{"title":"基于Wasserstein - Procrustes度量的基于协方差的功能数据软聚类","authors":"Valentina Masarotto, Guido Masarotto","doi":"10.1111/sjos.12692","DOIUrl":null,"url":null,"abstract":"Abstract We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein‐Procrustes distance, where the in‐between cluster variability is penalised by a term proportional to the entropy of the partition matrix. In this way, each covariance operator can be partially classified into more than one group. Such soft classification allows for clusters to overlap, and arises naturally in situations where the separation between all or some of the clusters is not well‐defined. We also discuss how to estimate the number of groups and to test for the presence of any cluster structure. The algorithm is illustrated using simulated and real data. An R implementation is available in the Supplementary materials. This article is protected by copyright. All rights reserved.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"78 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Covariance‐based soft clustering of functional data based on the Wasserstein‐Procrustes metric\",\"authors\":\"Valentina Masarotto, Guido Masarotto\",\"doi\":\"10.1111/sjos.12692\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein‐Procrustes distance, where the in‐between cluster variability is penalised by a term proportional to the entropy of the partition matrix. In this way, each covariance operator can be partially classified into more than one group. Such soft classification allows for clusters to overlap, and arises naturally in situations where the separation between all or some of the clusters is not well‐defined. We also discuss how to estimate the number of groups and to test for the presence of any cluster structure. The algorithm is illustrated using simulated and real data. An R implementation is available in the Supplementary materials. This article is protected by copyright. All rights reserved.\",\"PeriodicalId\":49567,\"journal\":{\"name\":\"Scandinavian Journal of Statistics\",\"volume\":\"78 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Scandinavian Journal of Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1111/sjos.12692\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scandinavian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/sjos.12692","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Covariance‐based soft clustering of functional data based on the Wasserstein‐Procrustes metric
Abstract We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein‐Procrustes distance, where the in‐between cluster variability is penalised by a term proportional to the entropy of the partition matrix. In this way, each covariance operator can be partially classified into more than one group. Such soft classification allows for clusters to overlap, and arises naturally in situations where the separation between all or some of the clusters is not well‐defined. We also discuss how to estimate the number of groups and to test for the presence of any cluster structure. The algorithm is illustrated using simulated and real data. An R implementation is available in the Supplementary materials. This article is protected by copyright. All rights reserved.
期刊介绍:
The Scandinavian Journal of Statistics is internationally recognised as one of the leading statistical journals in the world. It was founded in 1974 by four Scandinavian statistical societies. Today more than eighty per cent of the manuscripts are submitted from outside Scandinavia.
It is an international journal devoted to reporting significant and innovative original contributions to statistical methodology, both theory and applications.
The journal specializes in statistical modelling showing particular appreciation of the underlying substantive research problems.
The emergence of specialized methods for analysing longitudinal and spatial data is just one example of an area of important methodological development in which the Scandinavian Journal of Statistics has a particular niche.