Eigenvalues and constraints in mixture modeling: geometric and computational issues

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 o...

Full description

Saved in:
Bibliographic Details
Published in:Advances in data analysis and classification 2018-06, Vol.12 (2), p.203-233
Main Authors: García-Escudero, Luis Angel, Gordaliza, Alfonso, Greselin, Francesca, Ingrassia, Salvatore, Mayo-Iscar, Agustín
Format: Article
Language:English
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
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1862-5347
1862-5355
DOI:10.1007/s11634-017-0293-y