FiGLearn: Filter and Graph Learning using Optimal Transport

TL;DR

FiGLearn introduces a novel framework for jointly learning graphs and filters from observed signals using optimal transport, outperforming existing methods and enabling missing data inference.

Contribution

The paper proposes a new graph learning approach based on Wasserstein distance minimization, effectively capturing underlying data structures and filtering processes.

Findings

Outperforms state-of-the-art graph learning methods on synthetic data

Successfully infers missing values in temperature anomaly data

Demonstrates effectiveness in real-world applications

Abstract

In many applications, a dataset can be considered as a set of observed signals that live on an unknown underlying graph structure. Some of these signals may be seen as white noise that has been filtered on the graph topology by a graph filter. Hence, the knowledge of the filter and the graph provides valuable information about the underlying data generation process and the complex interactions that arise in the dataset. We hence introduce a novel graph signal processing framework for jointly learning the graph and its generating filter from signal observations. We cast a new optimisation problem that minimises the Wasserstein distance between the distribution of the signal observations and the filtered signal distribution model. Our proposed method outperforms state-of-the-art graph learning frameworks on synthetic data. We then apply our method to a temperature anomaly dataset, and further show how this framework can be used to infer missing values if only very little information is available.