A Comparison of Optimization Method for Non-negative Matrix Factorization


Wei-Cheng Chang

11:00:00 - 11:30:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Nonnegative Matrix Factorization (NMF) is often encountered in multivariate analysis and linear algebra. In this presentation, NMF is used as an effective dimension reduction method for finding representations of non-negative data. Many existing algorithms have been proposed to solve this problem. For example, Lee and Seung (2001, Advances in Neural Information Processing Systems) use multiplicative-update algorithm, Lin (2007, IEEE Transaction on Neural Networks) proposes a projected gradient method, Kim and Park (2008, Proceedings of the Seventeenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining,) applies a projected Newton method. Very recently, Hsieh and Dhillon (2011) suggest solving NMF problem by coordinate descent methods and the results show that their methods are more efficeint than other state-of-art methods. In this presentation, an implementation of projected gradient method proposed by Lin (2007) will be presented and reconstruction of the experiments result is also reported. In addition, the visualization of the basis W learned by different optimization methods will be shown and the findings on their difference will be provided in term of physical meanings. This finding will provide a guideline on face recognition.