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||Published - 2019|
|Event||Shape Modeling International (SMI) - Simon Fraser University, Vancouver, Canada|
Duration: 19 Jun 2019 → 21 Jun 2019
|Conference||Shape Modeling International (SMI)|
|Period||19/06/19 → 21/06/19|