NDLI: Sparse interactions: Identifying high-dimensional multilinear systems via compressed sensing

Content Provider	IEEE Xplore Digital Library
Author	Nazer, B. Nowak, R.D.
Copyright Year	2010
Description	Author affiliation: University of Wisconsin, Madison ECE Department, 53706, USA (Nazer, B.; Nowak, R.D.)
Abstract	This paper investigates the problem of identifying sparse multilinear systems. Such systems are characterized by multiplicative interactions between the input variables with sparsity meaning that relatively few of all conceivable interactions are present. This problem is motivated by the study of interactions among genes and proteins in living cells. The goal is to develop a sampling/sensing scheme to identify sparse multilinear systems using as few measurements as possible. We derive bounds on the number of measurements required for perfect reconstruction as a function of the sparsity level. Our results extend the notion of compressed sensing from the traditional notion of (linear) sparsity to more refined notions of sparsity encountered in nonlinear systems. In contrast to the linear sparsity models, in the multilinear case the pattern of sparsity may play a role in the sensing requirements.
Starting Page	1589
Ending Page	1596
File Size	492832
Page Count	8
File Format	PDF
ISBN	9781424482153
e-ISBN	9781424482160
DOI	10.1109/ALLERTON.2010.5707103
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-09-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Symmetric matrices Eigenvalues and eigenfunctions Vectors Sensors Random variables Nonlinear systems Compressed sensing
Content Type	Text
Resource Type	Article

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