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

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 it...

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Vydáno v:Machine learning Ročník 103; číslo 2; s. 285 - 306
Hlavní autoři: Kimura, Keigo, Kudo, Mineichi, Tanaka, Yuzuru
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2016
Springer Nature B.V
Témata:
Algorithms
Approximation
Artificial Intelligence
Computer Science
Control
Convergence
Divergence
Factorization
Mathematical analysis
Matrix
Mechatronics
Natural Language Processing (NLP)
Norms
Robotics
Simulation and Modeling
Tasks
Bregman Divergence
Orthogonal Factorization
Orthogonal nonnegative matrix factorization
Column-wise Update
ISSN:0885-6125, 1573-0565
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Shrnutí: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.
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ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-016-5553-0