Learning Graphs from Heavy-Tailed Data

In this chapter, we present advancements in graph learning for elliptical distributed data. More precisely, we model the inverse scatter matrixScatter matrix of a multivariate Student’s t-distribution as a Laplacian matrixLaplacian matrix associated to a graph whose nodeNode features (or signals) are observable. We design numerical algorithms, via the alternating direction method of multipliersAlternating direction method of multipliers (ADMM), to learn connected, k-component, bipartite, and k-component bipartite graphs suitable to be applied in datasets that contain outliersOutliers or whose assumption on the data-generating process is that it follows a multivariate Student’s t-distributionStudent’s t distribution. We measure the performance of graph learning algorithms in terms of graph modularityGraph modularity and nodeNode accuracy.