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Kernel Density Estimation on Spaces of Gaussian Distributions and Symmetric Positive Definite Matrices

Abstract : This paper analyzes the kernel density estimation on spaces of Gaussian distributions endowed with different metrics. Expressions of kernels are provided for the 2-Wasserstein metric on the space of multivariate Gaussians. For the Fisher metric the kernels are provided only for univariate Gaussians and multivariate centered Gaussians. The density estimation is successfully applied to a classification problem of electro-encephalographic signals.
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Submitted on : Friday, June 9, 2017 - 3:03:53 PM
Last modification on : Wednesday, November 17, 2021 - 12:27:14 PM
Long-term archiving on: : Sunday, September 10, 2017 - 1:18:37 PM

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Emmanuel Chevallier, Emmanuel Kalunga, Jesus Angulo. Kernel Density Estimation on Spaces of Gaussian Distributions and Symmetric Positive Definite Matrices. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, 10 (1), pp.191 - 215. ⟨10.1137/15M1053566⟩. ⟨hal-01535731⟩

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