of which is a 1d
indicator vector: (a_rows, a_columns, b_rows, b_columns).
References
----------
* Hochreiter, Bodenhofer, et. al., 2010. `FABIA: factor analysis
for bicluster acquisition
<https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2881408/>`__.
"""
if similarity == "jaccard":
similarity = _jaccard
matrix = _pairwise_similarity(a, b, similarity)
row_indices, col_indices = linear_sum_assignment(1.0 - matrix)
n_a = len(a[0])
n_b = len(b[0])
return matrix[row_indices, col_indices].sum() / max(n_a, n_b)

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"""Unsupervised evaluation metrics."""
# Authors: Robert Layton <robertlayton@gmail.com>
# Arnaud Fouchet <foucheta@gmail.com>
# Thierry Guillemot <thierry.guillemot.work@gmail.com>
# License: BSD 3 clause
import functools
import numpy as np
from ...utils import check_random_state
from ...utils import check_X_y
from ...utils import _safe_indexing
from ..pairwise import pairwise_distances_chunked
from ..pairwise import pairwise_distances
from ...preprocessing import LabelEncoder
def check_number_of_labels(n_labels, n_samples):
"""Check that number of labels are valid.
Parameters
----------
n_labels : int
Number of labels.
n_samples : int
Number of samples.
"""
if not 1 < n_labels < n_samples:
raise ValueError(
"Number of labels is %d. Valid values are 2 to n_samples - 1 (inclusive)"
% n_labels
)
def silhouette_score(
X, labels, *, metric="euclidean", sample_size=None, random_state=None, **kwds
):
"""Compute the mean Silhouette Coefficient of all samples.
The Silhouette Coefficient is calculated using the mean intra-cluster
distance (``a``) and the mean nearest-cluster distance (``b``) for each
sample. The Silhouette Coefficient for a sample is ``(b - a) / max(a,
b)``. To clarify, ``b`` is the distance between a sample and the nearest
cluster that the sample is not a part of.
Note that Silhouette Coefficient is only defined if number of labels
is ``2 <= n_labels <= n_samples - 1``.
This function returns the mean Silhouette Coefficient over all samples.
To obtain the values for each sample, use :func:`silhouette_samples`.
The best value is 1 and the worst value is -1. Values near 0 indicate
overlapping clusters. Negative values generally indicate that a sample has
been assigned to the wrong cluster, as a different cluster is more similar.
Read more in the :ref:`User Guide <silhouette_coefficient>`.
Parameters
----------
X : array-like of shape (n_samples_a, n_samples_a) if metric == \
"precomputed" or (n_samples_a, n_features) otherwise
An array of pairwise distances between samples, or a feature array.
labels : array-like of shape (n_samples,)
Predicted labels for each sample.
metric : str or callable, default='euclidean'
The metric to use when calculating distance between instances in a
feature array. If metric is a string, it must be one of the options
allowed by :func:`metrics.pairwise.pairwise_distances
<sklearn.metrics.pairwise.pairwise_distances>`. If ``X`` is
the distance array itself, use ``metric="precomputed"``.
sample_size : int, default=None
The size of the sample to use when computing the Silhouette Coefficient
on a random subset of the data.
If ``sample_size is None``, no sampling is used.
random_state : int, RandomState instance or None, default=None
Determines random number generation for selecting a subset of samples.
Used when ``sample_size is not None``.
Pass an int for reproducible results across multiple function calls.
See :term:`Glossary <random_state>`.
**kwds : optional keyword parameters
Any further parameters are passed directly to the distance function.
If using a scipy.spatial.distance metric, the parameters are still
metric dependent. See the scipy docs for usage examples.
Returns
-------
silhouette : float
Mean Silhouette Coefficient for all samples.
References
----------
.. [1] `Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
Interpretation and Validation of Cluster Analysis". Computational
and Applied Mathematics 20: 53-65.
<https://www.sciencedirect.com/science/article/pii/0377042787901257>`_
.. [2] `Wikipedia entry on the Silhouette Coefficient
<https://en.wikipedia.org/wiki/Silhouette_(clustering)>`_
"""
if sample_size is not None:
X, labels = check_X_y(X, labels, accept_sparse=["csc", "csr"])
random_state = check_random_state(random_state)
indices = random_state.permutation(X.shape[0])[:sample_size]
if metric == "precomputed":
X, labels = X[indices].T[indices].T, labels[indices]
else:
X, labels = X[indices], labels[indices]
return np.mean(silhouette_samples(X, labels, metric=metric, **kwds))
def _silhouette_reduce(D_chunk, start, labels, label_freqs):
"""Accumulate silhouette statistics for vertical chunk of X.
Parameters
----------
D_chunk : array-like of shape (n_chunk_samples, n_samples)
Precomputed distances for a chunk.
start : int
First index in the chunk.
labels : array-like of shape (n_samples,)
Corresponding cluster labels, encoded as {0, ..., n_clusters-1}.
label_freqs : array-like
Distribution of cluster labels in ``labels``.
"""
# accumulate distances from each sample to each cluster
clust_dists = np.zeros((len(D_chunk), len(label_freqs)), dtype=D_chunk.dtype)
for i in range(len(D_chunk)):
clust_dists[i] += np.bincount(
labels, weights=D_chunk[i], minlength=len(label_freqs)
)
# intra_index selects intra-cluster distances within clust_dists
intra_index = (np.arange(len(D_chunk)), labels[start : start + len(D_chunk)])
# intra_clust_dists are averaged over cluster size outside this function
intra_clust_dists = clust_dists[intra_index]
# of the remaining distances we normalise and extract the minimum
clust_dists[intra_index] = np.inf
clust_dists /= label_freqs
inter_clust_dists = clust_dists.min(axis=1)
return intra_clust_dists, inter_clust_dists
def silhouette_samples(X, labels, *, metric="euclidean", **kwds):
"""Compute the Silhouette Coefficient for each sample.
