{"title":"数据科学拓扑方法的各个方面。","authors":"Jelena Grbić, Jie Wu, Kelin Xia, Guo-Wei Wei","doi":"10.3934/fods.2022002","DOIUrl":null,"url":null,"abstract":"<p><p>We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.</p>","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9881677/pdf/nihms-1825620.pdf","citationCount":"0","resultStr":"{\"title\":\"ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE.\",\"authors\":\"Jelena Grbić, Jie Wu, Kelin Xia, Guo-Wei Wei\",\"doi\":\"10.3934/fods.2022002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.</p>\",\"PeriodicalId\":73054,\"journal\":{\"name\":\"Foundations of data science (Springfield, Mo.)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9881677/pdf/nihms-1825620.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Foundations of data science (Springfield, Mo.)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/fods.2022002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of data science (Springfield, Mo.)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/fods.2022002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE.
We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.
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