[{"supplementarymaterial":"no","language":[{"iso":"eng"}],"citation":{"short":"R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, Journal of Symbolic Computation 138 (2026).","mla":"Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>, vol. 138, 102598, Elsevier, 2026, doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>.","ama":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. 2026;138. doi:<a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">10.1016/j.jsc.2026.102598</a>","ista":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2026. Additive partial matchings induced by persistence maps. Journal of Symbolic Computation. 138, 102598.","ieee":"R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial matchings induced by persistence maps,” <i>Journal of Symbolic Computation</i>, vol. 138. Elsevier, 2026.","apa":"Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2026). Additive partial matchings induced by persistence maps. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>","chicago":"Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas. “Additive Partial Matchings Induced by Persistence Maps.” <i>Journal of Symbolic Computation</i>. Elsevier, 2026. <a href=\"https://doi.org/10.1016/j.jsc.2026.102598\">https://doi.org/10.1016/j.jsc.2026.102598</a>."},"article_type":"original","main_file_link":[{"url":"https://doi.org/10.1016/j.jsc.2026.102598","open_access":"1"}],"type":"journal_article","corr_author":"1","scopus_import":"1","publication":"Journal of Symbolic Computation","date_created":"2026-07-13T09:43:38Z","oa_version":"Published Version","status":"public","has_accepted_license":"1","external_id":{"arxiv":["2006.11100"]},"mathsc":["55N31","16G20"],"abstract":[{"lang":"eng","text":"Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and fast-to-compute invariant known as the persistence diagram. However, this is no longer the case for maps between persistence modules (i.e. persistence maps). We propose a new invariant for persistence maps, consisting of a partial matching between the persistence diagrams of the domain and codomain modules. We show that this invariant is additive with respect to the direct sum decomposition of persistence maps, is more discriminative than the image module, and is computable in cubic time. Furthermore, we provide an implementation and demonstrate its efficiency by integrating it with edge collapse techniques for flag complexes (e.g., Vietoris–Rips complexes). As a key technical contribution, we describe how to induce a persistence map between two flag complexes that have been independently simplified via edge collapses, even when a direct simplicial map between them is no longer available."}],"OA_type":"hybrid","OA_place":"publisher","intvolume":"       138","arxiv":1,"ddc":["500"],"date_updated":"2026-07-13T12:00:07Z","dataavailabilitystatement":"The code used for the computational experiments is available in https://github.com/Cimagroup/IBloFunMatch","author":[{"full_name":"Gonzalez-Diaz, Rocio","first_name":"Rocio","last_name":"Gonzalez-Diaz"},{"last_name":"Soriano Trigueros","first_name":"Manuel","orcid":"0000-0003-2449-1433","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","full_name":"Soriano Trigueros, Manuel"},{"first_name":"Alvaro","last_name":"Torras-Casas","full_name":"Torras-Casas, Alvaro"}],"volume":138,"month":"06","year":"2026","publication_status":"epub_ahead","_id":"22291","quality_controlled":"1","date_published":"2026-06-23T00:00:00Z","article_number":"102598","das_tickbox":"1","doi":"10.1016/j.jsc.2026.102598","acknowledgement":"This project was partially funded by MCIN/AEI and the NextGenerationEU/PRTR, under project TED2021-129438B-I00. The authors thank IMUS-Maria de Maeztu grant CEX2024-001517-M - Apoyo a Unidades de Excelencia María de Maeztu for supporting this research, funded by MICIU/AEI/ 10.13039/501100011033. The authors would also like to thank Lars M Salbu for fruitful discussions regarding the operators from Definition 4.1 and their relation with the order relations introduced in Definition 3.2.","publisher":"Elsevier","article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"PlanS_conform":"1","keyword":["Persistence module","Persistence map","Persistent homology"],"day":"23","researchdata_availability":"yes","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","license":"https://creativecommons.org/licenses/by/4.0/","title":"Additive partial matchings induced by persistence maps","oa":1},{"supplementarymaterial":"yes","language":[{"iso":"eng"}],"ec_funded":1,"citation":{"apa":"Dey, T. K., Lipiński, M., &#38; Soriano Trigueros, M. (2026). Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-026-09766-6\">https://doi.org/10.1007/s10208-026-09766-6</a>","ista":"Dey TK, Lipiński M, Soriano Trigueros M. 2026. Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. Foundations of Computational Mathematics.","ieee":"T. K. Dey, M. Lipiński, and M. Soriano Trigueros, “Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations,” <i>Foundations of Computational Mathematics</i>. Springer, 2026.","ama":"Dey TK, Lipiński M, Soriano Trigueros M. Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations. <i>Foundations of Computational Mathematics</i>. 2026. doi:<a href=\"https://doi.org/10.1007/s10208-026-09766-6\">10.1007/s10208-026-09766-6</a>","mla":"Dey, Tamal K., et al. “Conley-Morse Persistence Barcode: A Homological Signature of Combinatorial Bifurcations.” <i>Foundations of Computational Mathematics</i>, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s10208-026-09766-6\">10.1007/s10208-026-09766-6</a>.","short":"T.K. Dey, M. Lipiński, M. Soriano Trigueros, Foundations of Computational Mathematics (2026).","chicago":"Dey, Tamal K., Michał Lipiński, and Manuel Soriano Trigueros. “Conley-Morse Persistence Barcode: A Homological Signature of Combinatorial Bifurcations.” <i>Foundations of Computational Mathematics</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s10208-026-09766-6\">https://doi.org/10.1007/s10208-026-09766-6</a>."},"article_type":"original","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.1007/s10208-026-09766-6","open_access":"1"}],"corr_author":"1","publication":"Foundations of Computational Mathematics","oa_version":"Published Version","date_created":"2026-08-05T06:11:30Z","scopus_import":"1","has_accepted_license":"1","external_id":{"arxiv":["2504.17105"]},"status":"public","abstract":[{"lang":"eng","text":"Bifurcation characterizes the qualitative changes in parameterized dynamical systems and is one of the major topics in the field. In this work, we study combinatorial bifurcations within the framework of combinatorial dynamical systems—a young but already well-established theory. We introduce the Conley–Morse persistence barcode, a compact algebraic descriptor of combinatorial bifurcations. This barcode captures structural changes in a dynamical system at the level of Morse decompositions and provides a characterization of the nature of observed transitions in terms of the Conley index. The construction of the Conley–Morse persistence barcode builds upon ideas from topological persistence. Specifically, we consider a persistence module obtained from the Conley index of invariant sets indexed over a poset. Using gentle algebras, we prove that this module decomposes into simple intervals (bars) and compute them by adapting the zigzag persistence algorithm to our purpose."}],"OA_type":"hybrid","project":[{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"OA_place":"publisher","arxiv":1,"ddc":["500"],"date_updated":"2026-08-11T06:13:33Z","author":[{"full_name":"Dey, Tamal K.","first_name":"Tamal K.","last_name":"Dey"},{"last_name":"Lipiński","first_name":"Michał","orcid":"0000-0001-9789-9750","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","full_name":"Lipiński, Michał"},{"id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","full_name":"Soriano Trigueros, Manuel","last_name":"Soriano Trigueros","first_name":"Manuel","orcid":"0000-0003-2449-1433"}],"month":"08","year":"2026","publication_status":"epub_ahead","_id":"22648","date_published":"2026-08-04T00:00:00Z","quality_controlled":"1","das_tickbox":"0","doi":"10.1007/s10208-026-09766-6","acknowledgement":"M.L. