"""
Evaluation metrics related to clustering.
"""
# Created by Wenjie Du <wenjay.du@gmail.com>
# License: BSD-3-Clause
import numpy as np
from sklearn import metrics
[docs]
def calc_rand_index(
class_predictions: np.ndarray,
targets: np.ndarray,
) -> float:
"""Calculate Rand Index, a measure of the similarity between two data clusterings.
Refer to :cite:`rand1971RandIndex`.
Parameters
----------
class_predictions :
Clustering results returned by a clusterer.
targets :
Ground truth (correct) clustering results.
Returns
-------
RI :
Rand index.
References
----------
.. L. Hubert and P. Arabie, Comparing Partitions, Journal of
Classification 1985
https://link.springer.com/article/10.1007%2FBF01908075
.. https://en.wikipedia.org/wiki/Simple_matching_coefficient
.. https://en.wikipedia.org/wiki/Rand_index
"""
# # detailed implementation
# n = len(targets)
# TP = 0
# TN = 0
# for i in range(n - 1):
# for j in range(i + 1, n):
# if targets[i] != targets[j]:
# if class_predictions[i] != class_predictions[j]:
# TN += 1
# else:
# if class_predictions[i] == class_predictions[j]:
# TP += 1
#
# RI = n * (n - 1) / 2
# RI = (TP + TN) / RI
RI = metrics.rand_score(targets, class_predictions)
return RI
[docs]
def calc_adjusted_rand_index(
class_predictions: np.ndarray,
targets: np.ndarray,
) -> float:
"""Calculate adjusted Rand Index.
Parameters
----------
class_predictions :
Clustering results returned by a clusterer.
targets :
Ground truth (correct) clustering results.
Returns
-------
aRI :
Adjusted Rand index.
References
----------
.. [1] `L. Hubert and P. Arabie, Comparing Partitions,
Journal of Classification 1985
<https://link.springer.com/article/10.1007%2FBF01908075>`_
.. [2] `D. Steinley, Properties of the Hubert-Arabie
adjusted Rand index, Psychological Methods 2004
<https://psycnet.apa.org/record/2004-17801-007>`_
.. [3] https://en.wikipedia.org/wiki/Rand_index#Adjusted_Rand_index
"""
aRI = metrics.adjusted_rand_score(targets, class_predictions)
return aRI
[docs]
def calc_nmi(
class_predictions: np.ndarray,
targets: np.ndarray,
) -> float:
"""Calculate Normalized Mutual Information between two clusterings.
Parameters
----------
class_predictions :
Clustering results returned by a clusterer.
targets :
Ground truth (correct) clustering results.
Returns
-------
NMI : float,
Normalized Mutual Information
"""
NMI = metrics.normalized_mutual_info_score(targets, class_predictions)
return NMI
[docs]
def calc_cluster_purity(
class_predictions: np.ndarray,
targets: np.ndarray,
) -> float:
"""Calculate cluster purity.
Parameters
----------
class_predictions :
Clustering results returned by a clusterer.
targets :
Ground truth (correct) clustering results.
Returns
-------
cluster_purity :
cluster purity.
Notes
-----
This function is from the answer https://stackoverflow.com/a/51672699 on StackOverflow.
"""
contingency_matrix = metrics.cluster.contingency_matrix(targets, class_predictions)
cluster_purity = np.sum(np.amax(contingency_matrix, axis=0)) / np.sum(contingency_matrix)
return cluster_purity
[docs]
def calc_external_cluster_validation_metrics(
class_predictions: np.ndarray,
targets: np.ndarray,
) -> dict:
"""Computer all external cluster validation metrics available in PyPOTS and return as a dictionary.
Parameters
----------
class_predictions :
Clustering results returned by a clusterer.
targets :
Ground truth (correct) clustering results.
Returns
-------
external_cluster_validation_metrics : dict
A dictionary contains all external cluster validation metrics available in PyPOTS.
"""
ri = calc_rand_index(class_predictions, targets)
ari = calc_adjusted_rand_index(class_predictions, targets)
nmi = calc_nmi(class_predictions, targets)
cp = calc_cluster_purity(class_predictions, targets)
external_cluster_validation_metrics = {
"rand_index": ri,
"adjusted_rand_index": ari,
"nmi": nmi,
"cluster_purity": cp,
}
return external_cluster_validation_metrics
[docs]
def calc_silhouette(X: np.ndarray, predicted_labels: np.ndarray) -> float:
"""Compute the mean Silhouette Coefficient of all samples.
Parameters
----------
X : array-like of shape (n_samples_a, n_features)
A feature array, or learned latent representation, that can be used for clustering.
predicted_labels : array-like of shape (n_samples)
Predicted labels for each sample.
Returns
-------
silhouette_score : float
Mean Silhouette Coefficient for all samples. In short, the higher, the better.
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)>`_
"""
silhouette_score = metrics.silhouette_score(X, predicted_labels)
return silhouette_score
[docs]
def calc_chs(X: np.ndarray, predicted_labels: np.ndarray) -> float:
"""Compute the Calinski and Harabasz score (also known as the Variance Ratio Criterion).
X : array-like of shape (n_samples_a, n_features)
A feature array, or learned latent representation, that can be used for clustering.
predicted_labels : array-like of shape (n_samples)
Predicted labels for each sample.
Returns
-------
calinski_harabasz_score : float
The resulting Calinski-Harabasz score. In short, the higher, the better.
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>`_
"""
calinski_harabasz_score = metrics.calinski_harabasz_score(X, predicted_labels)
return calinski_harabasz_score
[docs]
def calc_dbs(X: np.ndarray, predicted_labels: np.ndarray) -> float:
"""Compute the Davies-Bouldin score.
Parameters
----------
X : array-like of shape (n_samples_a, n_features)
A feature array, or learned latent representation, that can be used for clustering.
predicted_labels : array-like of shape (n_samples)
Predicted labels for each sample.
Returns
-------
davies_bouldin_score : float
The resulting Davies-Bouldin score. In short, the lower, the better.
References
----------
.. [1] `Davies, David L.; Bouldin, Donald W. (1979).
"A Cluster Separation Measure"
IEEE Transactions on Pattern Analysis and Machine Intelligence.
PAMI-1 (2): 224-227
<https://ieeexplore.ieee.org/document/4766909>`_
"""
davies_bouldin_score = metrics.davies_bouldin_score(X, predicted_labels)
return davies_bouldin_score
[docs]
def calc_internal_cluster_validation_metrics(X: np.ndarray, predicted_labels: np.ndarray) -> dict:
"""Computer all internal cluster validation metrics available in PyPOTS and return as a dictionary.
Parameters
----------
X : array-like of shape (n_samples_a, n_features)
A feature array, or learned latent representation, that can be used for clustering.
predicted_labels : array-like of shape (n_samples)
Predicted labels for each sample.
Returns
-------
internal_cluster_validation_metrics : dict
A dictionary contains all internal cluster validation metrics available in PyPOTS.
"""
silhouette_score = calc_silhouette(X, predicted_labels)
calinski_harabasz_score = calc_chs(X, predicted_labels)
davies_bouldin_score = calc_dbs(X, predicted_labels)
internal_cluster_validation_metrics = {
"silhouette_score": silhouette_score,
"calinski_harabasz_score": calinski_harabasz_score,
"davies_bouldin_score": davies_bouldin_score,
}
return internal_cluster_validation_metrics