动态图上在线滤波，适应节点持续增长的现实网络。
Online Graph Filtering Over Expanding Graphs
- 基于在线学习设计可随图结构演化自适应的滤波器
- 在合成与真实数据上表现优于基线方法
- 适合处理节点数动态增长的时序图信号任务
图滤波是多种下游任务中处理图信号的核心工具。然而，传统图滤波通常针对节点数量固定的图设计，而现实世界网络往往随时间增长。这种拓扑演化通常可由随机模型描述，导致传统图滤波难以应对拓扑变化、不确定性以及输入数据的动态性。为此，我们提出一种基于在线学习原理的在线图滤波框架，设计了在拓扑已知与未知场景下的滤波器，并引入可适应演化的学习器。通过后悔值分析，揭示了在线算法、滤波阶数与增长图模型等因素的作用。数值实验在合成与真实数据上验证了该方法在图信号推断任务中的有效性，性能优于基线和现有先进方法。
原文摘要 · Abstract (English)
Graph filters are a staple tool for processing signals over graphs in a multitude of downstream tasks. However, they are commonly designed for graphs with a fixed number of nodes, despite real-world networks typically grow over time. This topological evolution is often known up to a stochastic model, thus, making conventional graph filters ill-equipped to withstand such topological changes, their uncertainty, as well as the dynamic nature of the incoming data. To tackle these issues, we propose an online graph filtering framework by relying on online learning principles. We design filters for scenarios where the topology is both known and unknown, including a learner adaptive to such evolution. We conduct a regret analysis to highlight the role played by the different components such as the online algorithm, the filter order, and the growing graph model. Numerical experiments with synthetic and real data corroborate the proposed approach for graph signal inference tasks and show a competitive performance w.r.t. baselines and state-of-the-art alternatives.
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