Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions

Families of mixtures of multivariate power exponential (MPE) distributions have already been introduced and shown to be competitive for cluster analysis in comparison to other mixtures of elliptical distributions, including mixtures of Gaussian distributions. A family of mixtures of multivariate ske...

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Bibliographic Details
Published in:Journal of classification Vol. 40; no. 1; pp. 145 - 167
Main Authors: Dang, Utkarsh J., Gallaugher, Michael P.B., Browne, Ryan P., McNicholas, Paul D.
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2023
Springer Nature B.V
Subjects:
Algorithms
Bioinformatics
Classification
Cluster analysis
Clustering
Decomposition
Eigenvalues
Expected values
Families & family life
Kurtosis
Manifolds (mathematics)
Marketing
Mathematics and Statistics
Maximization
Mixtures
Multivariate analysis
Normal distribution
Normality
Optimization
Parameter estimation
Pattern Recognition
Power
Psychometrics
Random variables
Search algorithms
Signal,Image and Speech Processing
Skewness
Statistical Theory and Methods
Statistics
Model-based classification
Multivariate skewed power exponential distribution
Mixture models
Model-based clustering
Generalized expectation-maximization algorithm
ISSN:0176-4268, 1432-1343
Online Access:Get full text
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Summary:Families of mixtures of multivariate power exponential (MPE) distributions have already been introduced and shown to be competitive for cluster analysis in comparison to other mixtures of elliptical distributions, including mixtures of Gaussian distributions. A family of mixtures of multivariate skewed power exponential distributions is proposed that combines the flexibility of the MPE distribution with the ability to model skewness. These mixtures are more robust to variations from normality and can account for skewness, varying tail weight, and peakedness of data. A generalized expectation-maximization approach, which combines minorization-maximization and optimization based on accelerated line search algorithms on the Stiefel manifold, is used for parameter estimation. These mixtures are implemented both in the unsupervised and semi-supervised classification frameworks. Both simulated and real data are used for illustration and comparison to other mixture families.
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ISSN:0176-4268
1432-1343
DOI:10.1007/s00357-022-09427-7