Correlated Noise: How it Breaks NMF, and What to Do About it

Authors:
Sergey M. Plis;Vamsi K. Potluru;Terran Lane;Vince D. Calhoun
Affiliations:
Computer Science Department, University of New Mexico, Albuquerque, USA 87131;Computer Science Department, University of New Mexico, Albuquerque, USA 87131;Computer Science Department, University of New Mexico, Albuquerque, USA 87131;Electrical and Computer Engineering Department, University of New Mexico, Albuquerque, USA 87131 and Mind Research Network, Albuquerque, USA 87106
Venue:
Journal of Signal Processing Systems
Year:
2011

Citing 5
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Abstract

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.