The Silhouette Coefficient is a measure of how well samples are clustered
with samples that are similar to themselves. Clustering models with a high
Silhouette Coefficient are said to be dense, where samples in the same
cluster are similar to each other, and well separated, where samples in
different clusters are not very similar to each other.
The Silhouette Coefficient is calculated using the mean intra-cluster
distance (``a``) and the mean nearest-cluster distance (``b``) for each
sample. The Silhouette Coefficient for a sample is ``(b - a) / max(a,
b)``.
Note that Silhouette Coefficient is only defined if number of labels
is 2 ``<= n_labels <= n_samples - 1``.
This function returns the Silhouette Coefficient for each sample.
The best value is 1 and the worst value is -1. Values near 0 indicate
overlapping clusters.
Read more in the :ref:`User Guide <silhouette_coefficient>`.
Parameters
----------
X : array-like of shape (n_samples_a, n_samples_a) if metric == \
"precomputed" or (n_samples_a, n_features) otherwise
An array of pairwise distances between samples, or a feature array.
labels : array-like of shape (n_samples,)
Label values for each sample.
metric : str or callable, default='euclidean'
The metric to use when calculating distance between instances in a
feature array. If metric is a string, it must be one of the options
allowed by :func:`sklearn.metrics.pairwise.pairwise_distances`.
If ``X`` is the distance array itself, use "precomputed" as the metric.
Precomputed distance matrices must have 0 along the diagonal.
**kwds : optional keyword parameters
Any further parameters are passed directly to the distance function.
If using a ``scipy.spatial.distance`` metric, the parameters are still
metric dependent. See the scipy docs for usage examples.
Returns
-------
silhouette : array-like of shape (n_samples,)
Silhouette Coefficients for each sample.
References
----------
.. [1] `Peter J. Rousseeuw (1987). "Silhouettes: a Graphical Aid to the
Interpretation and Validation of Cluster Analysis". Computational
and Applied Mathematics 20: 53-65.
<https://www.sciencedirect.com/science/article/pii/0377042787901257>`_
.. [2] `Wikipedia entry on the Silhouette Coefficient
<https://en.wikipedia.org/wiki/Silhouette_(clustering)>`_
"""
X, labels = check_X_y(X, labels, accept_sparse=["csc", "csr"])
# Check for non-zero diagonal entries in precomputed distance matrix
if metric == "precomputed":
error_msg = ValueError(
"The precomputed distance matrix contains non-zero "
"elements on the diagonal. Use np.fill_diagonal(X, 0)."
)
if X.dtype.kind == "f":
atol = np.finfo(X.dtype).eps * 100
if np.any(np.abs(np.diagonal(X)) > atol):
raise ValueError(error_msg)
elif np.any(np.diagonal(X) != 0): # integral dtype
raise ValueError(error_msg)
le = LabelEncoder()
labels = le.fit_transform(labels)
n_samples = len(labels)
label_freqs = np.bincount(labels)
check_number_of_labels(len(le.classes_), n_samples)
kwds["metric"] = metric
reduce_func = functools.partial(
_silhouette_reduce, labels=labels, label_freqs=label_freqs
)
results = zip(*pairwise_distances_chunked(X, reduce_func=reduce_func, **kwds))
intra_clust_dists, inter_clust_dists = results
intra_clust_dists = np.concatenate(intra_clust_dists)
inter_clust_dists = np.concatenate(inter_clust_dists)
denom = (label_freqs - 1).take(labels, mode="clip")
with np.errstate(divide="ignore", invalid="ignore"):
intra_clust_dists /= denom
sil_samples = inter_clust_dists - intra_clust_dists
with np.errstate(divide="ignore", invalid="ignore"):
sil_samples /= np.maximum(intra_clust_dists, inter_clust_dists)
# nan values are for clusters of size 1, and should be 0
return np.nan_to_num(sil_samples)
def calinski_harabasz_score(X, labels):
"""Compute the Calinski and Harabasz score.
It is also known as the Variance Ratio Criterion.
The score is defined as ratio of the sum of between-cluster dispersion and
of within-cluster dispersion.
Read more in the :ref:`User Guide <calinski_harabasz_index>`.
Parameters
----------
X : array-like of shape (n_samples, n_features)
A list of ``n_features``-dimensional data points. Each row corresponds
to a single data point.
labels : array-like of shape (n_samples,)
Predicted labels for each sample.
Returns
-------
score : float
The resulting Calinski-Harabasz score.
References
----------
.. [1] `T. Calinski and J. Harabasz, 1974. "A dendrite method for cluster
analysis". Communications in Statistics
<https://www.tandfonline.com/doi/abs/10.1080/03610927408827101>`_
"""
X, labels = check_X_y(X, labels)
le = LabelEncoder()
labels = le.fit_transform(labels)
n_samples, _ = X.shape
n_labels = len(le.classes_)
check_number_of_labels(n_labels, n_samples)
extra_disp, intra_disp = 0.0, 0.0
mean = np.mean(X, axis=0)
for k in range(n_labels):
cluster_k = X[labels == k]
mean_k = np.mean(cluster_k, axis=0)
extra_disp += len(cluster_k) * np.sum((mean_k - mean) ** 2)
intra_disp += np.sum((cluster_k - mean_k) ** 2)
return (
1.0
if intra_disp == 0.0
else extra_disp * (n_samples - n_labels) / (intra_disp * (n_labels - 1.0))
)
def davies_bouldin_score(X, labels):
"""Compute the Davies-Bouldin score.
The score is defined as the average similarity measure of each cluster with
its most similar cluster, where similarity is the ratio of within-cluster
distances to between-cluster distances. Thus, clusters which are farther
apart and less dispersed will result in a better score.
