{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:27:12Z","timestamp":1776842832638,"version":"3.51.2"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100005376","name":"American Mathematical Society","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100005376","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1916439"],"award-info":[{"award-number":["DMS 1916439"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2021R1C1C2014185"],"award-info":[{"award-number":["2021R1C1C2014185"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Journal on Mathematics of Data Science"],"published-print":{"date-parts":[[2025,6,30]]},"DOI":"10.1137\/24m1641312","type":"journal-article","created":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T07:33:14Z","timestamp":1746516794000},"page":"572-596","source":"Crossref","is-referenced-by-count":1,"title":["G-Mapper: Learning a Cover in the Mapper Construction"],"prefix":"10.1137","volume":"7","author":[{"given":"Enrique","family":"Alvarado","sequence":"first","affiliation":[{"name":"Department of Mathematics, Iowa State University, Ames, IA 50011 USA."}]},{"given":"Robin","family":"Belton","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Vassar College, Poughkeepsie, NY 12604 USA."}]},{"given":"Emily","family":"Fischer","sequence":"additional","affiliation":[{"name":"Umpqua Bank, Portland, OR 97204 USA."}]},{"given":"Kang-Ju","family":"Lee","sequence":"additional","affiliation":[{"name":"Corresponding author. Research Institute of Mathematics, Seoul National University, Seoul 08826, South Korea."}]},{"given":"Sourabh","family":"Palande","sequence":"additional","affiliation":[{"name":"Donald Danforth Plant Science Center, Olivette, MO 63132 USA."}]},{"given":"Sarah","family":"Percival","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131 USA."}]},{"given":"Emilie","family":"Purvine","sequence":"additional","affiliation":[{"name":"Mathematics of Data Science, Pacific Northwest National Laboratory, Seattle, WA, 98109."}]}],"member":"351","published-online":{"date-parts":[[2025,5,6]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1214\/aoms\/1177729437","volume":"23","author":"Anderson T. W.","year":"1952","journal-title":"Ann. Math. Statist."},{"key":"ref2","doi-asserted-by":"crossref","first-page":"e2003634119","DOI":"10.1073\/pnas.2003634119","volume":"119","author":"Berenhaut K. S.","year":"2022","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref3","volume-title":"Pattern Recognition with Fuzzy Objective Function Algorithms","author":"Bezdek J. C.","year":"2013"},{"key":"ref4","volume-title":"Pattern Recognition and Machine Learning","author":"Bishop C. M.","year":"2006"},{"key":"ref5","doi-asserted-by":"crossref","first-page":"105107","DOI":"10.1016\/j.knosys.2019.105107","volume":"189","author":"Bui Q.-T.","year":"2020","journal-title":"Knowl.-Based Syst."},{"key":"ref6","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1090\/S0273-0979-09-01249-X","volume":"46","author":"Carlsson G.","year":"2009","journal-title":"Bull. Amer. Math. Soc."},{"key":"ref7","first-page":"478","volume":"19","author":"Carri\u00e8re M.","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"ref9","first-page":"1","volume":"28","author":"Chen X.","year":"2009","journal-title":"ACM Trans. Graph."},{"key":"ref10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/gigascience\/gix070","volume":"6","author":"Chitwood D. H.","year":"2017","journal-title":"GigaScience"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1007\/s41468-023-00142-9","volume":"8","author":"Chowdhury S.","year":"2024","journal-title":"J. Appl. Comput. Topol."},{"key":"ref12","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s10208-008-9027-z","volume":"9","author":"Cohen-Steiner D.","year":"2009","journal-title":"Found. Comput. Math."},{"key":"ref13","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S1473-3099(20)30120-1","volume":"20","author":"Dong E.","year":"2020","journal-title":"Lancet Infect. Dis."},{"key":"ref14","volume-title":"Pattern Classification","author":"Duda R. O.","year":"2012"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1080\/01969727308546046","volume":"3","author":"Dunn J. C.","year":"1973","journal-title":"J. Cybernetics"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1201\/9780203753064-9","volume-title":"Goodness-of-Fit Techniques","author":"D\u2019Agostino R. B.","year":"2017"},{"key":"ref18","first-page":"035010","volume":"5","author":"Fesser L.","year":"2024","journal-title":"J. Phys.: Complex."},{"key":"ref19","first-page":"281","volume":"16","author":"Hamerly G.","year":"2003","journal-title":"Adv. Neur. Inform. Process. Syst."