Structured low-rank matrix factorization: Optimality, algorithm, and applications to image processing

Benjamin D. Haeffele, Eric D. Young, René Vidal

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

Abstract

Recently, convex solutions to low-rank matrix factorization problems have received increasing attention in machine learning. However, in many applications the data can display other structures beyond simply being low-rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current low-rank methods. In this paper we explore a matrix factorization technique suitable for large datasets that captures additional structure in the factors by using a projective tensor norm, which includes classical image regularizers such as total variation and the nuclear norm as particular cases. Although the resulting optimization problem is not convex, we show that under certain conditions on the factors, any local mini-mizer for the factors yields a global minimizer for their product. Examples in biomedical video segmentation and hyperspectral compressed recovery show the advantages of our approach on high-dimensional datasets.

Original languageEnglish (US)
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Pages4108-4117
Number of pages10
ISBN (Electronic)9781634393973
StatePublished - 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: Jun 21 2014Jun 26 2014

Publication series

Name31st International Conference on Machine Learning, ICML 2014
Volume5

Other

Other31st International Conference on Machine Learning, ICML 2014
Country/TerritoryChina
CityBeijing
Period6/21/146/26/14

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

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