A Kernel for Multi-Parameter Persistent Homology
This work addresses the need for topological data analysis tools in multivariate data analysis, though it appears incremental as it builds upon existing one-parameter kernels.
The authors tackled the problem of connecting multi-parameter persistent homology with machine learning by constructing a kernel that integrates a one-parameter kernel along straight lines, resulting in a stable and efficiently computable solution.
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.