Graph Learning From Filtered Signals: Graph System and Diffusion Kernel Identification

• Published in: IEEE transactions on signal and information processing over networks 2019-06, Vol.5 (2), p.360-374
• Main Authors: Egilmez, Hilmi E., Pavez, Eduardo, Ortega, Antonio
• Format: Article
• Language: English
• Subjects: Algorithms; Climate models; Covariance matrices; Diffusion; diffusion kernels; Estimation; Graph learning; graph signal processing; graph system identification; graph-based filtering; heat kernels; Information processing; Kernel; Kernels; Laplace equations; Signal processing; Signal processing algorithms; System identification
• ISSN: 2373-776X; 2373-776X; 2373-7778
• DOI: 10.1109/TSIPN.2018.2872157

This paper introduces a novel graph signal processing framework for building graph-based models from classes of filtered signals. In our framework, graph-based modeling is formulated as a graph system identification problem, where the goal is to learn a weighted graph (a graph Laplacian matrix) and a graph-based filter (a function of graph Laplacian matrices). In order to solve the proposed problem, an algorithm is developed to jointly identify a graph and a graph-based filter (GBF) from multiple signal/data observations. Our algorithm is valid under the assumption that GBFs are one-to-one functions. The proposed approach can be applied to learn diffusion (heat) kernels, which are popular in various fields for modeling diffusion processes. In addition, for specific choices of graph-based filters, the proposed problem reduces to a graph Laplacian estimation problem. Our experimental results demonstrate that the proposed algorithm outperforms the current state-of-the-art methods. We also implement our framework on a real climate dataset for modeling of temperature signals.