Model-based clustering with determinant-and-shape constraint

Model-based approaches to cluster analysis and mixture modeling often involve maximizing classification and mixture likelihoods. Without appropriate constrains on the scatter matrices of the components, these maximizations result in ill-posed problems. Moreover, without constrains, non-interesting o...

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Bibliographic Details
Published in:Statistics and computing 2020-09, Vol.30 (5), p.1363-1380
Main Authors: García-Escudero, Luis Angel, Mayo-Iscar, Agustín, Riani, Marco
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Cluster analysis
Clustering
Constraint modelling
Determinants
Ill posed problems
Mathematics and Statistics
Maximization
Optimization
Probability and Statistics in Computer Science
Scattering
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Upper bounds
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Summary:Model-based approaches to cluster analysis and mixture modeling often involve maximizing classification and mixture likelihoods. Without appropriate constrains on the scatter matrices of the components, these maximizations result in ill-posed problems. Moreover, without constrains, non-interesting or “spurious” clusters are often detected by the EM and CEM algorithms traditionally used for the maximization of the likelihood criteria. Considering an upper bound on the maximal ratio between the determinants of the scatter matrices seems to be a sensible way to overcome these problems by affine equivariant constraints. Unfortunately, problems still arise without also controlling the elements of the “shape” matrices. A new methodology is proposed that allows both control of the scatter matrices determinants and also the shape matrices elements. Some theoretical justification is given. A fast algorithm is proposed for this doubly constrained maximization. The methodology is also extended to robust model-based clustering problems.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-020-09950-w