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

Vassilis N. Ioannidis, Daniel Romero, Georgios B. Giannakis

Research output: Contribution to journalArticle

6 Scopus citations

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 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.

Original languageEnglish (US)
Pages (from-to)3228-3239
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume66
Issue number12
DOIs
StatePublished - Jun 15 2018

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Keywords

  • Graph signal reconstruction
  • dynamic models on graphs
  • kriged Kalman filtering
  • multi-kernel learning

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