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Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators
- Publication Year :
- 2022
-
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.<br />Comment: 48 pages, 13 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2201.08530
- Document Type :
- Working Paper