NDLI: A column-wise update algorithm for nonnegative matrix factorization in Bregman divergence with an orthogonal constraint

Content Provider	Springer Nature Link
Author	Kimura, Keigo Kudo, Mineichi Tanaka, Yuzuru
Copyright Year	2016
Abstract	Recently orthogonal nonnegative matrix factorization (ONMF), imposing an orthogonal constraint into NMF, has been attracting a great deal of attention. ONMF is more appropriate than standard NMF for a clustering task because the constrained matrix can be considered as an indicator matrix. Several iterative ONMF algorithms have been proposed, but they suffer from slow convergence because of their matrix-wise updating. In this paper, therefore, a column-wise update algorithm is proposed for speeding up ONMF. To make the idea possible, we transform the matrix-based orthogonal constraint into a set of column-wise orthogonal constraints. The algorithm is stated first with the Frobenius norm and then with Bregman divergence, both for measuring the degree of approximation. Experiments on one artificial and six real-life datasets showed that the proposed algorithms converge faster than the other conventional ONMF algorithms, more than four times in the best cases, due to their smaller numbers of iterations.
Starting Page	285
Ending Page	306
Page Count	22
File Format	PDF
ISSN	08856125
Journal	Machine Learning
Volume Number	103
Issue Number	2
e-ISSN	15730565
Language	English
Publisher	Springer US
Publisher Date	2016-03-11
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Orthogonal nonnegative matrix factorization Orthogonal Factorization Bregman Divergence Column-wise Update Artificial Intelligence (incl. Robotics) Control, Robotics, Mechatronics Computing Methodologies Simulation and Modeling Language Translation and Linguistics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Software

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