在线学习动态图结构,实时追踪信号流中的网络变化。
Online Proximal ADMM for Graph Learning from Streaming Smooth Signals
- 基于改进的ADMM算法,逐次处理信号流以降低内存开销。
- 在真实与合成数据上实现比现有方法更优的连接追踪性能。
- 适合需要实时更新图结构的传感器网络等场景使用。
图信号处理涉及利用图结构对多变量数据进行分析的算法与信号表示。通常图拓扑并不直接可用且可能随时间变化,因此从节点观测(如传感器数据)中学习动态图结构成为关键的第一步。本文提出一种新型在线图学习算法,通过连续处理平滑信号流来推断潜在图结构。与批量算法不同,该方法采用顺序处理策略,有效控制内存和计算成本。为解决由此产生的平滑性正则化、时变逆问题,我们构建了基于近端交替方向乘子法(proximal ADMM)的轻量级在线迭代。近端项自然引入时序变化正则化,我们在简化假设下证明该过程具有次线性静态遗憾。在合成与真实图上的可复现实验表明,该方法能有效适应流式信号并跟踪缓慢变化的网络连通性。相比当前最先进的在线图学习基线,本方法在次优性指标上表现更优。
原文摘要 · Abstract (English)
Graph signal processing deals with algorithms and signal representations that leverage graph structures for multivariate data analysis. Often said graph topology is not readily available and may be time-varying, hence (dynamic) graph structure learning from nodal (e.g., sensor) observations becomes a critical first step. In this paper, we develop a novel algorithm for online graph learning using observation streams, assumed to be smooth on the latent graph. Unlike batch algorithms for topology identification from smooth signals, our modus operandi is to process graph signals sequentially and thus keep memory and computational costs in check. To solve the resulting smoothness-regularized, time-varying inverse problem, we develop online and lightweight iterations built upon the proximal variant of the alternating direction method of multipliers (ADMM), well known for its fast convergence in batch settings. The proximal term in the topology updates seamlessly implements a temporal-variation regularization, and we argue the online procedure exhibits sublinear static regret under some simplifying assumptions. Reproducible experiments with synthetic and real graphs demonstrate the effectiveness of our method in adapting to streaming signals and tracking slowly-varying network connectivity. The proposed approach also exhibits better tracking performance (in terms of suboptimality), when compared to state-of-the-art online graph learning baselines.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。