Preprint article · Journal article
Theorems on Positive Data: On the Uniqueness of NMF
In
Computational Intelligence and Neuroscience
—
2008, Volume 2008, pp. 764206
Abstract
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution.
Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
| Language: | English |
|---|---|
| Publisher: | Hindawi Publishing Corporation |
| Year: | 2008 |
| Pages: | 764206 |
| ISSN: | 16875273 and 16875265 |
| Types: | Preprint article and Journal article |
| DOI: | 10.1155/2008/764206 |
| ORCIDs: | Hansen, Lars Kai |
