H. Honda, Phuong Dinh, Pham Thu Thao, Yuho Tabata, Bui Duc Anh
{"title":"Dimensionality reduction as a non-cooperative game","authors":"H. Honda, Phuong Dinh, Pham Thu Thao, Yuho Tabata, Bui Duc Anh","doi":"10.1109/ICAIIC57133.2023.10067075","DOIUrl":null,"url":null,"abstract":"A novel non-cooperative game theory-based approach for dimensionality reduction is proposed. We regard the sample elements in a higher-dimensional space as players in a game each of which has its strategy. A set of these strategies was implemented as an embedding of dimensionality reduction, which maps the sample elements into lower-dimensional spaces. Based on the theory of non-cooperative $N$-player games, we show the existence of Nash equilibria. We also provide an algorithm that yields Nash equilibrium based on the theory of nonlinear functional analysis.","PeriodicalId":105769,"journal":{"name":"2023 International Conference on Artificial Intelligence in Information and Communication (ICAIIC)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2023 International Conference on Artificial Intelligence in Information and Communication (ICAIIC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICAIIC57133.2023.10067075","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A novel non-cooperative game theory-based approach for dimensionality reduction is proposed. We regard the sample elements in a higher-dimensional space as players in a game each of which has its strategy. A set of these strategies was implemented as an embedding of dimensionality reduction, which maps the sample elements into lower-dimensional spaces. Based on the theory of non-cooperative $N$-player games, we show the existence of Nash equilibria. We also provide an algorithm that yields Nash equilibrium based on the theory of nonlinear functional analysis.