Perturbation of matrices and nonnegative rank with a view toward statistical models

Cristiano Bocci; Enrico Carlini; Fabio Rapallo

doi:10.1137/110825455

Perturbation of matrices and nonnegative rank with a view toward statistical models

Cristiano Bocci, Enrico Carlini, Fabio Rapallo

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

In this paper we study how perturbing a matri x changes its nonnegative rank. We prove that the nonnegative rank can only increase in a neighborhood of a matrix with no zero columns. Also, we describe some special families of perturbations. We show how our results relate to statistics in terms of the study of maximum likelihood estimation for mixture models.

Lingua originale	Inglese
pagine (da-a)	1500-1512
Numero di pagine	13
Rivista	SIAM Journal on Matrix Analysis and Applications
Volume	32
Numero di pubblicazione	4
DOI	https://doi.org/10.1137/110825455
Stato di pubblicazione	Pubblicato - 2011
Pubblicato esternamente	Sì

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10.1137/110825455

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abstract = "In this paper we study how perturbing a matri x changes its nonnegative rank. We prove that the nonnegative rank can only increase in a neighborhood of a matrix with no zero columns. Also, we describe some special families of perturbations. We show how our results relate to statistics in terms of the study of maximum likelihood estimation for mixture models.",

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AU - Carlini, Enrico

AU - Rapallo, Fabio

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KW - Frobenius norm

KW - Independence of random variables

KW - Jacobian matrix

KW - Mixture models

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Perturbation of matrices and nonnegative rank with a view toward statistical models

Abstract

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