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. T.D. acknowledges the support of NSF funds CCF-2437030 and DMS-2301360. The authors would like to thank the anonymous reviewers for their careful reading of the paper. Their feedback significantly improved the quality of the article. T.D. and M.L. would like to acknowledge many thought-provoking discussions with Marian Mrozek on combinatorial dynamical systems and their continuations. M.S.T. would like to thank Álvaro Sánchez for insightful discussions about representation theory. Open access funding provided by Institute of Science and Technology (IST Austria).","publisher":"Springer","article_processing_charge":"Yes (via OA deal)","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_identifier":{"eissn":["1615-3383"],"issn":["1615-3375"]},"PlanS_conform":"1","keyword":["Multivector field","Conley index","Morse decomposition","Bifurcation","Continuation","Zigzag persistence","Persistence barcode","Gentle algebra"],"day":"04","researchdata_availability":"no","department":[{"_id":"HeEd"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Conley-Morse persistence barcode: A homological signature of combinatorial bifurcations","oa":1},{"conference":{"name":"SoCG: Symposium on Computational Geometry","location":"New Brunswick, NJ, United States","start_date":"2026-06-02","end_date":"2026-06-05"},"file":[{"checksum":"9dfb96ee66985c724b499b0e5888dc8e","success":1,"date_updated":"2026-07-14T06:08:05Z","file_id":"22329","file_name":"2026_LIPIcSSoCG_Edelsbrunner.pdf","file_size":2902144,"content_type":"application/pdf","date_created":"2026-07-14T06:08:05Z","relation":"main_file","creator":"dernst","access_level":"open_access"}],"doi":"10.4230/LIPICS.SOCG.2026.41","acknowledgement":"The authors thank Jakub Leśkiewicz and Bartosz Furmanek for discussions\r\nthat helped improve the paper. Herbert Edelsbrunner: DFG Collaborative Research Center TRR 109, Austrian Science\r\nFund (FWF), grant no. I 02979-N35\r\nMichał Lipiński: European Union’s Horizon 2020 research and innovation programme under the\r\nMarie Skłodowska-Curie Grant Agreement No. 101034413\r\nMarian Mrozek: Polish National Science Center under Opus Grant 2019/35/B/ST1/00874 and Opus\r\nGrant 2025/57/B/ST1/00550","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","das_tickbox":"0","date_published":"2026-05-27T00:00:00Z","_id":"22299","quality_controlled":"1","article_number":"41:1-41:18","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The depth poset under transpositions in the filter","oa":1,"keyword":["Algebraic topology","Lefschetz complexes","persistent homology","vines and vineyards","birth-death pairs","shallow pairs","relations","partial orders","transpositions","Theory of computation → Computational geometry"],"researchdata_availability":"no","day":"27","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"article_processing_charge":"Yes","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_identifier":{"isbn":["9783959774185"],"eissn":["1868-8969"]},"OA_place":"publisher","intvolume":"       367","arxiv":1,"ddc":["500"],"date_updated":"2026-08-12T09:02:56Z","project":[{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"},{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"OA_type":"gold","type":"conference","corr_author":"1","oa_version":"Published Version","scopus_import":"1","publication":"42nd International Symposium on Computational Geometry","date_created":"2026-07-13T09:56:38Z","has_accepted_license":"1","status":"public","external_id":{"arxiv":["2511.21961"]},"abstract":[{"text":"The depth poset of a filtered Lefschetz complex reflects the dependencies between the cancellations of different shallow birth-death pairs. Using the fast algorithms for computing the depth poset in [Edelsbrunner et al., 2026] and for updating the persistence diagram under transpositions in [Cohen-Steiner et al., 2006], we give a complete case analysis of how transpositions of cells in the filter affect the depth poset. In addition, we present statistics on the depth poset for random point data and its sensitivity to the transpositions that occur in random straight-line homotopies.","lang":"eng"}],"supplementarymaterial":"no","language":[{"iso":"eng"}],"ec_funded":1,"citation":{"chicago":"Edelsbrunner, Herbert, Michał Lipiński, Marian Mrozek, Manuel Soriano Trigueros, and Fedor Zimin. “The Depth Poset under Transpositions in the Filter.