{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:34:32Z","timestamp":1787236472989,"version":"3.56.0"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"VR"},{"name":"Goran Gustafsson Foundation"},{"DOI":"10.13039\/501100001703","name":"\u00cacole Polytechnique F\u00e9d\u00e9rale de Lausanne","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001703","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000882","name":"University of Aberdeen","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000882","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Algebra Geometry"],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We propose the use of persistent homology in a supervised way. We believe homological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between persistent vector spaces leads to a model. Fitting this model is what we believe supervised homological persistence is. We develop theory behind constructing such models and we give evidence of the usefulness of this approach in concrete data analysis tasks.<\/jats:p>","DOI":"10.1137\/19m1243932","type":"journal-article","created":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T14:09:17Z","timestamp":1580393357000},"page":"69-98","source":"Crossref","is-referenced-by-count":8,"title":["Metrics and Stabilization in One Parameter Persistence"],"prefix":"10.1137","volume":"4","author":[{"given":"Wojciech","family":"Chach\u00f3lski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Henri","family":"Riihim\u00e4ki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,1,30]]},"reference":[{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TAES.2016.160405"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1214\/15-AOAS886"},{"key":"atypb4","unstructured":"C. Biscio and J. M\u00c3\u00b8ller,\n                      The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, with a View to Brain Artery Trees and Spatial Point Process Applications\n                      , preprint,https:\/\/arxiv.org\/abs\/1611.00630, 2016."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-014-9229-5"},{"key":"atypb6","unstructured":"O. G\u00e4fvert,\n                      Algorithms for Multidimensional Persistence\n                      , Master's thesis, KTH, Stockholm, Sweden, 2016,http:\/\/kth.diva-portal.org\/smash\/record.jsf?pid=diva2:939842."},{"key":"atypb7","unstructured":"O. G\u00e4fvert and W. Chach\u00f3lski,\n                      Stable Invariants for Multidimensional Persistence\n                      , preprint,https:\/\/arxiv.org\/abs\/1703.03632, 2017."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1520877113"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1214\/17-AAP1371"},{"key":"atypb10","first-page":"563","author":"Lemley R. A. J.","year":"2016","journal-title":"Washington, DC"},{"key":"atypb11","unstructured":"D. M. K. Meehan,\n                      An Isometry Theorem for Generalized Persistence Modules\n                      , preprint,https:\/\/arxiv.org\/abs\/1710.02858, 2017."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s12021-017-9341-1"},{"key":"atypb13","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1038\/s41467-017-00017-5","volume":"8","author":"Lee Y.","year":"2017","journal-title":"Nature Commun."},{"key":"atypb15","unstructured":"V. Puuska,\n                      Erosion Distance for Generalized Persistence Modules\n                      , preprint,https:\/\/arxiv.org\/abs\/1710.01577, 2017."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s41468-017-0008-7"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-016-9323-y"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1063\/1.4978997"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2655"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.2719"}],"container-title":["SIAM Journal on Applied Algebra and Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1243932","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:25:23Z","timestamp":1787232323000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1243932"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1243932"],"URL":"https:\/\/doi.org\/10.1137\/19m1243932","relation":{},"ISSN":["2470-6566"],"issn-type":[{"value":"2470-6566","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}