Bayesian Method For Supervised Hashing

Due to the rapid development of the Internet,past decades have witnessed the burgeon of images on websites like Facebook and Flickr.Therefore,it is of great urgency to develop efficient algorithms for searching relevant images from large databases.Given a dataset,hashing methods map data points from the original feature space to a binary hashing code space with pairwise similarities preserved.Recently,hashing methods have been merited for it can refine retrieval speed and storage cost considerably.Bayesian probabilistic techniques like variational inference have been widely adopted to tackle machine learning problems,but have seldom been used to solve the hashing problem.This paper combines the idea of mean-field variational inference in the Bayesian method with classical supervised hashing formulations and proposes two stateof-the-art algorithms to address the supervised hashing problem.Contributions of this paper are as follows:1.Most previous supervised hashing methods optimize a form of loss function with a regularization term,which can be viewed as a maximum a posterior(MAP)estimation of the hashing codes.Therefore,they are prone to overfitting unless hyper-parameters are tuned carefully.Based on modeling hashing codes as continuous random variables,this paper presents a novel fully Bayesian treatment for supervised hashing,in which hashing codes and hyper-parameters are automatically tuned during optimization.Also,automatic relevance determination is used to figure out most informative hashing bits.2.Since 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,most 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).Based on modeling hashing codes as discrete random variables,this paper proposes a simple yet effective Bayesian method for learning the conditional random field using a piecewise linearization of the sigmoid function.3.Extensive experimental results on four real-world image datasets show that these two methods can achieve superior performance over state-of-the-art methods with less training time.