Non-negative matrix factorization on Kernels

Authors:
Daoqiang Zhang;Zhi-Hua Zhou;Songcan Chen
Affiliations:
Department of Computer Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China and National Laboratory for Novel Software Technology, Nanjing University, Nanjin ...;National Laboratory for Novel Software Technology, Nanjing University, Nanjing, China;Department of Computer Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China
Venue:
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
Year:
2006

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Abstract

In this paper, we extend the original non-negative matrix factorization (NMF) to kernel NMF (KNMF). The advantages of KNMF over NMF are: 1) it could extract more useful features hidden in the original data through some kernel-induced nonlinear mappings; 2) it can deal with data where only relationships (similarities or dissimilarities) between objects are known; 3) it can process data with negative values by using some specific kernel functions (e.g. Gaussian). Thus, KNMF is more general than NMF. To further improve the performance of KNMF, we also propose the SpKNMF, which performs KNMF on sub-patterns of the original data. The effectiveness of the proposed algorithms is validated by extensive experiments on UCI datasets and the FERET face database.