发表机构
Graduate School of Information Science and Technology, Hokkaido University（北海道大学信息科学与技术研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于滤波拉普拉斯和最优传输的图字典学习框架，利用代理滤波图距离度量重构误差并通过反向传播优化，在聚类和分类任务上表现优于现有方法。
AI 中文摘要
我们提出了一种图字典学习（GDL）框架，其中每个图被表示为由其滤波拉普拉斯算子导出的零均值高斯分布。每个观测图通过在其滤波图距离（fGOT）下计算的、对全局结构性质敏感的图比较度量，由学习到的原子图的重心近似。观测图与其重心之间的重构误差通过代理fGOT（sfGOT）距离来度量，这是fGOT的一种可处理的近似，能够处理没有已知节点对应的图，并通过反向传播进行端到端最小化。我们进一步通过希尔伯特-施密特独立性准则的视角对sfGOT提供了新的解释，表明最小化两个图之间的sfGOT距离等价于最大化其节点谱嵌入之间的统计依赖性。在基准数据集上的实验表明，在图的聚类和分类任务上，我们的方法相比现有的GDL方法具有竞争力的性能。
英文摘要
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.
