Binary Optimized Hashing

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This paper studies the problem of learning to hash, which is essentially a mixed integer optimization problem, containing both the binary hash code output and the (continuous) parameters forming the hash functions. Different from existing relaxation methods in hashing, which have no theoretical guarantees for the error bound of the relaxations, we propose binary optimized hashing (BOH), in which we prove that if the loss function is Lipschitz continuous, the binary optimization problem can be relaxed to a bound constrained continuous optimization problem.