Learning Graph-structured Dictionaries for Sparse Representation of Diffusive Signals on Graphs

Shuyu Dong¹

Dictionary learning provides an efficient and flexible way for sparse representation of signals such as natural images. However for signals residing on the vertices of a graph instead of a regular domain, the graph structure of the input space carries important information that an unstructured dictionary may not be able to capture. In order to achieve better adaptability to input signals, it is also desirable to optimise the graph-structured information, which is otherwise predefined in heuristic manners. We address the problem of learning a graph-structured dictionary jointly with the graph for sparse representation of graph signals and propose to design the dictionary using a characteristic diffusion model. Experiments on synthetic and real datasets show that the proposed dictionaries not only have comparable representation performance than unstructured dictionaries but also significantly reduce overfitting of data.