The minimum score is zero, with lower values indicating better clustering.
Read more in the :ref:`User Guide <davies-bouldin_index>`.
.. versionadded:: 0.20
Parameters
----------
X : array-like of shape (n_samples, n_features)
A list of ``n_features``-dimensional data points. Each row corresponds
to a single data point.
labels : array-like of shape (n_samples,)
Predicted labels for each sample.
Returns
-------
score: float
The resulting Davies-Bouldin score.
References
----------
.. [1] Davies, David L.; Bouldin, Donald W. (1979).
`"A Cluster Separation Measure"
<https://ieeexplore.ieee.org/document/4766909>`__.
IEEE Transactions on Pattern Analysis and Machine Intelligence.
PAMI-1 (2): 224-227
"""
X, labels = check_X_y(X, labels)
le = LabelEncoder()
labels = le.fit_transform(labels)
n_samples, _ = X.shape
n_labels = len(le.classes_)
check_number_of_labels(n_labels, n_samples)
intra_dists = np.zeros(n_labels)
centroids = np.zeros((n_labels, len(X[0])), dtype=float)
for k in range(n_labels):
cluster_k = _safe_indexing(X, labels == k)
centroid = cluster_k.mean(axis=0)
centroids[k] = centroid
intra_dists[k] = np.average(pairwise_distances(cluster_k, [centroid]))
centroid_distances = pairwise_distances(centroids)
if np.allclose(intra_dists, 0) or np.allclose(centroid_distances, 0):
return 0.0
centroid_distances[centroid_distances == 0] = np.inf
combined_intra_dists = intra_dists[:, None] + intra_dists
scores = np.max(combined_intra_dists / centroid_distances, axis=1)
return np.mean(scores)

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import os
import numpy
from numpy.distutils.misc_util import Configuration
def configuration(parent_package="", top_path=None):
config = Configuration("cluster", parent_package, top_path)
libraries = []
if os.name == "posix":
libraries.append("m")
config.add_extension(
"_expected_mutual_info_fast",
sources=["_expected_mutual_info_fast.pyx"],
include_dirs=[numpy.get_include()],
libraries=libraries,
)
config.add_subpackage("tests")
return config
if __name__ == "__main__":
from numpy.distutils.core import setup
setup(**configuration().todict())

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"""Testing for bicluster metrics module"""
import numpy as np
from sklearn.utils._testing import assert_almost_equal
from sklearn.metrics.cluster._bicluster import _jaccard
from sklearn.metrics import consensus_score
def test_jaccard():
a1 = np.array([True, True, False, False])
a2 = np.array([True, True, True, True])
a3 = np.array([False, True, True, False])
a4 = np.array([False, False, True, True])
assert _jaccard(a1, a1, a1, a1) == 1
assert _jaccard(a1, a1, a2, a2) == 0.25
assert _jaccard(a1, a1, a3, a3) == 1.0 / 7
assert _jaccard(a1, a1, a4, a4) == 0
def test_consensus_score():
a = [[True, True, False, False], [False, False, True, True]]
b = a[::-1]
assert consensus_score((a, a), (a, a)) == 1
assert consensus_score((a, a), (b, b)) == 1
assert consensus_score((a, b), (a, b)) == 1
assert consensus_score((a, b), (b, a)) == 1
assert consensus_score((a, a), (b, a)) == 0
assert consensus_score((a, a), (a, b)) == 0
assert consensus_score((b, b), (a, b)) == 0
assert consensus_score((b, b), (b, a)) == 0
def test_consensus_score_issue2445():
"""Different number of biclusters in A and B"""
a_rows = np.array(
[
[True, True, False, False],
[False, False, True, True],
[False, False, False, True],
]
)
a_cols = np.array(
[
[True, True, False, False],
[False, False, True, True],
[False, False, False, True],
]
)
idx = [0, 2]
s = consensus_score((a_rows, a_cols), (a_rows[idx], a_cols[idx]))
# B contains 2 of the 3 biclusters in A, so score should be 2/3
assert_almost_equal(s, 2.0 / 3.0)

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from functools import partial