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">https://doi.org/10.4230/LIPICS.SOCG.2026.41</a>.","ista":"Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. 2026. The depth poset under transpositions in the filter. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 367, 41:1-41:18.","ama":"Edelsbrunner H, Lipiński M, Mrozek M, Soriano Trigueros M, Zimin F. The depth poset under transpositions in the filter. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">10.4230/LIPICS.SOCG.2026.41</a>","ieee":"H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, and F. Zimin, “The depth poset under transpositions in the filter,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367.","apa":"Edelsbrunner, H., Lipiński, M., Mrozek, M., Soriano Trigueros, M., &#38; Zimin, F. (2026). The depth poset under transpositions in the filter. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">https://doi.org/10.4230/LIPICS.SOCG.2026.41</a>","short":"H. Edelsbrunner, M. Lipiński, M. Mrozek, M. Soriano Trigueros, F. Zimin, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","mla":"Edelsbrunner, Herbert, et al. “The Depth Poset under Transpositions in the Filter.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 41:1-41:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPICS.SOCG.2026.41\">10.4230/LIPICS.SOCG.2026.41</a>."},"year":"2026","publication_status":"published","file_date_updated":"2026-07-14T06:08:05Z","volume":367,"month":"05","alternative_title":["LIPIcs"],"author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert"},{"first_name":"Michał","orcid":"0000-0001-9789-9750","last_name":"Lipiński","id":"dfffb474-4317-11ee-8f5c-fe3fc95a425e","full_name":"Lipiński, Michał"},{"full_name":"Mrozek, Marian","last_name":"Mrozek","first_name":"Marian","orcid":"0000-0002-0619-6417"},{"orcid":"0000-0003-2449-1433","first_name":"Manuel","last_name":"Soriano Trigueros","full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8"},{"last_name":"Zimin","first_name":"Fedor","id":"afd27eda-91c1-11f0-aad8-c6edbec24c04","full_name":"Zimin, Fedor"}]},{"ddc":["510"],"date_updated":"2025-12-09T13:46:42Z","OA_place":"publisher","OA_type":"hybrid","status":"public","has_accepted_license":"1","abstract":[{"lang":"eng","text":"Persistence modules (defined as a sequence of vector spaces and linear maps between them) are a key tool in topological data analysis. They are easy to interpret and fast to compute. However, when considering persistence maps (i.e. maps between persistence modules), these properties are lost. We propose a new invariant for persistence maps consisting of a partial matching such that: it is easy to interpret, it is more discriminative than the image of the persistence map, and can be calculated with cubical complexity."}],"type":"conference","corr_author":"1","publication":"Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation","scopus_import":"1","date_created":"2025-12-07T23:02:01Z","oa_version":"Published Version","language":[{"iso":"eng"}],"citation":{"mla":"Gonzalez-Diaz, Rocio, et al. “Additive Partial Matchings for Persistent Homology.” <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>, Association for Computing Machinery, 2025, pp. 188–96, doi:<a href=\"https://doi.org/10.1145/3747199.3747561\">10.1145/3747199.3747561</a>.","short":"R. Gonzalez-Diaz, M. Soriano Trigueros, A. Torras-Casas, in:, Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation, Association for Computing Machinery, 2025, pp. 188–196.","apa":"Gonzalez-Diaz, R., Soriano Trigueros, M., &#38; Torras-Casas, A. (2025). Additive partial matchings for persistent homology. In <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i> (pp. 188–196). Guanajuato, Mexico: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3747199.3747561\">https://doi.org/10.1145/3747199.3747561</a>","ama":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. Additive