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|Publication status||Unpublished - 2018|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||34th International Symposium on Computational Geometry: SoCG 2018 - Budapest, Hungary|
Duration: 11 Jun 2018 → 14 Jun 2018
|Conference||34th International Symposium on Computational Geometry|
|Period||11/06/18 → 14/06/18|