from itertools import chain
import pytest
import numpy as np
from sklearn.metrics.cluster import adjusted_mutual_info_score
from sklearn.metrics.cluster import adjusted_rand_score
from sklearn.metrics.cluster import rand_score
from sklearn.metrics.cluster import completeness_score
from sklearn.metrics.cluster import fowlkes_mallows_score
from sklearn.metrics.cluster import homogeneity_score
from sklearn.metrics.cluster import mutual_info_score
from sklearn.metrics.cluster import normalized_mutual_info_score
from sklearn.metrics.cluster import v_measure_score
from sklearn.metrics.cluster import silhouette_score
from sklearn.metrics.cluster import calinski_harabasz_score
from sklearn.metrics.cluster import davies_bouldin_score
from sklearn.utils._testing import assert_allclose
# Dictionaries of metrics
# ------------------------
# The goal of having those dictionaries is to have an easy way to call a
# particular metric and associate a name to each function:
# - SUPERVISED_METRICS: all supervised cluster metrics - (when given a
# ground truth value)
# - UNSUPERVISED_METRICS: all unsupervised cluster metrics
#
# Those dictionaries will be used to test systematically some invariance
# properties, e.g. invariance toward several input layout.
#
SUPERVISED_METRICS = {
"adjusted_mutual_info_score": adjusted_mutual_info_score,
"adjusted_rand_score": adjusted_rand_score,
"rand_score": rand_score,
"completeness_score": completeness_score,
"homogeneity_score": homogeneity_score,
"mutual_info_score": mutual_info_score,
"normalized_mutual_info_score": normalized_mutual_info_score,
"v_measure_score": v_measure_score,
"fowlkes_mallows_score": fowlkes_mallows_score,
}
UNSUPERVISED_METRICS = {
"silhouette_score": silhouette_score,
"silhouette_manhattan": partial(silhouette_score, metric="manhattan"),
"calinski_harabasz_score": calinski_harabasz_score,
"davies_bouldin_score": davies_bouldin_score,
}
# Lists of metrics with common properties
# ---------------------------------------
# Lists of metrics with common properties are used to test systematically some
# functionalities and invariance, e.g. SYMMETRIC_METRICS lists all metrics
# that are symmetric with respect to their input argument y_true and y_pred.
#
# --------------------------------------------------------------------
# Symmetric with respect to their input arguments y_true and y_pred.
# Symmetric metrics only apply to supervised clusters.
SYMMETRIC_METRICS = [
"adjusted_rand_score",
"rand_score",
"v_measure_score",
"mutual_info_score",
"adjusted_mutual_info_score",
"normalized_mutual_info_score",
"fowlkes_mallows_score",
]
NON_SYMMETRIC_METRICS = ["homogeneity_score", "completeness_score"]
# Metrics whose upper bound is 1
NORMALIZED_METRICS = [
"adjusted_rand_score",
"rand_score",
"homogeneity_score",
"completeness_score",
"v_measure_score",
"adjusted_mutual_info_score",
"fowlkes_mallows_score",
"normalized_mutual_info_score",
]
rng = np.random.RandomState(0)
y1 = rng.randint(3, size=30)
y2 = rng.randint(3, size=30)
def test_symmetric_non_symmetric_union():
assert sorted(SYMMETRIC_METRICS + NON_SYMMETRIC_METRICS) == sorted(
SUPERVISED_METRICS
)
# 0.22 AMI and NMI changes
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize(
"metric_name, y1, y2", [(name, y1, y2) for name in SYMMETRIC_METRICS]
)
def test_symmetry(metric_name, y1, y2):
metric = SUPERVISED_METRICS[metric_name]
assert metric(y1, y2) == pytest.approx(metric(y2, y1))
@pytest.mark.parametrize(
"metric_name, y1, y2", [(name, y1, y2) for name in NON_SYMMETRIC_METRICS]
)
def test_non_symmetry(metric_name, y1, y2):
metric = SUPERVISED_METRICS[metric_name]
assert metric(y1, y2) != pytest.approx(metric(y2, y1))
# 0.22 AMI and NMI changes
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize("metric_name", NORMALIZED_METRICS)
def test_normalized_output(metric_name):
upper_bound_1 = [0, 0, 0, 1, 1, 1]
upper_bound_2 = [0, 0, 0, 1, 1, 1]
metric = SUPERVISED_METRICS[metric_name]
assert metric([0, 0, 0, 1, 1], [0, 0, 0, 1, 2]) > 0.0
assert metric([0, 0, 1, 1, 2], [0, 0, 1, 1, 1]) > 0.0
assert metric([0, 0, 0, 1, 2], [0, 1, 1, 1, 1]) < 1.0
assert metric([0, 0, 0, 1, 2], [0, 1, 1, 1, 1]) < 1.0
assert metric(upper_bound_1, upper_bound_2) == pytest.approx(1.0)
lower_bound_1 = [0, 0, 0, 0, 0, 0]
lower_bound_2 = [0, 1, 2, 3, 4, 5]
score = np.array(
[metric(lower_bound_1, lower_bound_2), metric(lower_bound_2, lower_bound_1)]
)
assert not (score < 0).any()
# 0.22 AMI and NMI changes
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize("metric_name", chain(SUPERVISED_METRICS, UNSUPERVISED_METRICS))
def test_permute_labels(metric_name):
# All clustering metrics do not change score due to permutations of labels
# that is when 0 and 1 exchanged.
y_label = np.array([0, 0, 0, 1, 1, 0, 1])
y_pred = np.array([1, 0, 1, 0, 1, 1, 0])
if metric_name in SUPERVISED_METRICS:
metric = SUPERVISED_METRICS[metric_name]
score_1 = metric(y_pred, y_label)
assert_allclose(score_1, metric(1 - y_pred, y_label))
assert_allclose(score_1, metric(1 - y_pred, 1 - y_label))
assert_allclose(score_1, metric(y_pred, 1 - y_label))
