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 multikernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a preselected dictionary. The novel multikernel 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.
Bibliographical noteFunding Information:
Manuscript received November 23, 2017; revised March 2, 2018 and March 25, 2018; accepted March 26, 2018. Date of publication April 20, 2018; date of current version May 10, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Oliver Lezoray. This work was supported by NSF under Grants 1442686, 1500713, and 1508993. This paper was presented in part at the 25th European Signal Processing Conference, Kos island, Greece, Aug.–Sep., 2017. (Corresponding author: Vassilis N. Ioannidis.) V. N. Ioannidis and G. B. Giannakis are with the Department of Electrical and Computer Engineering and the Digital Technology Center, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:, email@example.com; firstname.lastname@example.org).
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- Graph signal reconstruction
- dynamic models on graphs
- kriged Kalman filtering
- multi-kernel learning