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

Research output: Contribution to journal › Article › 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.

Original language	English
Pages (from-to)	1500-1512
Number of pages	13
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	32
Issue number	4
DOIs	https://doi.org/10.1137/110825455
Publication status	Published - 2011
Externally published	Yes

Keywords

Frobenius norm
Independence of random variables
Jacobian matrix
Mixture models

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10.1137/110825455

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title = "Perturbation of matrices and nonnegative rank with a view toward statistical models",

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 - Bocci, Cristiano

AU - Carlini, Enrico

AU - Rapallo, Fabio

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AB - 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.

KW - Frobenius norm

KW - Independence of random variables

KW - Jacobian matrix

KW - Mixture models

UR - https://www.scopus.com/pages/publications/84856262691

U2 - 10.1137/110825455

DO - 10.1137/110825455

M3 - Article

SN - 0895-4798

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JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 4

ER -

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

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Keywords

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