Moo K Chung, Hyekyoung Lee, Victor Solo, Richard J Davidson, Seth D Pollak
{"title":"Topological Distances Between Brain Networks.","authors":"Moo K Chung, Hyekyoung Lee, Victor Solo, Richard J Davidson, Seth D Pollak","doi":"10.1007/978-3-319-67159-8_19","DOIUrl":null,"url":null,"abstract":"<p><p>Many existing brain network distances are based on matrix norms. The element-wise differences may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A few extreme edge weights may severely affect the distance. Thus it is necessary to develop network distances that recognize topology. In this paper, we introduce Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (KS) distances. GH-distance is often used in persistent homology based brain network models. The superior performance of KS-distance is contrasted against matrix norms and GH-distance in random network simulations with the ground truths. The KS-distance is then applied in characterizing the multimodal MRI and DTI study of maltreated children.</p>","PeriodicalId":92190,"journal":{"name":"Connectomics in neuroimaging : First International Workshop, CNI 2017, held in conjunction with MICCAI 2017, Quebec City, QC, Canada, September 14, 2017, proceedings. CNI (Workshop) (1st : 2017 : Quebec, Quebec)","volume":"10511 ","pages":"161-170"},"PeriodicalIF":0.0000,"publicationDate":"2017-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/978-3-319-67159-8_19","citationCount":"42","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Connectomics in neuroimaging : First International Workshop, CNI 2017, held in conjunction with MICCAI 2017, Quebec City, QC, Canada, September 14, 2017, proceedings. CNI (Workshop) (1st : 2017 : Quebec, Quebec)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/978-3-319-67159-8_19","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2017/9/2 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 42
Abstract
Many existing brain network distances are based on matrix norms. The element-wise differences may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A few extreme edge weights may severely affect the distance. Thus it is necessary to develop network distances that recognize topology. In this paper, we introduce Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (KS) distances. GH-distance is often used in persistent homology based brain network models. The superior performance of KS-distance is contrasted against matrix norms and GH-distance in random network simulations with the ground truths. The KS-distance is then applied in characterizing the multimodal MRI and DTI study of maltreated children.