Publications [#373608] of Hau-Tieng Wu

Papers Published

1. Shnitzer, T; Wu, HT; Talmon, R, Spatiotemporal analysis using Riemannian composition of diffusion operators, Applied and Computational Harmonic Analysis, vol. 68 (January, 2024) [doi]
   (last updated on 2024/08/30)

   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.