else:
metric = UNSUPERVISED_METRICS[metric_name]
X = np.random.randint(10, size=(7, 10))
score_1 = metric(X, y_pred)
assert_allclose(score_1, metric(X, 1 - y_pred))
# 0.22 AMI and NMI changes
@pytest.mark.filterwarnings("ignore::FutureWarning")
@pytest.mark.parametrize("metric_name", chain(SUPERVISED_METRICS, UNSUPERVISED_METRICS))
# For all clustering metrics Input parameters can be both
# in the form of arrays lists, positive, negative or string
def test_format_invariance(metric_name):
y_true = [0, 0, 0, 0, 1, 1, 1, 1]
y_pred = [0, 1, 2, 3, 4, 5, 6, 7]
def generate_formats(y):
y = np.array(y)
yield y, "array of ints"
yield y.tolist(), "list of ints"
yield [str(x) + "-a" for x in y.tolist()], "list of strs"
yield (
np.array([str(x) + "-a" for x in y.tolist()], dtype=object),
"array of strs",
)
yield y - 1, "including negative ints"
yield y + 1, "strictly positive ints"
if metric_name in SUPERVISED_METRICS:
metric = SUPERVISED_METRICS[metric_name]
score_1 = metric(y_true, y_pred)
y_true_gen = generate_formats(y_true)
y_pred_gen = generate_formats(y_pred)
for (y_true_fmt, fmt_name), (y_pred_fmt, _) in zip(y_true_gen, y_pred_gen):
assert score_1 == metric(y_true_fmt, y_pred_fmt)
else:
metric = UNSUPERVISED_METRICS[metric_name]
X = np.random.randint(10, size=(8, 10))
score_1 = metric(X, y_true)
assert score_1 == metric(X.astype(float), y_true)
y_true_gen = generate_formats(y_true)
for y_true_fmt, fmt_name in y_true_gen:
assert score_1 == metric(X, y_true_fmt)
@pytest.mark.parametrize("metric", SUPERVISED_METRICS.values())
def test_single_sample(metric):
# only the supervised metrics support single sample
for i, j in [(0, 0), (0, 1), (1, 0), (1, 1)]:
metric([i], [j])
@pytest.mark.parametrize(
"metric_name, metric_func", dict(SUPERVISED_METRICS, **UNSUPERVISED_METRICS).items()
)
def test_inf_nan_input(metric_name, metric_func):
if metric_name in SUPERVISED_METRICS:
invalids = [
([0, 1], [np.inf, np.inf]),
([0, 1], [np.nan, np.nan]),
([0, 1], [np.nan, np.inf]),
]
else:
X = np.random.randint(10, size=(2, 10))
invalids = [(X, [np.inf, np.inf]), (X, [np.nan, np.nan]), (X, [np.nan, np.inf])]
with pytest.raises(ValueError, match=r"contains (NaN|infinity)"):
for args in invalids:
metric_func(*args)

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import warnings
import numpy as np
import pytest
from sklearn.metrics.cluster import adjusted_mutual_info_score
from sklearn.metrics.cluster import adjusted_rand_score
from sklearn.metrics.cluster import rand_score
from sklearn.metrics.cluster import completeness_score
from sklearn.metrics.cluster import contingency_matrix
from sklearn.metrics.cluster import pair_confusion_matrix
from sklearn.metrics.cluster import entropy
from sklearn.metrics.cluster import expected_mutual_information
from sklearn.metrics.cluster import fowlkes_mallows_score
from sklearn.metrics.cluster import homogeneity_completeness_v_measure
from sklearn.metrics.cluster import homogeneity_score
from sklearn.metrics.cluster import mutual_info_score
from sklearn.metrics.cluster import normalized_mutual_info_score
from sklearn.metrics.cluster import v_measure_score
from sklearn.metrics.cluster._supervised import _generalized_average
from sklearn.metrics.cluster._supervised import check_clusterings
from sklearn.utils import assert_all_finite
from sklearn.utils._testing import assert_almost_equal
from numpy.testing import assert_array_equal, assert_array_almost_equal, assert_allclose
score_funcs = [
adjusted_rand_score,
rand_score,
homogeneity_score,
completeness_score,
v_measure_score,
adjusted_mutual_info_score,
normalized_mutual_info_score,
]
def test_error_messages_on_wrong_input():
for score_func in score_funcs:
expected = (
r"Found input variables with inconsistent numbers " r"of samples: \[2, 3\]"
)
with pytest.raises(ValueError, match=expected):
score_func([0, 1], [1, 1, 1])
expected = r"labels_true must be 1D: shape is \(2"
with pytest.raises(ValueError, match=expected):
score_func([[0, 1], [1, 0]], [1, 1, 1])
expected = r"labels_pred must be 1D: shape is \(2"
with pytest.raises(ValueError, match=expected):
score_func([0, 1, 0], [[1, 1], [0, 0]])
def test_generalized_average():
a, b = 1, 2
methods = ["min", "geometric", "arithmetic", "max"]
means = [_generalized_average(a, b, method) for method in methods]
assert means[0] <= means[1] <= means[2] <= means[3]
c, d = 12, 12
means = [_generalized_average(c, d, method) for method in methods]
assert means[0] == means[1] == means[2] == means[3]
def test_perfect_matches():
for score_func in score_funcs:
assert score_func([], []) == pytest.approx(1.0)
assert score_func([0], [1]) == pytest.approx(1.0)
assert score_func([0, 0, 0], [0, 0, 0]) == pytest.approx(1.0)
assert score_func([0, 1, 0], [42, 7, 42]) == pytest.approx(1.0)
assert score_func([0.0, 1.0, 0.0], [42.0, 7.0, 42.0]) == pytest.approx(1.0)
assert score_func([0.0, 1.0, 2.0], [42.0, 7.0, 2.0]) == pytest.approx(1.0)
assert score_func([0, 1, 2], [42, 7, 2]) == pytest.approx(1.0)
score_funcs_with_changing_means = [
normalized_mutual_info_score,
adjusted_mutual_info_score,
]
