Inference of Spatio-Temporal Functions over Graphs via Multi-Kernel Kriged Kalman Filtering

TL;DR

This paper introduces a graph-aware, kernel-based kriged Kalman filter for efficient online reconstruction of dynamic signals on graphs, capable of adapting to evolving topologies without requiring prior statistical information.

Contribution

It develops a multi-kernel learning framework that automatically selects the best kernel for spatio-temporal graph signals, improving reconstruction accuracy and computational efficiency.

Findings

Outperforms state-of-the-art methods in synthetic data tests.

Effectively adapts to changing network topologies.

Reduces computational complexity via eigenstructure exploitation.

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.