{"title":"An efficient iterative method for solving the graph regularization Q-weighted nonnegative matrix factorization problem in multi-view clustering","authors":"Chunmei Li, Dan Tian, Xuefeng Duan, Naya Yang","doi":"10.1016/j.apnum.2024.07.010","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the graph regularization Q-weighted nonnegative matrix factorization problem in multi-view clustering. Based on the Q-weighted norm property, this problem is transformed into the minimization problem of the trace function. The necessary condition for the existence of a solution is given. The proximal alternating nonnegative least squares method and its acceleration method are designed to solve it. The convergence theorem is also given. The feasibility and effectiveness of the proposed methods are verified by numerical experiments.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"205 ","pages":"Pages 255-266"},"PeriodicalIF":2.4000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424001909","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/8/2 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
In this paper, we consider the graph regularization Q-weighted nonnegative matrix factorization problem in multi-view clustering. Based on the Q-weighted norm property, this problem is transformed into the minimization problem of the trace function. The necessary condition for the existence of a solution is given. The proximal alternating nonnegative least squares method and its acceleration method are designed to solve it. The convergence theorem is also given. The feasibility and effectiveness of the proposed methods are verified by numerical experiments.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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