Low rank approximation using error correcting coding matrices

Shashanka Ubaru, Arya Mazumdar, Yousef Saad

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

7 Scopus citations

Abstract

Low-rank matrix approximation is an integral component of tools such as principal component analysis (PCA), as well as is an important instrument used in applications like web search, text mining and computer vision, e.g., face recognition. Recently, randomized algorithms were proposed to effectively construct low rank approximations of large matrices. In this paper, we show how matrices from error correcting codes can be used to find such low rank approximations. The benefits of using these code matrices are the following: (i) They are easy to generate and they reduce randomness significantly, (ii) Code matrices have low coherence and have a better chance of preserving the geometry of an entire subspace of vectors; (iii) Unlike Fourier transforms or Hadamard matrices, which require sampling O(Hogfc) columns for a rank-fc approximation, the log factor is not necessary in the case of code matrices, (iv) Under certain conditions, the approximation errors can be better and the singular values obtained can be more accurate, than those obtained using Gaussian random matrices and other structured random matrices.

Original languageEnglish (US)
Title of host publication32nd International Conference on Machine Learning, ICML 2015
EditorsFrancis Bach, David Blei
PublisherInternational Machine Learning Society (IMLS)
Pages702-710
Number of pages9
ISBN (Electronic)9781510810587
StatePublished - Jan 1 2015
Event32nd International Conference on Machine Learning, ICML 2015 - Lile, France
Duration: Jul 6 2015Jul 11 2015

Publication series

Name32nd International Conference on Machine Learning, ICML 2015
Volume1

Other

Other32nd International Conference on Machine Learning, ICML 2015
CountryFrance
CityLile
Period7/6/157/11/15

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