Volume 10, Issue 2
Numerical Methods for $Q$-Weighted Nonnegative Matrix Tri-Factorization

East Asian J. Appl. Math., 10 (2020), pp. 256-273.

Published online: 2020-04

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• Abstract

The $Q$-weighted nonnegative matrix tri-factorisation problem arising in clustering analysis is considered and a necessary condition for its optimal solution is obtained. The problem is solved by the proximal alternating nonnegative least squares method supplemented by an acceleration scheme. The convergence of the methods is studied. Numerical examples show the feasibility and efﬁciency of the methods proposed.

• Keywords

Nonnegative matrix factorisation, necessary condition, PANLS method, ELS technique, clustering analysis.

15A48, 15A23, 65F30

lengyue123@126.com (Chun-Mei Li)

zchen@gznu.edu.cn (Zhen Chen)

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@Article{EAJAM-10-256, author = {Li , Chun-MeiLu , Lin-Zhang and Chen , Zhen}, title = {Numerical Methods for $Q$-Weighted Nonnegative Matrix Tri-Factorization }, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {2}, pages = {256--273}, abstract = {

The $Q$-weighted nonnegative matrix tri-factorisation problem arising in clustering analysis is considered and a necessary condition for its optimal solution is obtained. The problem is solved by the proximal alternating nonnegative least squares method supplemented by an acceleration scheme. The convergence of the methods is studied. Numerical examples show the feasibility and efﬁciency of the methods proposed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150419.140719}, url = {http://global-sci.org/intro/article_detail/eajam/16137.html} }
TY - JOUR T1 - Numerical Methods for $Q$-Weighted Nonnegative Matrix Tri-Factorization AU - Li , Chun-Mei AU - Lu , Lin-Zhang AU - Chen , Zhen JO - East Asian Journal on Applied Mathematics VL - 2 SP - 256 EP - 273 PY - 2020 DA - 2020/04 SN - 10 DO - http://doi.org/10.4208/eajam.150419.140719 UR - https://global-sci.org/intro/article_detail/eajam/16137.html KW - Nonnegative matrix factorisation, necessary condition, PANLS method, ELS technique, clustering analysis. AB -

The $Q$-weighted nonnegative matrix tri-factorisation problem arising in clustering analysis is considered and a necessary condition for its optimal solution is obtained. The problem is solved by the proximal alternating nonnegative least squares method supplemented by an acceleration scheme. The convergence of the methods is studied. Numerical examples show the feasibility and efﬁciency of the methods proposed.

Chun-MeiLi, Lin-ZhangLu & ZhenChen. (2020). Numerical Methods for $Q$-Weighted Nonnegative Matrix Tri-Factorization . East Asian Journal on Applied Mathematics. 10 (2). 256-273. doi:10.4208/eajam.150419.140719
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