Persistence B-spline grids: stable vector representation of persistence diagrams based on data fitting
Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological f...
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| Veröffentlicht in: | Machine learning 2024-03, Vol.113 (3), p.1373-1420 |
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| container_title | Machine learning |
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| creator | Dong, Zhetong Lin, Hongwei Zhou, Chi Zhang, Ben Li, Gengchen |
| description | Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological features. From the perspective of data fitting, a stable vector representation, namely,
persistence B-spline grid
(PBSG), is developed based on the efficient technique of progressive-iterative approximation for least-squares B-spline function fitting. We theoretically prove that the PBSG method is stable with respect to the metric of 1-Wasserstein distance defined on the PD space. The developed method was tested on a synthetic data set, data sets of randomly generated PDs, data of a dynamical system, and 3D CAD models, showing its effectiveness and efficiency. |
| doi_str_mv | 10.1007/s10994-023-06492-w |
| format | Article |
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persistence B-spline grid
(PBSG), is developed based on the efficient technique of progressive-iterative approximation for least-squares B-spline function fitting. We theoretically prove that the PBSG method is stable with respect to the metric of 1-Wasserstein distance defined on the PD space. The developed method was tested on a synthetic data set, data sets of randomly generated PDs, data of a dynamical system, and 3D CAD models, showing its effectiveness and efficiency.</description><identifier>ISSN: 0885-6125</identifier><identifier>EISSN: 1573-0565</identifier><identifier>DOI: 10.1007/s10994-023-06492-w</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Approximation ; Artificial Intelligence ; B spline functions ; Bar codes ; Computer Science ; Control ; Data analysis ; Datasets ; Homology ; Iterative methods ; Machine Learning ; Mechatronics ; Methods ; Natural Language Processing (NLP) ; Representations ; Robotics ; Simulation and Modeling ; Synthetic data ; Three dimensional models ; Topology</subject><ispartof>Machine learning, 2024-03, Vol.113 (3), p.1373-1420</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-4306fbd6b4e1c37550bd0e60e627462bbfad601e8bc430492c9f9ed7adb03b0c3</cites><orcidid>0000-0002-9337-9624</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10994-023-06492-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10994-023-06492-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Dong, Zhetong</creatorcontrib><creatorcontrib>Lin, Hongwei</creatorcontrib><creatorcontrib>Zhou, Chi</creatorcontrib><creatorcontrib>Zhang, Ben</creatorcontrib><creatorcontrib>Li, Gengchen</creatorcontrib><title>Persistence B-spline grids: stable vector representation of persistence diagrams based on data fitting</title><title>Machine learning</title><addtitle>Mach Learn</addtitle><description>Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological features. From the perspective of data fitting, a stable vector representation, namely,
persistence B-spline grid
(PBSG), is developed based on the efficient technique of progressive-iterative approximation for least-squares B-spline function fitting. We theoretically prove that the PBSG method is stable with respect to the metric of 1-Wasserstein distance defined on the PD space. 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persistence B-spline grid
(PBSG), is developed based on the efficient technique of progressive-iterative approximation for least-squares B-spline function fitting. We theoretically prove that the PBSG method is stable with respect to the metric of 1-Wasserstein distance defined on the PD space. The developed method was tested on a synthetic data set, data sets of randomly generated PDs, data of a dynamical system, and 3D CAD models, showing its effectiveness and efficiency.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10994-023-06492-w</doi><tpages>48</tpages><orcidid>https://orcid.org/0000-0002-9337-9624</orcidid></addata></record> |
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| subjects | Approximation Artificial Intelligence B spline functions Bar codes Computer Science Control Data analysis Datasets Homology Iterative methods Machine Learning Mechatronics Methods Natural Language Processing (NLP) Representations Robotics Simulation and Modeling Synthetic data Three dimensional models Topology |
| title | Persistence B-spline grids: stable vector representation of persistence diagrams based on data fitting |
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