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.
Original language | English (US) |
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Pages (from-to) | 351-359 |
Number of pages | 9 |
Journal | Journal of Signal Processing Systems |
Volume | 65 |
Issue number | 3 |
DOIs | |
State | Published - Dec 2011 |
Externally published | Yes |
Keywords
- 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