提出一种基于距离感知拉普拉斯的子图滤波代数，提升不完整图数据下的信号处理性能。
Filter Learning for Subgraphs: Algebras and Performance Risk Bounds
- 构建距离感知拉普拉斯的子图滤波代数，实现结构可控的滤波器设计
- 在真实数据集上，性能优于多项式滤波、分布无关算子和直接数值学习基线
- 理论给出性能风险界，量化学习算子对全局映射的逼近程度，适合图信号处理研究者
依赖频谱信息的图信号处理任务通常假设可获取完整的图拓扑，但实际中常不可行。本文提出子图滤波学习（SFL）的系统性框架，其中子图支持的算子在部分观测下近似环境图滤波器。将SFL建模为统计学习问题，最优子图算子本质上依赖于数据。为解决直接估计的困难，提出基于距离感知拉普拉斯构造的子图滤波代数，定义了一类结构化且可控的滤波器，以实现有效逼近。进一步在最小二乘损失下建立性能风险界，量化学习算子对受限环境映射的逼近能力。实验表明，在真实数据集上，所提代数模型在子图滤波任务中始终优于多项式滤波、分布无关算子及尝试从数据中恢复底层结构的直接数值滤波学习基线。
原文摘要 · Abstract (English)
Graph signal processing tasks that leverage spectral information typically assume access to the complete graph topology, which is often unavailable in practice. We propose a systematic framework for subgraph filter learning (SFL), where subgraph-supported operators approximate ambient graph filters under partial observations. We formulate SFL as a statistical learning problem in which optimal subgraph operators are inherently data-dependent. To address the difficulty of directly estimating such operators, we develop a subgraph filter algebra based on distance-aware Laplacian constructions, defining a structured and controllable class of filters for effective approximation. We further establish performance risk bounds under the least squares loss, quantifying how well the learned operator approximates the restricted ambient mapping. Experiments real-world datasets show that, for SFL tasks, the proposed algebraic models consistently outperform polynomial filters, distribution-agnostic operators, and direct numerical filter learning baselines that attempt to recover the underlying structure from data.
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。