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This paper addresses the problem of jointly clustering two segmentations of closely correlated images. We focus in particular on the application of reconstructing neuronal structures in over-segmented electron microscopy images. We formulate the problem of co-clustering as a quadratic semi-assignment problem and investigate convex relaxations using semidefinite and linear programming. We further introduce a linear programming method with manageable number of constraints and present an approach for learning the cost function. Our method increases computational efficiency by orders of magnitude while maintaining accuracy, automatically finds the optimal number of clusters, and empirically tends to produce binary assignment solutions. We illustrate our approach in simulations and in experiments with real EM data.