Kernel method for persistence diagrams via kernel embedding and weight factor

Abstract

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy topological properties. Nowadays, it is highly desired to develop a statistical framework on persistence diagrams to deal with practical data. This paper proposes a kernel method on persistence diagrams. A theoretical contribution of our method is that the proposed kernel allows one to control the effect of persistence, and, if necessary, noisy topological properties can be discounted in data analysis. Furthermore, the method provides a fast approximation technique. The method is applied into several problems including practical data in physics, and the results show the advantage compared to the existing kernel method on persistence diagrams.

12 figures, 30 pages

References in corpus (5)

• Statistical topological data analysis using persistence landscapes
• Kernel Mean Embedding of Distributions: A Review and Beyond
• Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks
• Persistence weighted Gaussian kernel for topological data analysis
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Cited by in corpus (4)

• Sliced Wasserstein Kernel for Persistence Diagrams
• Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization
• Topology-Informed Machine Learning for Efficient Prediction of Solid Oxide Fuel Cell Electrode Polarization
• Persistence Diagrams with Linear Machine Learning Models