A Quadratic Penalty Method for Hypergraph Matching Event

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Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this talk, we reformulate the hypergraph matching problem as a sparse constrained optimization problem. By dropping the sparse constraint, we show that the resulting relaxation problem can recover the global minimizer of the original problem. The critical step in solving the original problem is to identify the location of nonzero entries (referred as support set) in a global minimizer. Inspired by such observations, we penalize the equality constraints and apply the quadratic penalty method to solve the relaxation problem. Under reasonable assumptions, we show that the support set of the global minimizer in hypergraph matching problem can be correctly identified when the number of iterations is sufficiently large. A projected gradient method is applied as a subsolver to solve the quadratic penalty subproblem. Numerical results demonstrate that the exact recovery of support set indeed happens, and the proposed algorithm is efficient in terms of both accuracy and speed. This is a joint work with C.F. Cui, L.Q. Qi and H. Yan.