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.

翻译：低通图滤波器是图及其他非欧几里得域上信号处理的基础。然而，对于参数化图族，此类滤波器的计算成本可能极高，因为对应低频子空间的计算需要重复求解特征值问题。我们提出一种基于格拉斯曼流形上法坐标的黎曼插值的新型低通图滤波器插值算法。我们推导了子空间插值的误差界估计，并针对诱导参数化图族提出了两种可能的应用。首先，我们认为节点特征的时间演化可通过相似性校正来调整网络的同质性程度，从而转化为演化的图拓扑。其次，我们提出一种由给定静态图诱导的点积图族，该图族能够通过滤波器插值促进节点分类，从而推断出改进的消息传递方案。