AI 中文总结
研究图信号处理中部分观测下图滤波器学习问题，基于距离感知拉普拉斯构造开发子图滤波器代数，建立性能风险界，实验表明该代数模型在SFL任务中优于其他基线。
AI 中文摘要
利用频谱信息的图信号处理任务通常假定可访问完整的图拓扑结构，但实际中往往无法获取。我们提出了一个用于子图滤波器学习（SFL）的系统框架，其中子图支持的算子在部分观测下近似环境图滤波器。我们将SFL表述为一个统计学习问题，其中最优子图算子本质上依赖于数据。为解决直接估计此类算子的困难，我们基于距离感知拉普拉斯构造开发了一个子图滤波器代数，定义了一类结构化且可控的滤波器以进行有效近似。我们还在最小二乘损失下建立了性能风险界，量化了学习到的算子对受限环境映射的近似程度。实验表明，对于SFL任务，所提出的代数模型始终优于多项式滤波器、与分布无关的算子以及试图从数据中恢复底层结构的直接数值滤波器学习基线。
英文摘要
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.
CommentsSubmitted to IEEE TSP
