Graph Signal Inference by Learning Narrowband Spectral Kernels

TL;DR

This paper introduces a novel graph signal model using narrowband spectral kernels, enabling effective signal inference on graphs with complex spectral distributions, and demonstrates improved interpolation accuracy over existing methods.

Contribution

It proposes a flexible joint learning algorithm for graph signals with multi-band spectra, accommodating signals from different graphs, and provides theoretical analysis of reconstruction performance.

Findings

Achieves high signal interpolation accuracy on various graph datasets.

Outperforms existing methods in spectral kernel-based graph signal inference.

Provides theoretical insights into joint learning benefits across multiple graphs.

Abstract

While a common assumption in graph signal analysis is the smoothness of the signals or the band-limitedness of their spectrum, in many instances the spectrum of real graph data may be concentrated at multiple regions of the spectrum, possibly including mid-to-high-frequency components. In this work, we propose a novel graph signal model where the signal spectrum is represented through the combination of narrowband kernels in the graph frequency domain. We then present an algorithm that jointly learns the model by optimizing the kernel parameters and the signal representation coefficients from a collection of graph signals. Our problem formulation has the flexibility of permitting the incorporation of signals possibly acquired on different graphs into the learning algorithm. We then theoretically study the signal reconstruction performance of the proposed method, by also elaborating on when joint learning on multiple graphs is preferable to learning an individual model on each graph. Experimental results on several graph data sets shows that the proposed method offers quite satisfactory signal interpolation accuracy in comparison with a variety of reference approaches in the literature.