Upper Bound of Bayesian Generalization Error in Non-negative Matrix Factorization
This provides a theoretical foundation for optimizing NMF in applications like text mining and bioinformatics, though it is incremental as it builds on existing Bayesian learning frameworks.
The paper tackles the lack of theoretical understanding of non-negative matrix factorization (NMF) as a learning machine by deriving an upper bound for its Bayesian generalization error, showing it can be smaller than that of regular statistical models.
Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization method of NMF has not yet established. In this paper, we study the real log canonical threshold of NMF and give an upper bound of the generalization error in Bayesian learning. The results show that the generalization error of the matrix factorization can be made smaller than regular statistical models if Bayesian learning is applied.