论文标题
使用扩散算子的Riemannian组成的时空分析
Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators
论文作者
论文摘要
近年来，多元时间序列变得丰富，因为许多数据收购系统通过多个传感器同时记录信息。在本文中，我们假设变量与某些几何形状有关，并提出了一种基于操作的时空分析方法。我们的方法结合了通常单独考虑的三个组件：（i）用于构建变量几何形状的构建操作员的多种多样学习，（ii）对称对称的对称的对称的正定定义矩阵的Riemannian几何，用于对应于不同时间样本的操作员的多尺度组成，以及（III）对不同动力学模式的组合操作员的光谱分析。我们提出了一种类似于经典小波分析的方法，我们称这种方法是riemannian多分辨率分析（RMRA）。我们在复合算子的光谱分析上提供了一些理论结果，并证明了有关模拟和实际数据的建议方法。
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.
