Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators

• URL: http://arxiv.org/abs/2201.08530v1
• Date: Fri, 21 Jan 2022 03:52:33 GMT
• Title: Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators
• Authors: Tal Shnitzer, Hau-Tieng Wu and Ronen Talmon
• Abstract summary: We assume the variables pertain to some geometry and present an operator-based approach for time-series analysis. Our approach combines three components that are often considered separately: (i) manifold for learning operators representing the geometry of the matrices, (ii) symmetric positive-definite geometry for multiscale composition of operators corresponding to different time samples, and (iii) spectral analysis of the composite operators for extracting different dynamic modes.
• Score: 11.533336104503311
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an operator-based approach for spatiotemporal analysis. Our approach combines three components that are often considered separately: (i) manifold learning for building operators representing the geometry of the variables, (ii) Riemannian geometry of symmetric positive-definite matrices for multiscale composition of operators corresponding to different time samples, and (iii) spectral analysis of the composite operators for extracting different dynamic modes. We propose a method that is analogous to the classical wavelet analysis, which we term Riemannian multi-resolution analysis (RMRA). We provide some theoretical results on the spectral analysis of the composite operators, and we demonstrate the proposed method on simulations and on real data.

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