用柯普曼框架建模动态图信号演化，实现预测与补全
Learning Time-Varying Graph Signals via Koopman
- 基于柯普曼自编码器学习图信号的非线性动态演化规律
- 在隐空间中将图结构转为向量序列，捕捉时间变化特征
- 适用于传感器数据、无人机轨迹等动态图场景
现实世界中的大量数据，如分布式传感器采集的海面温度、多架无人机轨迹等，可自然表示为具有非欧几里得结构的图，且常随时间演变形成时变图。有效建模与分析此类动态图数据对预测图演化和重构缺失图数据至关重要。本文提出一种基于柯普曼自编码器（KAE）的框架来处理时变图数据。具体而言，假设存在一个隐藏的非线性动力系统，其状态向量对应时变图信号的图嵌入。首先通过图嵌入将图数据转化为向量时间序列，以有限维隐空间表示结构信息。在该隐空间中，应用KAE学习驱动图特征时间演化的潜在非线性动力学，从而支持预测与重构任务。
原文摘要 · Abstract (English)
A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting non-Euclidean structures. These graph representations may evolve over time, forming time-varying graphs. Effectively modeling and analyzing such dynamic graph data is critical for tasks like predicting graph evolution and reconstructing missing graph data. In this paper, we propose a framework based on the Koopman autoencoder (KAE) to handle time-varying graph data. Specifically, we assume the existence of a hidden non-linear dynamical system, where the state vector corresponds to the graph embedding of the time-varying graph signals. To capture the evolving graph structures, the graph data is first converted into a vector time series through graph embedding, representing the structural information in a finite-dimensional latent space. In this latent space, the KAE is applied to learn the underlying non-linear dynamics governing the temporal evolution of graph features, enabling both prediction and reconstruction tasks.
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