evclust.egmm#
- This module contains the main function for Evidential Gaussian Mixture Model (EGMM). :
Lianmeng Jiao, Thierry Denœux, Zhun-ga Liu, Quan Pan, EGMM: An evidential version of the Gaussian mixture model for clustering, Applied Soft Computing, Volume 129, 2022, 109619, ISSN 1568-4946.
Module Contents#
- evclust.egmm.egmm(X, c, type='simple', pairs=None, Omega=True, max_iter=20, epsi=0.001, init='kmeans', disp=True)[source]#
Evidential Gaussian Mixture Model (EGMM) clustering algorithm. Model parameters are estimated by Expectation-Maximization algorithm and by extending the classical GMM in the belief function framework directly.
Parameters:#
- X (ndarray):
Input data of shape (n_samples, n_features).
- c (int):
Number of clusters.
- type (str, optional):
Type of focal sets (‘simple’, ‘full’, ‘pairs’). Default is ‘simple’.
- pairs (ndarray, None):
Set of pairs to be included in the focal sets; if None, all pairs are included. Used only if type=”pairs”.
- Omega (bool):
If True (default), the whole frame is included (for types ‘simple’ and ‘pairs’).
- max_iter ( int, optional):
Maximum number of iterations. Default is 100.
- epsi (float, optional):
Convergence tolerance for the algorithm. Default is 1e-6.
- init (str, optional):
Initialization method (‘random’ or ‘kmeans’). Default is ‘random’.
Returns:#
The credal partition (an object of class “credpart”).
Example:#
from evclust.egmm import egmm import numpy as np import matplotlib.pyplot as plt np.random.seed(42); n = 200 X1 = np.random.normal(loc=[1, 3], scale=0.5, size=(n//3, 2)) X2 = np.random.normal(loc=[7, 5], scale=0.3, size=(n//3, 2)) X3 = np.random.normal(loc=[10, 2], scale=0.7, size=(n//3, 2)) X = np.vstack([X1, X2, X3]) clus = egmm(X, c=3, type='full', max_iter=20, epsi=1e-3, init='kmeans') clus['F'] # Focal sets clus['g'] # Cluster centroids clus['mass'] # Mass functions clus['y_pl'] # Maximum plausibility clusters
References:#
Lianmeng Jiao, Thierry Denœux, Zhun-ga Liu, Quan Pan, EGMM: An evidential version of the Gaussian mixture model for clustering, Applied Soft Computing, Volume 129, 2022, 109619, ISSN 1568-4946.
See also
extractMass(),makeF(),init_params_random_egmm(),init_params_kmeans_egmm()Note
Keywords : Belief function theory, Evidential partition, Gaussian mixture model, Model-based clustering, Expectation–Maximization The parameters in EGMM are estimated by a specially designed Expectation–Maximization (EM) algorithm. A validity index allowing automatic determination of the proper number of clusters is also provided. The proposed EGMM is as simple as the classical GMM, but can generate a more informative evidential partition for the considered dataset.