means = {"min", "geometric", "arithmetic", "max"}
for score_func in score_funcs_with_changing_means:
for mean in means:
assert score_func([], [], average_method=mean) == pytest.approx(1.0)
assert score_func([0], [1], average_method=mean) == pytest.approx(1.0)
assert score_func(
[0, 0, 0], [0, 0, 0], average_method=mean
) == pytest.approx(1.0)
assert score_func(
[0, 1, 0], [42, 7, 42], average_method=mean
) == pytest.approx(1.0)
assert score_func(
[0.0, 1.0, 0.0], [42.0, 7.0, 42.0], average_method=mean
) == pytest.approx(1.0)
assert score_func(
[0.0, 1.0, 2.0], [42.0, 7.0, 2.0], average_method=mean
) == pytest.approx(1.0)
assert score_func(
[0, 1, 2], [42, 7, 2], average_method=mean
) == pytest.approx(1.0)
def test_homogeneous_but_not_complete_labeling():
# homogeneous but not complete clustering
h, c, v = homogeneity_completeness_v_measure([0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 2, 2])
assert_almost_equal(h, 1.00, 2)
assert_almost_equal(c, 0.69, 2)
assert_almost_equal(v, 0.81, 2)
def test_complete_but_not_homogeneous_labeling():
# complete but not homogeneous clustering
h, c, v = homogeneity_completeness_v_measure([0, 0, 1, 1, 2, 2], [0, 0, 1, 1, 1, 1])
assert_almost_equal(h, 0.58, 2)
assert_almost_equal(c, 1.00, 2)
assert_almost_equal(v, 0.73, 2)
def test_not_complete_and_not_homogeneous_labeling():
# neither complete nor homogeneous but not so bad either
h, c, v = homogeneity_completeness_v_measure([0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 2, 2])
assert_almost_equal(h, 0.67, 2)
assert_almost_equal(c, 0.42, 2)
assert_almost_equal(v, 0.52, 2)
def test_beta_parameter():
# test for when beta passed to
# homogeneity_completeness_v_measure
# and v_measure_score
beta_test = 0.2
h_test = 0.67
c_test = 0.42
v_test = (1 + beta_test) * h_test * c_test / (beta_test * h_test + c_test)
h, c, v = homogeneity_completeness_v_measure(
[0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 2, 2], beta=beta_test
)
assert_almost_equal(h, h_test, 2)
assert_almost_equal(c, c_test, 2)
assert_almost_equal(v, v_test, 2)
v = v_measure_score([0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 2, 2], beta=beta_test)
assert_almost_equal(v, v_test, 2)
def test_non_consecutive_labels():
# regression tests for labels with gaps
h, c, v = homogeneity_completeness_v_measure([0, 0, 0, 2, 2, 2], [0, 1, 0, 1, 2, 2])
assert_almost_equal(h, 0.67, 2)
assert_almost_equal(c, 0.42, 2)
assert_almost_equal(v, 0.52, 2)
h, c, v = homogeneity_completeness_v_measure([0, 0, 0, 1, 1, 1], [0, 4, 0, 4, 2, 2])
assert_almost_equal(h, 0.67, 2)
assert_almost_equal(c, 0.42, 2)
assert_almost_equal(v, 0.52, 2)
ari_1 = adjusted_rand_score([0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 2, 2])
ari_2 = adjusted_rand_score([0, 0, 0, 1, 1, 1], [0, 4, 0, 4, 2, 2])
assert_almost_equal(ari_1, 0.24, 2)
assert_almost_equal(ari_2, 0.24, 2)
ri_1 = rand_score([0, 0, 0, 1, 1, 1], [0, 1, 0, 1, 2, 2])
ri_2 = rand_score([0, 0, 0, 1, 1, 1], [0, 4, 0, 4, 2, 2])
assert_almost_equal(ri_1, 0.66, 2)
assert_almost_equal(ri_2, 0.66, 2)
def uniform_labelings_scores(score_func, n_samples, k_range, n_runs=10, seed=42):
# Compute score for random uniform cluster labelings
random_labels = np.random.RandomState(seed).randint
scores = np.zeros((len(k_range), n_runs))
for i, k in enumerate(k_range):
for j in range(n_runs):
labels_a = random_labels(low=0, high=k, size=n_samples)
labels_b = random_labels(low=0, high=k, size=n_samples)
scores[i, j] = score_func(labels_a, labels_b)
return scores
def test_adjustment_for_chance():
# Check that adjusted scores are almost zero on random labels
n_clusters_range = [2, 10, 50, 90]
n_samples = 100
n_runs = 10
scores = uniform_labelings_scores(
adjusted_rand_score, n_samples, n_clusters_range, n_runs
)
max_abs_scores = np.abs(scores).max(axis=1)
assert_array_almost_equal(max_abs_scores, [0.02, 0.03, 0.03, 0.02], 2)
def test_adjusted_mutual_info_score():
# Compute the Adjusted Mutual Information and test against known values
labels_a = np.array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3])
labels_b = np.array([1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 3, 3, 2, 2])
# Mutual information
mi = mutual_info_score(labels_a, labels_b)
assert_almost_equal(mi, 0.41022, 5)
# with provided sparse contingency
C = contingency_matrix(labels_a, labels_b, sparse=True)
mi = mutual_info_score(labels_a, labels_b, contingency=C)
assert_almost_equal(mi, 0.41022, 5)
# with provided dense contingency
C = contingency_matrix(labels_a, labels_b)
mi = mutual_info_score(labels_a, labels_b, contingency=C)
assert_almost_equal(mi, 0.41022, 5)
# Expected mutual information
n_samples = C.sum()
emi = expected_mutual_information(C, n_samples)
assert_almost_equal(emi, 0.15042, 5)
# Adjusted mutual information
ami = adjusted_mutual_info_score(labels_a, labels_b)
assert_almost_equal(ami, 0.27821, 5)
ami = adjusted_mutual_info_score([1, 1, 2, 2], [2, 2, 3, 3])
assert ami == pytest.approx(1.0)
# Test with a very large array
a110 = np.array([list(labels_a) * 110]).flatten()
b110 = np.array([list(labels_b) * 110]).flatten()
