A sparse nonnegative matrix factorization technique for graph matching problems

• We present a graph matching method based on NMF with sparse constraints.
• Our sparse model can incorporate the mapping constraints approximately.
• We show the link between the sparsity of the solution and its effectiveness.
• Experimental results show the effectiveness of our graph matching method.

Graph matching problem that incorporates pairwise constraints can be cast as an Integer Quadratic Programming (IQP). Since it is NP-hard, approximate methods are required. In this paper, a new approximate method based on nonnegative matrix factorization with sparse constraints is presented. Firstly, the graph matching is formulated as an optimization problem with nonnegative and sparse constraints, followed by an efficient algorithm to solve this constrained problem. Then, we show the strong relationship between the sparsity of the relaxation solution and its effectiveness for graph matching based on our model. A key benefit of our method is that the solution is sparse and thus can approximately impose the one-to-one mapping constraints in the optimization process naturally. Therefore, our method can approximate the original IQP problem more closely than other approximate methods. Extensive and comparative experimental results on both synthetic and real-world data demonstrate the effectiveness of our graph matching method.