RT info:eu-repo/semantics/article
T1 Model-Based Clustering with Determinant-and-Shape Constraints
A1 García Escudero, Luis Ángel
A1 Mayo Iscar, Agustín
A1 Riani, Marco
AB 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.
YR 2020
FD 2020
LK http://uvadoc.uva.es/handle/10324/42437
UL http://uvadoc.uva.es/handle/10324/42437
LA spa
NO Statistics and Computing 30, 1363-1380 (2020)
DS UVaDOC
RD 04-abr-2025