Optimizing Circulant Support Vector Machines: the Exact Solution

Binary hashing is an established approach for fast, approximate image search. The idea is to learn a hash function that maps a query image to a binary vector so that Hamming distances approximate image similarities. An important subproblem in binary hashing is to solve a set of independent classification problems, usually using support vector machines (SVMs). In this paper, we show that the hash function performs faster if we learn a set of circulant SVMs instead of the independent ones. Unlike the previously proposed algorithm that finds a suboptimal solution of the circulant SVMs, we show that the problem can be solved exactly and efficiently by casting it as a convex maximum margin classification problem on a modified dataset. We confirm experimentally that our approach solves the classification problem and the image search task better than the previous method.