Faster subset selection for matrices and applications

Haim Avron, Christos Boutsidis

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

We study the following problem of subset selection for matrices: given a matrix X ε ℝnxm (m > n) and a sampling parameter k (n ≤ k ≤ m), select a subset of k columns from X such that the pseudoinverse of the sampled matrix has as small a norm as possible. In this work, we focus on the Frobenius and the spectral matrix norms. We describe several novel (deterministic and randomized) approximation algorithms for this problem with approximation bounds that are optimal up to constant factors. Additionally, we show that the combinatorial problem of finding a low-stretch spanning tree in an undirected graph corresponds to subset selection, and discuss various implications of this reduction.

Original languageEnglish
Pages (from-to)1464-1499
Number of pages36
JournalSIAM Journal on Matrix Analysis and Applications
Volume34
Issue number4
DOIs
StatePublished - 2013
Externally publishedYes

Keywords

  • Feature selection
  • K-means clustering
  • Low-rank approximations
  • Low-stretch spanning trees
  • Sparse approximation
  • Subset selection
  • Volume sampling

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