partial matchings for persistent homology. In: <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>. Association for Computing Machinery; 2025:188-196. doi:<a href=\"https://doi.org/10.1145/3747199.3747561\">10.1145/3747199.3747561</a>","ieee":"R. Gonzalez-Diaz, M. Soriano Trigueros, and A. Torras-Casas, “Additive partial matchings for persistent homology,” in <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>, Guanajuato, Mexico, 2025, pp. 188–196.","ista":"Gonzalez-Diaz R, Soriano Trigueros M, Torras-Casas A. 2025. Additive partial matchings for persistent homology. Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation. ISSAC: International Symposium on Symbolic and Algebraic Computation, 188–196.","chicago":"Gonzalez-Diaz, Rocio, Manuel Soriano Trigueros, and Alvaro Torras-Casas. “Additive Partial Matchings for Persistent Homology.” In <i>Proceedings of the 2025 International Symposium on Symbolic and Algebraic Computation</i>, 188–96. Association for Computing Machinery, 2025. <a href=\"https://doi.org/10.1145/3747199.3747561\">https://doi.org/10.1145/3747199.3747561</a>."},"file_date_updated":"2025-12-09T13:43:17Z","publication_status":"published","year":"2025","month":"11","author":[{"full_name":"Gonzalez-Diaz, Rocio","first_name":"Rocio","last_name":"Gonzalez-Diaz"},{"full_name":"Soriano Trigueros, Manuel","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","last_name":"Soriano Trigueros","orcid":"0000-0003-2449-1433","first_name":"Manuel"},{"last_name":"Torras-Casas","first_name":"Alvaro","full_name":"Torras-Casas, Alvaro"}],"page":"188-196","conference":{"end_date":"2025-08-01","start_date":"2025-07-28","location":"Guanajuato, Mexico","name":"ISSAC: International Symposium on Symbolic and Algebraic Computation"},"publisher":"Association for Computing Machinery","doi":"10.1145/3747199.3747561","acknowledgement":"Álvaro Torras-Casas contract is funded by the French Agence Nationale de la Recherche through the project reference ANR-22-CPJ1-0047-01. Rocio Gonzalez-Diaz is partially funded by the European Union under grant agreement no. 101070028-2 (REXASI-PRO).","file":[{"date_created":"2025-12-09T13:43:17Z","content_type":"application/pdf","relation":"main_file","creator":"dernst","access_level":"open_access","success":1,"checksum":"1c299cca165a20e2518afe4fda63dbf1","date_updated":"2025-12-09T13:43:17Z","file_id":"20751","file_name":"2025_ISSAC_GonzalezDiaz.pdf","file_size":761617}],"_id":"20729","date_published":"2025-11-10T00:00:00Z","quality_controlled":"1","title":"Additive partial matchings for persistent homology","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"HeEd"}],"day":"10","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_identifier":{"isbn":["9798400720758"]},"article_processing_charge":"Yes (in subscription journal)"},{"citation":{"chicago":"Ali, Dashti, Aras Asaad, Maria-Jose Jimenez, Vidit Nanda, Eduardo Paluzo-Hidalgo, and Manuel Soriano Trigueros. “A Survey of Vectorization Methods in Topological Data Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/tpami.2023.3308391\">https://doi.org/10.1109/tpami.2023.3308391</a>.","ieee":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, and M. Soriano Trigueros, “A survey of vectorization methods in topological data analysis,” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 45, no. 12. IEEE, pp. 14069–14080, 2023.","ista":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. 2023. A survey of vectorization methods in topological data analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence. 45(12), 14069–14080.","ama":"Ali D, Asaad A, Jimenez M-J, Nanda V, Paluzo-Hidalgo E, Soriano Trigueros M. A survey of vectorization methods in topological data analysis. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. 2023;45(12):14069-14080. doi:<a href=\"https://doi.org/10.1109/tpami.2023.3308391\">10.1109/tpami.2023.3308391</a>","apa":"Ali, D., Asaad, A., Jimenez, M.