Title :
Uniqueness of Non-Negative Matrix Factorization
Author_Institution :
Department of of Electronic Systems, Aalborg University, Niels Jernes Vej 12, DK-9220 Aalborg, Denmark, email: hla@es.aau.dk
Abstract :
In this paper, two new properties of stochastic vectors are introduced and a strong uniqueness theorem on non-negative matrix factorizations (NMF) is introduced. It is described how the theorem can be applied to two of the common application areas of NMF, namely music analysis and probabilistic latent semantic analysis. Additionally, the theorem can be used for selecting the model order and the sparsity parameter in sparse NMFs.
Keywords :
Acoustic noise; Closed-form solution; Feature extraction; Image analysis; Mathematical model; Principal component analysis; Sparse matrices; Spectrogram; Stochastic systems; Text analysis; Non-negative matrix factorization (NMF); model selection; non-negativity; sparse NMF;
Conference_Titel :
Statistical Signal Processing, 2007. SSP '07. IEEE/SP 14th Workshop on
Conference_Location :
Madison, WI, USA
Print_ISBN :
978-1-4244-1198-6
Electronic_ISBN :
978-1-4244-1198-6
DOI :
10.1109/SSP.2007.4301215
