Supervised Hashing based on Energy Minimization
This work addresses the problem of optimizing retrieval speed and storage cost while preserving semantic information in supervised hashing, which is incremental as it builds on existing formulations like KSH and SPLH.
The paper tackled the performance deterioration in supervised hashing methods due to relaxation techniques by converting consistency equations into linear systems using a linear approximation of the sigmoid function, resulting in new methods EM-KSH and EM-SPLH that showed superiority in experiments on three datasets.
Recently, supervised hashing methods have attracted much attention since they can optimize retrieval speed and storage cost while preserving semantic information. Because hashing codes learning is NP-hard, many methods resort to some form of relaxation technique. But the performance of these methods can easily deteriorate due to the relaxation. Luckily, many supervised hashing formulations can be viewed as energy functions, hence solving hashing codes is equivalent to learning marginals in the corresponding conditional random field (CRF). By minimizing the KL divergence between a fully factorized distribution and the Gibbs distribution of this CRF, a set of consistency equations can be obtained, but updating them in parallel may not yield a local optimum since the variational lower bound is not guaranteed to increase. In this paper, we use a linear approximation of the sigmoid function to convert these consistency equations to linear systems, which have a closed-form solution. By applying this novel technique to two classical hashing formulations KSH and SPLH, we obtain two new methods called EM (energy minimizing based)-KSH and EM-SPLH. Experimental results on three datasets show the superiority of our methods.