FiGLearn: Filter and Graph Learning using Optimal Transport
This work addresses the challenge of uncovering hidden graph structures and filters from noisy data, which is crucial for understanding complex interactions in domains like climate science, but it appears incremental as it builds on existing graph learning frameworks.
The paper tackles the problem of jointly learning an unknown graph structure and its generating filter from observed signals by introducing a novel graph signal processing framework that minimizes the Wasserstein distance between observed and modeled signal distributions. It outperforms state-of-the-art methods on synthetic data and demonstrates application to temperature anomaly data for inferring missing values.
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.