Approximate low-rank factorization with structured factors
Approximate low-rank factorization with structured factors
An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing factorization problem is nonconvex. An alternating projections algorithm is developed, which is globally convergent to a locally optimal solution. Although the algorithm is developed for a specific application in microarray data analysis, the approach is applicable to other types of structure.
rank revealing factorization, numerical rank, low-rank approximation, maximum likelihood PCA, total least squares, errors-in-variables, microarray data.
3411-3420
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Niranjan, Mahesan
5cbaeea8-7288-4b55-a89c-c43d212ddd4f
August 2010
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Niranjan, Mahesan
5cbaeea8-7288-4b55-a89c-c43d212ddd4f
Markovsky, Ivan and Niranjan, Mahesan
(2010)
Approximate low-rank factorization with structured factors.
Computational Statistics and Data Analysis, 54, .
Abstract
An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing factorization problem is nonconvex. An alternating projections algorithm is developed, which is globally convergent to a locally optimal solution. Although the algorithm is developed for a specific application in microarray data analysis, the approach is applicable to other types of structure.
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Published date: August 2010
Keywords:
rank revealing factorization, numerical rank, low-rank approximation, maximum likelihood PCA, total least squares, errors-in-variables, microarray data.
Organisations:
Southampton Wireless Group
Identifiers
Local EPrints ID: 267440
URI: http://eprints.soton.ac.uk/id/eprint/267440
ISSN: 0167-9473
PURE UUID: 2c9e82f5-392a-4b4e-be3f-11304c01015b
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Date deposited: 01 Jun 2009 14:12
Last modified: 15 Mar 2024 03:29
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Author:
Ivan Markovsky
Author:
Mahesan Niranjan
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