Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification
This work addresses graph signal processing for modeling diffusion processes, such as in climate data, but appears incremental as it builds on existing graph Laplacian estimation frameworks.
The paper tackles the problem of learning graph-based models from filtered signals by formulating it as a graph system identification problem, developing an algorithm to jointly identify a graph and a graph-based filter, and demonstrating that it outperforms state-of-the-art methods in experiments.
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.