},{"key":"ref20","first-page":"1","volume":"4","author":"Hu X.","year":"2004","journal-title":"Neural Inform. Process. Lett. Rev."},{"key":"ref21","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.ins.2022.11.139","volume":"622","author":"Ikotun A. M.","year":"2023","journal-title":"Inform. Sci."},{"key":"ref22","volume-title":"Algorithms for Clustering Data","author":"Jain A. K.","year":"1988"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF02289588","volume":"32","author":"Johnson S. C.","year":"1967","journal-title":"Psychometrika"},{"key":"ref26","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1214\/aos\/1176348772","volume":"20","author":"Leroux B. G.","year":"1992","journal-title":"Ann. Statist."},{"key":"ref27","first-page":"311ra174","volume":"7","author":"Li L.","year":"2015","journal-title":"Sci. Transl. Med."},{"key":"ref28","first-page":"167","volume-title":"Mathematical Software \u2013 ICMS","author":"Maria C.","year":"2014"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1080\/01621459.1951.10500769","volume":"46","author":"Massey F. J.","year":"1951","journal-title":"J. Amer. Stat. Assoc."},{"key":"ref30","first-page":"341","volume":"4","author":"McLachlan G. J.","year":"2014","journal-title":"Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"7265","DOI":"10.1073\/pnas.1102826108","volume":"108","author":"Nicolau M.","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"e1011845","DOI":"10.1371\/journal.pcbi.1011845","volume":"20","author":"Percival S.","year":"2024","journal-title":"Plos Comput. Biol."},{"key":"ref34","doi-asserted-by":"crossref","unstructured":"A. Rathore, N. Chalapathi, S. Palande, and B. Wang, TopoAct: Visually exploring the shape of activations in deep learning, in Computer Graphics Forum, Wiley Online Library, 2021, pp. 382\u2013397, https:\/\/doi.org\/10.1111\/cgf.14195.","DOI":"10.1111\/cgf.14195"},{"key":"ref35","first-page":"186","volume":"22","author":"Rathore A.","year":"2023","journal-title":"Inform. Visual."},{"key":"ref36","first-page":"847","volume":"222","author":"Reeb G.","year":"1946","journal-title":"Comptes Rendus Acad. Sciences Paris"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s11634-013-0134-6","volume":"7","author":"R\u00f6blitz S.","year":"2013","journal-title":"Adv. Data Anal. Classi."},{"key":"ref38","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1080\/01621459.1997.10474044","volume":"92","author":"Roeder K.","year":"1997","journal-title":"J. Amer. Statist. Assoc."},{"key":"ref39","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","volume":"20","author":"Rousseeuw P. J.","year":"1987","journal-title":"J. Comput. Appl. Math."},{"key":"ref40","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1093\/biomet\/52.3-4.591","volume":"52","author":"Shapiro S. S.","year":"1965","journal-title":"Biometrika"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"80716","DOI":"10.1109\/ACCESS.2020.2988796","volume":"8","author":"Sinaga K. P.","year":"2020","journal-title":"IEEE Access"},{"key":"ref42","first-page":"091","volume":"2","author":"Singh G.","year":"2007","journal-title":"PBG@ Eurographics"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1080\/01621459.1974.10480196","volume":"69","author":"Stephens M. A.","year":"1974","journal-title":"J. Amer. Statist. Assoc."},{"key":"ref44","first-page":"1","volume":"22","author":"Tauzin G.","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"ref45","first-page":"2579","volume":"9","author":"Van der Maaten L.","year":"2008","journal-title":"J. Mach. Learn. Res."},{"key":"ref46","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.21105\/joss.01315","volume":"4","author":"Van Veen H. J.","year":"2019","journal-title":"J. Open Source Software"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11222-007-9033-z","volume":"17","author":"Von Luxburg U.","year":"2007","journal-title":"Stat. Comput."},{"key":"ref51","first-page":"41","volume-title":"IEEE Topological Data Analysis and Visualization (TopoInVis)","author":"Zhou Y.","year":"2023"}],"container-title":["SIAM Journal on Mathematics of Data Science"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T07:33:33Z","timestamp":1746516813000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1641312"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,6]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6,30]]}},"alternative-id":["10.1137\/24M1641312"],"URL":"https:\/\/doi.org\/10.1137\/24m1641312","relation":{},"ISSN":["2577-0187"],"issn-type":[{"value":"2577-0187","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,6]]}}}