{"title":"分区的正定核","authors":"Jyrko Correa-Morris","doi":"10.37394/23206.2023.22.77","DOIUrl":null,"url":null,"abstract":"This paper presents a comprehensive exploration of various families of positive definite kernels for comparing partitions. It not only reviews existing examples from the literature but also introduces novel classes of positive definite kernels. These new classes include kernels based on agreement and ones designed using the concept of hidden variables. The study also focuses on assessing the compatibility of these kernels with structural properties that capture the intrinsic notion of proximity between partitions. Notably, agreement-based kernels are demonstrated to align well with this notion. Moreover, the paper provides two generic procedures for designing hidden-feature-based kernels that also adhere to the specified structural properties.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"117 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Positive Definite Kernels for Partitions\",\"authors\":\"Jyrko Correa-Morris\",\"doi\":\"10.37394/23206.2023.22.77\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a comprehensive exploration of various families of positive definite kernels for comparing partitions. It not only reviews existing examples from the literature but also introduces novel classes of positive definite kernels. These new classes include kernels based on agreement and ones designed using the concept of hidden variables. The study also focuses on assessing the compatibility of these kernels with structural properties that capture the intrinsic notion of proximity between partitions. Notably, agreement-based kernels are demonstrated to align well with this notion. Moreover, the paper provides two generic procedures for designing hidden-feature-based kernels that also adhere to the specified structural properties.\",\"PeriodicalId\":55878,\"journal\":{\"name\":\"WSEAS Transactions on Mathematics\",\"volume\":\"117 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23206.2023.22.77\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23206.2023.22.77","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
This paper presents a comprehensive exploration of various families of positive definite kernels for comparing partitions. It not only reviews existing examples from the literature but also introduces novel classes of positive definite kernels. These new classes include kernels based on agreement and ones designed using the concept of hidden variables. The study also focuses on assessing the compatibility of these kernels with structural properties that capture the intrinsic notion of proximity between partitions. Notably, agreement-based kernels are demonstrated to align well with this notion. Moreover, the paper provides two generic procedures for designing hidden-feature-based kernels that also adhere to the specified structural properties.
期刊介绍:
WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.