Spatiotemporal analysis using Riemannian composition of diffusion operators

Tal Shnitzer, Hau Tieng Wu, Ronen Talmon

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number101583
JournalApplied and Computational Harmonic Analysis
Volume68
DOIs
StatePublished - Jan 2024

Keywords

  • Diffusion maps
  • Manifold learning
  • Riemannian geometry
  • Symmetric positive-definite matrices

ASJC Scopus subject areas

  • Applied Mathematics

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