Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering
This work addresses the challenge of online spatio-temporal signal inference in network science applications, representing an incremental improvement with a novel multi-kernel learning approach.
The paper tackled the problem of reconstructing dynamic signals on graphs from partial observations by developing a multi-kernel kriged Kalman filter that adapts to signal dynamics and evolving topologies, demonstrating superior performance in numerical tests compared to state-of-the-art methods.
Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multi-kernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a pre-selected dictionary. The novel multi-kernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.