-J., Nanda, V., Paluzo-Hidalgo, E., &#38; Soriano Trigueros, M. (2023). A survey of vectorization methods in topological data analysis. <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>. IEEE. <a href=\"https://doi.org/10.1109/tpami.2023.3308391\">https://doi.org/10.1109/tpami.2023.3308391</a>","short":"D. Ali, A. Asaad, M.-J. Jimenez, V. Nanda, E. Paluzo-Hidalgo, M. Soriano Trigueros, IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (2023) 14069–14080.","mla":"Ali, Dashti, et al. “A Survey of Vectorization Methods in Topological Data Analysis.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>, vol. 45, no. 12, IEEE, 2023, pp. 14069–80, doi:<a href=\"https://doi.org/10.1109/tpami.2023.3308391\">10.1109/tpami.2023.3308391</a>."},"article_type":"original","language":[{"iso":"eng"}],"publication":"IEEE Transactions on Pattern Analysis and Machine Intelligence","scopus_import":"1","date_created":"2024-01-08T09:59:46Z","oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods. Besides describing an organizational framework for these methods, we comprehensively benchmark them against three well-known classification tasks. Surprisingly, we discover that the best-performing method is a simple vectorization, which consists only of a few elementary summary statistics. Finally, we provide a convenient web application which has been designed to facilitate exploration and experimentation with various vectorization methods."}],"has_accepted_license":"1","external_id":{"isi":["001104973300002"]},"status":"public","intvolume":"        45","date_updated":"2025-09-09T14:08:56Z","ddc":["000"],"page":"14069-14080","author":[{"first_name":"Dashti","last_name":"Ali","full_name":"Ali, Dashti"},{"full_name":"Asaad, Aras","last_name":"Asaad","first_name":"Aras"},{"last_name":"Jimenez","first_name":"Maria-Jose","full_name":"Jimenez, Maria-Jose"},{"first_name":"Vidit","last_name":"Nanda","full_name":"Nanda, Vidit"},{"last_name":"Paluzo-Hidalgo","first_name":"Eduardo","full_name":"Paluzo-Hidalgo, Eduardo"},{"last_name":"Soriano Trigueros","first_name":"Manuel","orcid":"0000-0003-2449-1433","id":"15ebd7cf-15bf-11ee-aebd-bb4bb5121ea8","full_name":"Soriano Trigueros, Manuel"}],"issue":"12","volume":45,"month":"12","year":"2023","file_date_updated":"2024-01-08T10:09:14Z","publication_status":"published","quality_controlled":"1","_id":"14739","date_published":"2023-12-01T00:00:00Z","file":[{"access_level":"open_access","creator":"dernst","relation":"main_file","date_created":"2024-01-08T10:09:14Z","content_type":"application/pdf","file_size":2370988,"file_id":"14740","file_name":"2023_IEEEToP_Ali.pdf","date_updated":"2024-01-08T10:09:14Z","success":1,"checksum":"465c28ef0b151b4b1fb47977ed5581ab"}],"acknowledgement":"The work of Maria-Jose Jimenez, Eduardo Paluzo-Hidalgo and Manuel Soriano-Trigueros was supported in part by the Spanish grant Ministerio de Ciencia e Innovacion under Grants TED2021-129438B-I00 and PID2019-107339GB-I00, and in part by REXASI-PRO H-EU project, call HORIZON-CL4-2021-HUMAN-01-01 under Grant 101070028. The work of\r\nMaria-Jose Jimenez was supported by a grant of Convocatoria de la Universidad de Sevilla para la recualificacion del sistema universitario español, 2021-23, funded by the European Union, NextGenerationEU. The work of Vidit Nanda was supported in part by EPSRC under Grant EP/R018472/1 and in part by US AFOSR under Grant FA9550-22-1-0462. \r\nWe are grateful to the team of GUDHI and TEASPOON developers, for their work and their support. We are also grateful to Streamlit for providing extra resources to deploy the web app\r\nonline on Streamlit community cloud. We thank the anonymous referees for their helpful suggestions.","doi":"10.1109/tpami.2023.3308391","isi":1,"publisher":"IEEE","article_processing_charge":"Yes (in subscription journal)","publication_identifier":{"eissn":["1939-3539"],"issn":["0162-8828"]},"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"day":"01","keyword":["Applied Mathematics","Artificial Intelligence","Computational Theory and Mathematics","Computer Vision and Pattern Recognition","Software"],"department":[{"_id":"HeEd"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","oa":1,"title":"A survey of vectorization methods in topological data analysis"}]