Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applications
This work addresses efficiency challenges in graph signal processing for researchers and practitioners, though it appears incremental as it builds on existing interpolation methods.
The paper tackles the high computational cost of computing low-pass graph filters for parametric graph families by proposing a novel algorithm based on Riemannian interpolation on the Grassmann manifold, deriving an error bound estimate and applying it to adjust network homophily and improve node classification.
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.