Supervised Discrete Hashing

Abstract

Recently, learning based hashing techniques have attracted broad research interests due to the resulting efficient storage and retrieval of images, videos, documents, etc. However, a major difficulty of learning to hash lies in handling the discrete constraints imposed on the needed hash codes, which typically makes hash optimizations very challenging (NP-hard in general). In this work, we propose a new supervised hashing framework, where the learning objective for hashing is to make the optimal binary hash codes for classification. By introducing an auxiliary variable, we reformulate the objective such that it can be solved substantially efficiently by using a regularization algorithm. One of the key steps in the algorithm is to solve the regularization sub-problem associated with the NP-hard binary optimization. We show that with cyclic coordinate descent, the sub-problem admits an analytical solution. As such, a high-quality discrete solution can eventually be obtained in an efficient computing manner, which enables to tackle massive datasets. We evaluate the proposed approach, dubbed Supervised Discrete Hashing (SDH), on four large image datasets, and demonstrate that SDH outperforms the state-of-the-art hashing methods in large-scale image retrieval.