A kernel for multi-parameter persistent homology. Issue 2 (December 2019)

• Record Type: Journal Article
• Authors: Corbet, René; Fugacci, Ulderico; Kerber, Michael; Landi, Claudia; Wang, Bei
• Is Part Of: Computers & graphics. Issue 2(2019)
• Publication Date: 2019-12
• Subjects: Topological data analysis -- Machine learning -- Persistent homology -- Multivariate analysis; Computer graphics -- Periodicals; Computer graphics; Periodicals; 006.605
• DOI: 10.1016/j.cagx.2019.100005
• Languages: English
• ISSNs: 2590-1486

Abstract

Highlights: 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. Graphical abstract: 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.