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...
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Published in | Advances in data analysis and classification Vol. 12; no. 2; pp. 203 - 233 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2018
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1862-5347 1862-5355 |
DOI: | 10.1007/s11634-017-0293-y |