Dictionary Learning for High Dimensional Graph Signals

Yael Yankelevsky, Michael Elad

Abstract: In recent years there is a growing interest in operating on graph signals. One systematic and productive such line of work is incorporating sparsity-inspired models to this data type, offering these signals a description as sparse linear combinations of atoms from a given dictionary. In this paper, we propose a dictionary learning algorithm for this task that is capable of handling high dimensional data. We incorporate the underlying graph topology by forcing the learned dictionary atoms to be sparse combinations of graph wavelet functions. The resulting atoms thus adhere to the underlying graph structure and possess a desired multi-scale property, yet they capture the prominent features of the data of interest. This results in both adaptive representations and an efficient implementation. Experimental results on different datasets, representing both synthetic and real network data, demonstrate the effectiveness of the proposed algorithm for graph signal processing.