提出在流形上插值低通图滤波器，加速参数化图族的计算。
Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applications
- 在格拉斯曼流形上用黎曼插值法实现低通图滤波器的快速估计。
- 理论给出子空间插值误差上界，验证了方法可靠性。
- 适用于动态图演化建模和改进节点分类的消息传递机制。
低通图滤波器是图信号处理及其它非欧几里得域中的基础工具。然而，对于参数化图族，其计算代价高昂，因需反复求解特征值问题以获得低频子空间。本文提出一种基于格拉斯曼流形正规坐标系上的黎曼插值的低通图滤波器插值新算法。推导了子空间插值的误差界，并提出两种潜在应用：其一，通过相似性修正调整网络同质性程度，将节点特征的时序演化映射为图拓扑变化；其二，基于给定静态图构建点积图族，借助滤波器插值优化节点分类中的消息传递机制。
原文摘要 · Abstract (English)
Low-pass graph filters are fundamental for signal processing on graphs and other non-Euclidean domains. However, the computation of such filters for parametric graph families can be prohibitively expensive as computation of the corresponding low-frequency subspaces, requires the repeated solution of an eigenvalue problem. We suggest a novel algorithm of low-pass graph filter interpolation based on Riemannian interpolation in normal coordinates on the Grassmann manifold. We derive an error bound estimate for the subspace interpolation and suggest two possible applications for induced parametric graph families. First, we argue that the temporal evolution of the node features may be translated to the evolving graph topology via a similarity correction to adjust the homophily degree of the network. Second, we suggest a dot product graph family induced by a given static graph which allows to infer improved message passing scheme for node classification facilitated by the filter interpolation.
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