Convolutional approximations to linear dimensionality reduction operators

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2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), ISSN: 1520-6149, Page: 5885-5889

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Swayambhoo Jain; Jarvis Haupt
Institute of Electrical and Electronics Engineers (IEEE)
Computer Science; Engineering
conference paper description
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.