Title: Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering,
Abstract: 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.