Divergence Functions of Non negative Matrix Factorization: A Comparison Study

Abstract

Non negative Matrix Factorization (NMF) has become one of the most popular models in data mining for its good performance in unsupervised learning applications. Recently, a variety of divergence functions have been extensively studied for NMF. But, there is still lack of analysis on the relationships between the divergence functions and the applications. This article tries to give some preliminary results on this interesting problem. Our experiments show that the most familiar two divergence functions—the least squares error and the K-L divergence—are competent for unsupervised learning such as gene expression data clustering and image processing.

Keywords:

• Blind source separation
• Comparison
• Clustering
• Divergence function
• Image processing
• Non negative matrix factorization

Mathematics Subject Classification:

• 15A23
• 90C30

Acknowledgment

The author is very appreciated for the reviewers’ valuable comments. This work is supported by the Foundation of Academic Discipline Program at Central University of Finance and Economics, P. R. China.