Network Flow Formulations for Learning Binary Hashing

Abstract

The problem of learning binary hashing seeks the identification of a binary mapping for a set of n examples such that the corresponding Hamming distances preserve high fidelity with a given $n \times n$ n × n matrix of distances (or affinities). This formulation has numerous applications in efficient search and retrieval of images (and other high dimensional data) on devices with storage/processing constraints. As a result, the problem has received much attention recently in vision and machine learning and a number of interesting solutions have been proposed. A common feature of most existing solutions is that they adopt continuous iterative optimization schemes which is then followed by a post-hoc rounding process to recover a feasible discrete solution. In this paper, we present a fully combinatorial network-flow based formulation for a relaxed version of this problem. The main maximum flow/minimum cut modules which drive our algorithm can be solved efficiently and can directly learn the binary codes. Despite its simplicity, we show that on most widely used benchmarks, our proposal yields competitive performance relative to a suite of nine different state of the art algorithms.