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.
|Publication status||Unpublished - 2018|
|Event||Algebraic Topology: Methods, Computation and Science - IST Austria, Klosterneuburg, Austria|
Duration: 25 Jun 2018 → 29 Jun 2018
Conference number: 8
|Conference||Algebraic Topology: Methods, Computation and Science|
|Period||25/06/18 → 29/06/18|