ami = adjusted_mutual_info_score(a110, b110)
assert_almost_equal(ami, 0.38, 2)
def test_expected_mutual_info_overflow():
# Test for regression where contingency cell exceeds 2**16
# leading to overflow in np.outer, resulting in EMI > 1
assert expected_mutual_information(np.array([[70000]]), 70000) <= 1
def test_int_overflow_mutual_info_fowlkes_mallows_score():
# Test overflow in mutual_info_classif and fowlkes_mallows_score
x = np.array(
[1] * (52632 + 2529)
+ [2] * (14660 + 793)
+ [3] * (3271 + 204)
+ [4] * (814 + 39)
+ [5] * (316 + 20)
)
y = np.array(
[0] * 52632
+ [1] * 2529
+ [0] * 14660
+ [1] * 793
+ [0] * 3271
+ [1] * 204
+ [0] * 814
+ [1] * 39
+ [0] * 316
+ [1] * 20
)
assert_all_finite(mutual_info_score(x, y))
assert_all_finite(fowlkes_mallows_score(x, y))
def test_entropy():
ent = entropy([0, 0, 42.0])
assert_almost_equal(ent, 0.6365141, 5)
assert_almost_equal(entropy([]), 1)
assert entropy([1, 1, 1, 1]) == 0
def test_contingency_matrix():
labels_a = np.array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3])
labels_b = np.array([1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 3, 3, 2, 2])
C = contingency_matrix(labels_a, labels_b)
C2 = np.histogram2d(labels_a, labels_b, bins=(np.arange(1, 5), np.arange(1, 5)))[0]
assert_array_almost_equal(C, C2)
C = contingency_matrix(labels_a, labels_b, eps=0.1)
assert_array_almost_equal(C, C2 + 0.1)
def test_contingency_matrix_sparse():
labels_a = np.array([1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3])
labels_b = np.array([1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 3, 3, 3, 2, 2])
C = contingency_matrix(labels_a, labels_b)
C_sparse = contingency_matrix(labels_a, labels_b, sparse=True).toarray()
assert_array_almost_equal(C, C_sparse)
with pytest.raises(ValueError, match="Cannot set 'eps' when sparse=True"):
contingency_matrix(labels_a, labels_b, eps=1e-10, sparse=True)
def test_exactly_zero_info_score():
# Check numerical stability when information is exactly zero
for i in np.logspace(1, 4, 4).astype(int):
labels_a, labels_b = (np.ones(i, dtype=int), np.arange(i, dtype=int))
assert normalized_mutual_info_score(labels_a, labels_b) == pytest.approx(0.0)
assert v_measure_score(labels_a, labels_b) == pytest.approx(0.0)
assert adjusted_mutual_info_score(labels_a, labels_b) == pytest.approx(0.0)
assert normalized_mutual_info_score(labels_a, labels_b) == pytest.approx(0.0)
for method in ["min", "geometric", "arithmetic", "max"]:
assert adjusted_mutual_info_score(
labels_a, labels_b, average_method=method
) == pytest.approx(0.0)
assert normalized_mutual_info_score(
labels_a, labels_b, average_method=method
) == pytest.approx(0.0)
def test_v_measure_and_mutual_information(seed=36):
# Check relation between v_measure, entropy and mutual information
for i in np.logspace(1, 4, 4).astype(int):
random_state = np.random.RandomState(seed)
labels_a, labels_b = (
random_state.randint(0, 10, i),
random_state.randint(0, 10, i),
)
assert_almost_equal(
v_measure_score(labels_a, labels_b),
2.0
* mutual_info_score(labels_a, labels_b)
/ (entropy(labels_a) + entropy(labels_b)),
0,
)
avg = "arithmetic"
assert_almost_equal(
v_measure_score(labels_a, labels_b),
normalized_mutual_info_score(labels_a, labels_b, average_method=avg),
)
def test_fowlkes_mallows_score():
# General case
score = fowlkes_mallows_score([0, 0, 0, 1, 1, 1], [0, 0, 1, 1, 2, 2])
assert_almost_equal(score, 4.0 / np.sqrt(12.0 * 6.0))
# Perfect match but where the label names changed
perfect_score = fowlkes_mallows_score([0, 0, 0, 1, 1, 1], [1, 1, 1, 0, 0, 0])
assert_almost_equal(perfect_score, 1.0)
# Worst case
worst_score = fowlkes_mallows_score([0, 0, 0, 0, 0, 0], [0, 1, 2, 3, 4, 5])
assert_almost_equal(worst_score, 0.0)
def test_fowlkes_mallows_score_properties():
# handcrafted example
labels_a = np.array([0, 0, 0, 1, 1, 2])
labels_b = np.array([1, 1, 2, 2, 0, 0])
expected = 1.0 / np.sqrt((1.0 + 3.0) * (1.0 + 2.0))
# FMI = TP / sqrt((TP + FP) * (TP + FN))
score_original = fowlkes_mallows_score(labels_a, labels_b)
assert_almost_equal(score_original, expected)
# symmetric property
score_symmetric = fowlkes_mallows_score(labels_b, labels_a)
assert_almost_equal(score_symmetric, expected)
# permutation property
score_permuted = fowlkes_mallows_score((labels_a + 1) % 3, labels_b)
assert_almost_equal(score_permuted, expected)
# symmetric and permutation(both together)
score_both = fowlkes_mallows_score(labels_b, (labels_a + 2) % 3)
assert_almost_equal(score_both, expected)
@pytest.mark.parametrize(
"labels_true, labels_pred",
[
(["a"] * 6, [1, 1, 0, 0, 1, 1]),
([1] * 6, [1, 1, 0, 0, 1, 1]),
([1, 1, 0, 0, 1, 1], ["a"] * 6),
([1, 1, 0, 0, 1, 1], [1] * 6),
(["a"] * 6, ["a"] * 6),
],
)
def test_mutual_info_score_positive_constant_label(labels_true, labels_pred):
# Check that MI = 0 when one or both labelling are constant
# non-regression test for #16355
assert mutual_info_score(labels_true, labels_pred) == 0
def test_check_clustering_error():
# Test warning message for continuous values
rng = np.random.RandomState(42)
noise = rng.rand(500)
wavelength = np.linspace(0.01, 1, 500) * 1e-6
