Correlated noise: How it Breaks NMF, and What to Do about it

Sergey M. Plis, Vamsi K. Potluru, Terran Lane, Vince D. Calhoun

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Non-negative matrix factorization (NMF) is a problem of decomposing multivariate data into a set of features and their corresponding activations. When applied to experimental data, NMF has to cope with noise, which is often highly correlated. We show that correlated noise can break the Donoho and Stodden separability conditions of a dataset and a regular NMF algorithm will fail to decompose it, even when given freedom to be able to represent the noise as a separate feature. To cope with this issue, we present an algorithm for NMF with a generalized least squares objective function (glsNMF) and derive multiplicative updates for the method together with proving their convergence. The new algorithm successfully recovers the true representation from the noisy data. Robust performance can make glsNMF a valuable tool for analyzing empirical data.

Original languageEnglish (US)
Pages (from-to)351-359
Number of pages9
JournalJournal of Signal Processing Systems
Issue number3
StatePublished - Dec 2011
Externally publishedYes


  • Correlated noise
  • Nonnegative matrix factorization
  • Separability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Modeling and Simulation
  • Hardware and Architecture


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