The Wasserstein metric in factor analysis

Lipeng Ning, Tryphon T Georgiou

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

Abstract

We consider the problem of approximating a (nonnegative definite) covariance matrix by the sum of two structured covariances-one which is diagonal and one which has low-rank. Such an additive decomposition follows the dictum of factor analysis where linear relations are sought between variables corrupted by independent measurement noise. We use as distance the Wasserstein metric between their respective distributions (assumed Gaussian) which induces a metric between nonnegative definite matrices, in general. The rank-constraint renders the optimization non-convex. We propose alternating between optimization with respect to each of the two summands. Properties of these optimization problems and the performance of the approach are being analyzed.

Original languageEnglish (US)
Title of host publicationSIAM Conference on Control and Its Applications 2013
EditorsWei Kang, Qing Zhang, Fariba Fahroo
PublisherSociety for Industrial and Applied Mathematics Publications
Pages8-12
Number of pages5
ISBN (Electronic)9781510813298
StatePublished - Jan 1 2013
EventSIAM Conference on Control and Its Applications 2013 - San Diego, United States
Duration: Jul 8 2013Jul 10 2013

Publication series

NameSIAM Conference on Control and Its Applications 2013

Other

OtherSIAM Conference on Control and Its Applications 2013
CountryUnited States
CitySan Diego
Period7/8/137/10/13

Keywords

  • Factor analysis
  • Optimal transport
  • System identification

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