  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.

Machine Learning;Computational Geometry;Algebraic Topology;Machine Learning