Eigenvalues and constraints in mixture modeling: geometric and computational issues

• Published in: Advances in data analysis and classification Vol. 12; no. 2; pp. 203 - 233
• Main Authors: García-Escudero, Luis Angel, Gordaliza, Alfonso, Greselin, Francesca, Ingrassia, Salvatore, Mayo-Iscar, Agustín
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018; Springer Nature B.V
• Subjects: Chemistry and Earth Sciences; Clustering; Computer Science; Constraint modelling; Data Mining and Knowledge Discovery; Economics; Eigenvalues; Euclidean geometry; Finance; Health Sciences; Humanities; Insurance; Law; Management; Mathematics and Statistics; Medicine; Parameter estimation; Physics; Regular Article; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; 62F30 Inference under constraints; 62F10 Point estimation; Model-based clustering; 62F12 Asymptotic properties of estimators; Mixture model; Eigenvalues; 62F35 Robustness and adaptive procedures; EM algorithm
• ISSN: 1862-5347; 1862-5355
• DOI: 10.1007/s11634-017-0293-y

This paper presents a review about the usage of eigenvalues restrictions for constrained parameter estimation in mixtures of elliptical distributions according to the likelihood approach. The restrictions serve a twofold purpose: to avoid convergence to degenerate solutions and to reduce the onset of non interesting (spurious) local maximizers, related to complex likelihood surfaces. The paper shows how the constraints may play a key role in the theory of Euclidean data clustering. The aim here is to provide a reasoned survey of the constraints and their applications, considering the contributions of many authors and spanning the literature of the last 30 years.