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.

A kernel for multi-parameter persistent homology / Corbet, René; Fugacci, Ulderico; Kerber, Michael; Landi, Claudia; Wang, Bei. - In: COMPUTERS & GRAPHICS. X. - ISSN 2590-1486. - 2:(2019), pp. 1-11. [10.1016/j.cagx.2019.100005]

A kernel for multi-parameter persistent homology

Landi, Claudia;
2019

Abstract

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.
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A kernel for multi-parameter persistent homology / Corbet, René; Fugacci, Ulderico; Kerber, Michael; Landi, Claudia; Wang, Bei. - In: COMPUTERS & GRAPHICS. X. - ISSN 2590-1486. - 2:(2019), pp. 1-11. [10.1016/j.cagx.2019.100005]
Corbet, René; Fugacci, Ulderico; Kerber, Michael; Landi, Claudia; Wang, Bei
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1178404
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