Graph-Dictionary Signal Model for Sparse Representations of Multivariate Data

Dictionary learning (Rubinstein require capturing complex relations between et al., 2010) is a representation learning framework variables. We define a novel Graph-which aims to recover a finite set of atoms, called a Dictionary signal model, where a finite set dictionary, that can encode data through sparse coefficients. of graphs characterizes relationships in data On the other hand, graphs provide a natural distribution through a weighted sum of their representation of structured data with pairwise relationships, Laplacians. We propose a framework to infer described by edges between nodes. However, the graph dictionary representation from these relationships are often hidden, and we must infer observed data, along with a bilinear generalization them from data. of the primal-dual splitting algorithm to solve the learning problem. Our new formulation In this work, we introduce a novel Graph-Dictionary allows to include a priori knowledge signal model, GraphDict in short, to jointly address the on signal properties, as well as on underlying representation and the structure learning problems.