{"title":"高维最优输运的GenCol算法:重心和Wasserstein样条的一般公式及其应用","authors":"Friesecke, Gero, Penka, Maximilian","doi":"10.1137/22m1524254","DOIUrl":null,"url":null,"abstract":"We extend the recently introduced genetic column generation algorithm for high-dimensional multi-marginal optimal transport from symmetric to general problems. We use the algorithm to calculate accurate mesh-free Wasserstein barycenters and cubic Wasserstein splines.","PeriodicalId":74797,"journal":{"name":"SIAM journal on mathematics of data science","volume":"7 4","pages":"0"},"PeriodicalIF":1.9000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"The GenCol Algorithm for High-Dimensional Optimal Transport: General Formulation and Application to Barycenters and Wasserstein Splines\",\"authors\":\"Friesecke, Gero, Penka, Maximilian\",\"doi\":\"10.1137/22m1524254\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend the recently introduced genetic column generation algorithm for high-dimensional multi-marginal optimal transport from symmetric to general problems. We use the algorithm to calculate accurate mesh-free Wasserstein barycenters and cubic Wasserstein splines.\",\"PeriodicalId\":74797,\"journal\":{\"name\":\"SIAM journal on mathematics of data science\",\"volume\":\"7 4\",\"pages\":\"0\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM journal on mathematics of data science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1524254\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM journal on mathematics of data science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/22m1524254","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The GenCol Algorithm for High-Dimensional Optimal Transport: General Formulation and Application to Barycenters and Wasserstein Splines
We extend the recently introduced genetic column generation algorithm for high-dimensional multi-marginal optimal transport from symmetric to general problems. We use the algorithm to calculate accurate mesh-free Wasserstein barycenters and cubic Wasserstein splines.
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