Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applications

TL;DR

This paper introduces a novel Grassmannian interpolation method for low-pass graph filters, enabling efficient parametric filter computation and applications in dynamic graph analysis and improved node classification.

Contribution

It proposes a Riemannian interpolation algorithm on the Grassmann manifold for low-pass graph filters, with theoretical error bounds and practical applications.

Findings

Derived an error bound estimate for subspace interpolation.

Applied the method to model evolving graph topologies.

Enhanced message passing schemes for node classification.

Abstract

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.