ADMM-based Bipartite Graph Approximation

Because the spectrum folding phenomenon affects the down-sampling of graph signals, both critically sampled and oversampled graph filter banks with down-sampling operations can only be applied to bipartite graphs. However, general graph signals may not reside on bipartite graph structures. In this paper, we present a novel bipartite graph approximation algorithm, which aims to find a bipartite graph sufficiently close to the original graph. To tackle this problem, we first show that, if the non-negativity constraint of adjacency matrices is removed, closed-form solutions can be readily obtained by the eigenvalue decomposition. Based on this fact, an alternating direction method of multipliers (ADMM) is further developed to achieve a real adjacency matrix. Experimental results show that the proposed algorithm outperforms the other proposals in terms of approximation accuracy.