Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applications
Anton Savostianov, Michael T. Schaub, Benjamin Stamm
低通滤波器是图形和其他非欧几里得域信号处理的基础。 然而,对于参数图家族来说,计算这种过滤器可能非常昂贵,因为计算相应的低频子空间需要反复解决特征值问题。 我们建议一种基于黎曼插值在格拉斯曼流形上正常坐标中的低通图滤波器插值的新算法。 我们得出子空间插值的错误绑定估计值,并提出了诱导参数化图家族的两个可能的应用。 首先,我们认为节点特征的时间演变可以通过相似性校正转化为不断发展的图形拓扑,以调整网络的均匀程度。 其次,我们建议由给定的静态图形诱导的点产品图家族,该图允许推断过滤器插值促进的节点分类的改进消息传递方案。
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 ...