A Kernel for Multi-Parameter Persistent Homology
Machine Learning
2019-06-06 v2 Computational Geometry
Algebraic Topology
Machine Learning
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.
Cite
@article{arxiv.1809.10231,
title = {A Kernel for Multi-Parameter Persistent Homology},
author = {René Corbet and Ulderico Fugacci and Michael Kerber and Claudia Landi and Bei Wang},
journal= {arXiv preprint arXiv:1809.10231},
year = {2019}
}
Comments
24 pages, 5 figures