Efficient structure detection via random consensus graph

In this paper, we propose an efficient method to detect the underlying structures in data. The same as RANSAC, we randomly sample MSSs (minimal size samples) and generate hypotheses. Instead of analyzing each hypothesis separately, the consensus information in all hypotheses is naturally fused into a hypergraph, called random consensus graph, with real structures corresponding to its dense subgraphs. The sampling process is essentially a progressive refinement procedure of the random consensus graph. Due to the huge number of hyperedges, it is generally inefficient to detect dense subgraphs on random consensus graphs. To overcome this issue, we construct a pairwise graph which approximately retains the dense subgraphs of the random consensus graph. The underlying structures are then revealed by detecting the dense subgraphs of the pair-wise graph. Since our method fuses information from all hypotheses, it can robustly detect structures even under a small number of MSSs. The graph framework enables our method to simultaneously discover multiple structures. Besides, our method is very efficient, and scales well for large scale problems. Extensive experiments illustrate the superiority of our proposed method over previous approaches, achieving several orders of magnitude speedup along with satisfactory accuracy and robustness.