{"title":"Sketch-based multiplicative updating algorithms for symmetric nonnegative tensor factorizations with applications to face image clustering","authors":"","doi":"10.1007/s10898-024-01374-4","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Nonnegative tensor factorizations (NTF) have applications in statistics, computer vision, exploratory multi-way data analysis, and blind source separation. This paper studies randomized multiplicative updating algorithms for symmetric NTF via random projections and random samplings. For random projections, we consider two methods to generate the random matrix and analyze the computational complexity, while for random samplings the uniform sampling strategy and its variants are examined. The mixing of these two strategies is then considered. Some theoretical results are presented based on the bounds of the singular values of sub-Gaussian matrices and the fact that randomly sampling rows from an orthogonal matrix results in a well-conditioned matrix. These algorithms are easy to implement, and their efficiency is verified via test tensors from both synthetic and real datasets, such as for clustering facial images.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10898-024-01374-4","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Nonnegative tensor factorizations (NTF) have applications in statistics, computer vision, exploratory multi-way data analysis, and blind source separation. This paper studies randomized multiplicative updating algorithms for symmetric NTF via random projections and random samplings. For random projections, we consider two methods to generate the random matrix and analyze the computational complexity, while for random samplings the uniform sampling strategy and its variants are examined. The mixing of these two strategies is then considered. Some theoretical results are presented based on the bounds of the singular values of sub-Gaussian matrices and the fact that randomly sampling rows from an orthogonal matrix results in a well-conditioned matrix. These algorithms are easy to implement, and their efficiency is verified via test tensors from both synthetic and real datasets, such as for clustering facial images.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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