Hash Bit Selection: A Unified Solution for Selection Problems in Hashing

Recent years have witnessed the active development of hashing techniques for nearest neighbor search over big datasets. However, to apply hashing techniques successfully, there are several important issues remaining open in selecting features, hashing algorithms, parameter settings, kernels, etc. In this work, we unify all these selection problems into a hash bit selection framework, i.e. selecting the most informative hash bits from a pool of candidate bits generated by different types of hashing methods using different feature spaces and/or parameter settings, etc. We represent the bit pool as a vertx- and edge-weighted graph with the candidate bits as vertices. The vertex weight represents the bit quality in terms of similarity preservation, and the edge weight reflects independence (non-redundancy) between bits. Then we formulate the bit selection problem as quadratic programming on the graph, and solve it efficiently by replicator dynamics. Moreover, a theoretical study is provided to reveal a very interesting insight: the selected bits actually are the normalized ominant set of the candidate bit graph. We conducted extensive large-scale experiments for three important application scenarios of hash techniques, i.e., hashing with multiple features, multiple hashing algorithms, and multiple bit hashing. We demonstrate that our bit selection approach can achieve superior performance over both naive selection methods and state-of-the-art hashing methods under each scenario, with significant accuracy gains ranging from 10% to 50% relatively.