用滤波器与最优传输构建图字典，实现更精准的图表示学习。
A dictionary learning framework for graphs via filters and optimal transport
- 将图建模为滤波拉普拉斯的高斯分布，通过最优传输计算图间距离。
- 端到端优化重构误差，实现无节点对应关系下的图重建。
- 理论揭示距离最小化等价于节点谱嵌入间的统计相关性最大化。
我们提出一种图字典学习（GDL）框架，将每张图表示为基于其滤波拉普拉斯的零均值高斯分布。每张观测图通过学习得到的原子图的巴氏中心进行近似，该巴氏中心在滤波图距离（fGOT）下计算，此距离对全局结构敏感。观测图与其巴氏中心之间的重构误差由可计算的近似距离sfGOT衡量，该距离适用于无已知节点对应关系的图，并通过反向传播端到端优化。我们进一步从希尔伯特-施密特独立性准则视角重新解释sfGOT，证明最小化两图间的sfGOT距离等价于最大化其节点谱嵌入间的统计依赖性。在基准数据集上的实验表明，该方法在图聚类和分类任务中性能优于现有GDL方法。
原文摘要 · Abstract (English)
We propose a graph dictionary learning (GDL) framework where each graph is represented as a zero-mean Gaussian distribution derived from its filtered Laplacian. Each observed graph is approximated by a barycenter over learned atom graphs, computed under the filter graph distance (fGOT), a graph comparison metric sensitive to global structural properties. The reconstruction error between the observed graph and its barycenter is measured by the surrogate fGOT (sfGOT) distance, a tractable approximation of fGOT that handles graphs without known node correspondence, and is minimized end-to-end via backpropagation. We further provide a novel interpretation of sfGOT through the lens of the Hilbert-Schmidt Independence Criterion, showing that minimizing the sfGOT distance between two graphs is equivalent to maximizing statistical dependence between the spectral embedding of their nodes. Experiments on benchmark datasets demonstrate competitive performance over existing GDL methods on graph clustering and classification tasks.
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