A kernel for multi-parameter persistent homology

• Main Authors: René Corbet, Ulderico Fugacci, Michael Kerber, Claudia Landi, Bei Wang
• Format: Article
• Language: English
• Published: Elsevier 2019-12-01
• Series: Computers & Graphics: X
• Online Access: http://www.sciencedirect.com/science/article/pii/S2590148619300056

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. Keywords: Topological data analysis, Machine learning, Persistent homology, Multivariate analysis