msg = (
"Clustering metrics expects discrete values but received "
"continuous values for label, and continuous values for "
"target"
)
with pytest.warns(UserWarning, match=msg):
check_clusterings(wavelength, noise)
def test_pair_confusion_matrix_fully_dispersed():
# edge case: every element is its own cluster
N = 100
clustering1 = list(range(N))
clustering2 = clustering1
expected = np.array([[N * (N - 1), 0], [0, 0]])
assert_array_equal(pair_confusion_matrix(clustering1, clustering2), expected)
def test_pair_confusion_matrix_single_cluster():
# edge case: only one cluster
N = 100
clustering1 = np.zeros((N,))
clustering2 = clustering1
expected = np.array([[0, 0], [0, N * (N - 1)]])
assert_array_equal(pair_confusion_matrix(clustering1, clustering2), expected)
def test_pair_confusion_matrix():
# regular case: different non-trivial clusterings
n = 10
N = n**2
clustering1 = np.hstack([[i + 1] * n for i in range(n)])
clustering2 = np.hstack([[i + 1] * (n + 1) for i in range(n)])[:N]
# basic quadratic implementation
expected = np.zeros(shape=(2, 2), dtype=np.int64)
for i in range(len(clustering1)):
for j in range(len(clustering2)):
if i != j:
same_cluster_1 = int(clustering1[i] == clustering1[j])
same_cluster_2 = int(clustering2[i] == clustering2[j])
expected[same_cluster_1, same_cluster_2] += 1
assert_array_equal(pair_confusion_matrix(clustering1, clustering2), expected)
@pytest.mark.parametrize(
"clustering1, clustering2",
[(list(range(100)), list(range(100))), (np.zeros((100,)), np.zeros((100,)))],
)
def test_rand_score_edge_cases(clustering1, clustering2):
# edge case 1: every element is its own cluster
# edge case 2: only one cluster
assert_allclose(rand_score(clustering1, clustering2), 1.0)
def test_rand_score():
# regular case: different non-trivial clusterings
clustering1 = [0, 0, 0, 1, 1, 1]
clustering2 = [0, 1, 0, 1, 2, 2]
# pair confusion matrix
D11 = 2 * 2 # ordered pairs (1, 3), (5, 6)
D10 = 2 * 4 # ordered pairs (1, 2), (2, 3), (4, 5), (4, 6)
D01 = 2 * 1 # ordered pair (2, 4)
D00 = 5 * 6 - D11 - D01 - D10 # the remaining pairs
# rand score
expected_numerator = D00 + D11
expected_denominator = D00 + D01 + D10 + D11
expected = expected_numerator / expected_denominator
assert_allclose(rand_score(clustering1, clustering2), expected)
def test_adjusted_rand_score_overflow():
"""Check that large amount of data will not lead to overflow in
`adjusted_rand_score`.
Non-regression test for:
https://github.com/scikit-learn/scikit-learn/issues/20305
"""
rng = np.random.RandomState(0)
y_true = rng.randint(0, 2, 100_000, dtype=np.int8)
y_pred = rng.randint(0, 2, 100_000, dtype=np.int8)
with warnings.catch_warnings():
warnings.simplefilter("error", RuntimeWarning)
adjusted_rand_score(y_true, y_pred)
@pytest.mark.parametrize("average_method", ["min", "arithmetic", "geometric", "max"])
def test_normalized_mutual_info_score_bounded(average_method):
"""Check that nmi returns a score between 0 (included) and 1 (excluded
for non-perfect match)
Non-regression test for issue #13836
"""
labels1 = [0] * 469
labels2 = [1] + labels1[1:]
labels3 = [0, 1] + labels1[2:]
# labels1 is constant. The mutual info between labels1 and any other labelling is 0.
nmi = normalized_mutual_info_score(labels1, labels2, average_method=average_method)
assert nmi == 0
# non constant, non perfect matching labels
nmi = normalized_mutual_info_score(labels2, labels3, average_method=average_method)
assert 0 <= nmi < 1

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import warnings
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 = [[0.0], [1.0], [1.0], [2.0], [3.0], [3.0]]
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, 0.5, 0.5, 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": 0.43,
"BEL": 0.39,
"FRA": 0.35,
"ISR": 0.30,
"BRA": 0.22,
"EGY": 0.20,
"ZAI": 0.19,
"CUB": 0.40,
"USS": 0.34,
"CHI": 0.33,
"YUG": 0.26,
"IND": -0.04,
}
score1 = 0.28
# Data from Figure 3
labels2 = [1, 2, 3, 3, 1, 1, 2, 1, 1, 3, 3, 2]
expected2 = {
"USA": 0.47,
"FRA": 0.44,
"BEL": 0.42,
"ISR": 0.37,
"EGY": 0.02,
"ZAI": 0.28,
"BRA": 0.25,
"IND": 0.17,
"CUB": 0.48,
"USS": 0.44,
"YUG": 0.31,
"CHI": 0.31,
}
score2 = 0.33
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 1.0 == calinski_harabasz_score(np.ones((10, 2)), [0] * 5 + [1] * 5)
# Assert the value is 0. when all the mean cluster are equal
assert 0.0 == 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 warnings.catch_warnings():
warnings.simplefilter("error", RuntimeWarning)
davies_bouldin_score(X, labels)
# 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), (5.0 / 4) / 3)
def test_silhouette_score_integer_precomputed():
"""Check that silhouette_score works for precomputed metrics that are integers.
Non-regression test for #22107.
"""
result = silhouette_score(
[[0, 1, 2], [1, 0, 1], [2, 1, 0]], [0, 0, 1], metric="precomputed"
)
assert result == pytest.approx(1 / 6)
# non-zero on diagonal for ints raises an error
with pytest.raises(ValueError, match="contains non-zero"):
silhouette_score(
[[1, 1, 2], [1, 0, 1], [2, 1, 0]], [0, 0, 1], metric="precomputed"
)