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 language | English |
---|---|
Article number | 101583 |
Journal | Applied and Computational Harmonic Analysis |
Volume | 68 |
DOIs | |
State | Published - Jan 2024 |
Keywords
- Diffusion maps
- Manifold learning
- Riemannian geometry
- Symmetric positive-definite matrices
All Science Journal Classification (ASJC) codes
- Applied Mathematics