Persistence Weighted Gaussian Kernel for Probability Distributions on the Space of Persistence Diagrams
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A persistence diagram characterizes robust geometric and topological features in data. Data, which will be treated here, are assumed to be drawn from a probability distribution and then the corresponding persistence diagrams have randomness. This paper reveals relationships between distributions and persistence diagrams in the viewpoint of (1) the strong law of large numbers and the central limit theorem, (2) confidence intervals, and (3) stability properties via the persistence weighted Gaussian kernel which is a statistical method for persistence diagrams. In numerical experiments for distributions, our method is compared against other statistical methods for persistence diagrams.
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