A kernel for multi-parameter persistent homology

•We propose the first kernel construction for multi-parameter persistent homology.•Our kernel is generic, stable and can be approximated in polynomial time.•Connect topological data analysis and machine learning for multivariate analysis.•Our technique is applicable to shape analysis, recognition an...

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Vydáno v:Computers & graphics. X Ročník 2; s. 100005
Hlavní autoři: Corbet, René, Fugacci, Ulderico, Kerber, Michael, Landi, Claudia, Wang, Bei
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.12.2019
Témata:
Machine learning
Multivariate analysis
Persistent homology
Topological data analysis
Persistent homology
Multivariate analysis
Topological data analysis
Machine learning
Persistent Homology
Multivariate Analysis
Machine Learning
Topological Data Analysis
ISSN:2590-1486, 2590-1486
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Shrnutí:•We propose the first kernel construction for multi-parameter persistent homology.•Our kernel is generic, stable and can be approximated in polynomial time.•Connect topological data analysis and machine learning for multivariate analysis.•Our technique is applicable to shape analysis, recognition and classification. [Display omitted] Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques with applicability on shape analysis, recognition and classification. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.
Bibliografie:ObjectType-Article-1
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ISSN:2590-1486
2590-1486
DOI:10.1016/j.cagx.2019.100005