Study On The Characteristic Of Pattern Expression Non-Negative Matrix Factorization

Non-negative Matrix Factorization (NMF) now receives broad attention for its insensibility of whether the sources are statistically dependent and whether they follow Gaussian distribution. The algorithm Pattern Expression Non-negative Matrix Factorization (PE-NMF) is extended from NMF from the view point of using basis vectors to express unevenly distributed data more effectively.Researches on the characteristics of PE-NMF concentrate on the following aspects: (1) verifying the conclusion that Independent Component Analysis (ICA) model can only perform on the condition that not more than 1 source follows Gaussian distribution, and also verifying the conclusion that PE-NMF can gain good performance either when sources are statistically dependent or when sources follow Gaussian distribution; (2) studying the influence of initialization and iteration times on the performance of PE-NMF. Experiments show that the initialization affects the performance significantly, and it is pointed out that this effect can not be counteracted only by increasing iteration times;(3) studying the influence of correlation among sources on the performance of PE-NMF. Experiments show that the performance decreases with as the correlation among sources increases. And it is also pointed out that, although it gains goodish performance to recover the sources, the algorithm can not distinguish among real sources; (4) studying the influence of Gaussian noises on the performance of PE-NMF. Experiments show that it can effectively recover sources from observations which contain Gaussian noises ;(5) proposing a new method to resolve signal separation problems by using PE-NMF assisted by ICA, which has two advantages compared to classical NMF: much better signal separation performance and automatically ascertaining the number of sources.