A convex model for nonnegative matrix factorization and dimensionality reduction on physical space.

Journal Article

A collaborative convex framework for factoring a data matrix X into a nonnegative product AS , with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We use l(1, ∞) regularization to select the dictionary from the data and show that this leads to an exact convex relaxation of l(0) in the case of distinct noise-free data. We also show how to relax the restriction-to- X constraint by initializing an alternating minimization approach with the solution of the convex model, obtaining a dictionary close to but not necessarily in X. We focus on applications of the proposed framework to hyperspectral endmember and abundance identification and also show an application to blind source separation of nuclear magnetic resonance data.

Full Text

Duke Authors

Cited Authors

  • Esser, E; Möller, M; Osher, S; Sapiro, G; Xin, J

Published Date

  • July 2012

Published In

Volume / Issue

  • 21 / 7

Start / End Page

  • 3239 - 3252

PubMed ID

  • 22410332

Electronic International Standard Serial Number (EISSN)

  • 1941-0042

Digital Object Identifier (DOI)

  • 10.1109/TIP.2012.2190081


  • eng

Conference Location

  • United States