Graph Learning from Multi-Attribute Smooth Signals

We consider the problem of estimating the structure of an undirected weighted graph underlying a set of smooth multi-attribute signals. Most existing methods for graph estimation are based on single-attribute models where one associates a scalar data variable with each node of the graph, and the problem is to infer the graph topology that captures the relationships between these variables. An example is image graphs for grayscale texture images for modeling dependence of a pixel on neighboring pixels. In multi-attribute graphical models, each node represents a vector, as for example, in color image graphs where one has three variables (RGB color components) per pixel node. In this paper, we extend the single attribute approach of Kalofolias (2016) to multi-attribute data. An alternating direction method of multipliers (ADMM) algorithm is presented to optimize the objective function to infer the graph topology. Numerical results based on synthetic as well as real data are presented.