Nonconvex graph learning: sparsity, heavy tails, and clustering

Graph learning has been an active research area that finds applications across a number of fields including finance, health care, and social sciences. In this chapter, we present an overview of recent advancements in the area of learning graphs from data, in particular undirected, weighted graphs. We focus on actual practical requirements for such models, e.g., imposing sparsity and handling data with outliers or heavy tails, as well as showcasing the applicability of these models on tasks such as clustering. We illustrate the performance of state-of-the-art graph learning frameworks on both synthetic and real-world datasets including financial time-series data and handwritten digits image data.