open access

https://hdl.handle.net/2115/48772

On the clustering aspect of nonnegative matrix factorization

英語

Karush-Kuhn-Tucker conditions

2010-08

IEEE

2010 International Conference On Electronics and Information Engineering (ICEIE)

1

V1-405-V1-408

The clustering aspect of various nonnegative matrix factorization (NMF) objectives which include standard NMF, orthogonal NMF, sparse NMF, Semi-NMF, and Convex NMF have been reported in many papers. However, there is still no comprehensive study that provides a theoretical explanation on this aspect yet. In this work, we provide such explanation by showing that at the respective stationary points in nonnegative orthant of the feasible regions, which are the solutions pursued by NMF algorithms, the NMF objectives are equivalent to the graph clustering objective, therefore the clustering aspect of NMF has a solid justification.

会議発表論文

Accepted Manuscript

© 2010 IEEE. Reprinted, with permission, from Mirzal, A., Furukawa, M., On the clustering aspect of nonnegative matrix factorization, 2010 International Conference On Electronics and Information Engineering (ICEIE), Aug. 2010. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Hokkaido University products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.