Filtering Topological Signals Across Multiplex Networks and Knowledge Graphs

Develop a signal processing framework that filters topological signals—i.e., node and edge signals—across multiplex networks or knowledge graphs composed of multiple interacting layers, leveraging inter-layer information without resorting to simple aggregation of layers. The framework should jointly process signals across layers to exploit the structural and topological dependencies among layers while preserving layer-specific information, enabling accurate reconstruction and denoising of multi-layer topological signals.

Background

The paper introduces Dirac-equation signal processing (DESP) and its iterated version (IDESP) to jointly process node and edge signals on single-layer networks, demonstrating improved performance over Hodge-Laplacian-based methods and Dirac signal processing. While these methods effectively handle signals on single-layer graphs, many real-world datasets are structured as multiplex networks or knowledge graphs, where multiple layers (or relation types) coexist and interact.

Extending DESP/IDESP to multiplex settings requires addressing how to incorporate inter-layer topology and cross-layer dependencies into the filtering process without collapsing layers into a single aggregate structure. This would allow leveraging complementary information present across layers to enhance signal reconstruction and denoising, which is currently left unresolved and explicitly posed as an open question in the paper.