Title :
Correlated noise: How it breaks NMF, and what to do about it
Author :
Plis, Sergey M. ; Potluru, Vamsi K. ; Calhoun, Vince D. ; Lane, Terran
Author_Institution :
Comput. Sci. Dept., Univ. of New Mexico, Albuquerque, NM, USA
Abstract :
Non-negative matrix factorization (NMF) is an algorithm for decomposing multivariate data into a signal dictionary and its 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.
Keywords :
data handling; least squares approximations; matrix algebra; correlated noise; generalized least squares objective function; multivariate data decomposition; nonnegative matrix factorization; Computer networks; Convergence; Data engineering; Dictionaries; Least squares methods; Matrix decomposition; Noise robustness; Principal component analysis; White noise; Working environment noise; GLS; NMF; correlated noise; parts based representation;
Conference_Titel :
Machine Learning for Signal Processing, 2009. MLSP 2009. IEEE International Workshop on
Conference_Location :
Grenoble
Print_ISBN :
978-1-4244-4947-7
Electronic_ISBN :
978-1-4244-4948-4
DOI :
10.1109/MLSP.2009.5306187