Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 65, Issue 3, Pages 764-778Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2016.2620116
Keywords
Graph signal reconstruction; kernel regression; multi-kernel learning
Categories
Funding
- ARO [W911NF-15-1-0492]
- NSF [1343248, 1442686, 1514056]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1514056] Funding Source: National Science Foundation
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [1343248] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1442686] Funding Source: National Science Foundation
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A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data. Estimating such signals in all vertices given noisy observations of their values on a subset of vertices has been extensively analyzed in the literature of signal processing on graphs (SPoG). This paper advocates kernel regression as a framework generalizing popular SPoG modeling and reconstruction and expanding their capabilities. Formulating signal reconstruction as a regression task on reproducing kernel Hilbert spaces of graph signals permeates benefits from statistical learning, offers fresh insights, and allows for estimators that leverage richer forms of prior information than existing alternatives. A number of SPoG notions such as bandlimitedness, graph filters, and the graph Fourier transform are naturally accommodated in the kernel framework. Additionally, this paper capitalizes on the so-called representer theorem to devise simpler versions of existing Tikhonov regularized estimators, and offers a novel probabilistic interpretation of kernel methods on graphs based on graphical models. Motivated by the challenges of selecting the bandwidth parameter in SPoG estimators or the kernel map in kernel-based methods, this paper further proposes two multikernel approaches with complementary strengths. Whereas the first enables estimation of the unknown bandwidth of bandlimited signals, the second allows for efficient graph filter selection. Numerical tests with synthetic as well as real data demonstrate the merits of the proposed methods relative to state-of-the-art alternatives.
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