Graph Learning from Data under Structural and Laplacian Constraints

RAPHS are generic mathematical structures consisting of sets of vertices and edges, which are used for modeling pairwise relations (edges) between a number of objects (vertices). In practice, this representation is often extended to weighted graphs, for which a set of scalar values (weights) are assigned to edges and potentially to vertices. Thus, weighted graphs offer general and flexible representations for modeling affinity relations between the objects of interest. Many practical problems can be represented using weighted graphs. For example, a broad class of combinatorial problems such as weighted matching, shortest-path and network-flow [2] are defined using weighted graphs. In signal/data-oriented problems, weighted graphs provide concise (sparse) representations for robust modeling of signals/data [3]. Such graphbased models are also useful for analyzing and visualizing the relations between their samples/features. Moreover, weighted graphs naturally emerge in networked data applications, such as learning, signal processing and analysis on computer, social, sensor, energy, transportation and biological networks [4], where the signals/data are inherently related to a graph associated with the underlying network.