Convolutional approximations to linear dimensionality reduction operators

Swayambhoo Jain, Jarvis D Haupt

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This paper examines the existence of efficiently implementable approximations of a general real linear dimensionality reduction (LDR) operator. The specific focus is on approximating a given LDR operator with a partial circulant structured matrix (a matrix whose rows are related by circular shifts) as these constructions allow for low-memory footprint and computationally efficient implementations. Our main contributions are theoretical: we quantify how well general matrices may be approximated (in a Frobenius sense) by partial circulant structured matrices, and also consider a variation of this problem where the aim is only to accurately approximate the action of a given LDR operator on a restricted set of inputs. For the latter setting, we also propose a sparsity-regularized alternating minimization based algorithm for learning partial circulant approximations from data, and provide experimental evidence demonstrating the potential efficacy of this approach on real-world data.

Original languageEnglish (US)
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5885-5889
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - Jun 16 2017
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: Mar 5 2017Mar 9 2017

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
CountryUnited States
CityNew Orleans
Period3/5/173/9/17

Keywords

  • Circulant matrices
  • big data
  • matrix factorization
  • sparse regularization
  • subspace learning

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