Inference of Spatio-Temporal Functions Over Graphs via Multikernel 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 kernelbased 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.

Kernel Regression on Graphs in Random Fourier Features Space

“…The objective of typical learning strategies over graphs is to model f (•) : R K → R K in the case where both xn and tn belong to the same graph G. Previous research on learning over networks include, e.g., dictionary learning [11], linear [12,13] and nonlinear graph filtering [18], kriged Kalman filtering [10], and kernel regression strategies [14][15][16][17].…”

“…A major area of research in GSP is learning over graphs, which aims at discovering patterns in the data and graph structure to allow, e.g., prediction and reconstruction of graph signals [10][11][12][13][14][15][16][17][18].…”

A Modified Spatiotemporal Mixed-Effects Model for Interpolating Missing Values in Spatiotemporal Observation Data Series

“…e third type is the spatiotemporal interpolation method including Kriged Kalman Filter (KKF), Space Time Kalman Filter (STKF), and Spatiotemporal Mixed-Effects (STME). KKF is a spatiotemporal Kalman interpolation algorithm combined with Kriging interpolation and Kalman filter [16][17][18]. It mainly uses Kriging interpolation to construct spatial field to describe spatial correlation between stations and uses the Kalman filter to describe the temporal correlation of the data.…”

Online Graph-Adaptive Learning With Scalability and Privacy

“…The same task has been studied recently as signal reconstruction over graphs, see e.g., [11], [12], [13], [14], [15], where signal values on unobserved nodes can be estimated by properly introducing a graph-aware prior. Kernel-based methods for learning over graphs offer a unifying framework that includes linear and nonlinear function estimators [13], [16], [17]. The nonlinear methods outperform the linear ones but suffer from the curse of dimensionality [18], rendering them less attractive for large-scale networks.…”

“…Adaptive learning over graphs has been also investigated for tracking and learning over possibly dynamic networks, e.g., [19], [17]. Least mean-squares and recursive least-squares adaptive schemes have been developed in [19], without explicitly accounting for evolving network topologies.…”