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A Kernel for Multi-Parameter Persistent Homology (1809.10231v2)
Published 26 Sep 2018 in cs.LG, cs.CG, math.AT, and stat.ML
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. 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.