Semi-supervised Discriminant Hashing

Hashing refers to methods for embedding high dimensional data into a similarity-preserving low-dimensional Hamming space such that similar objects are indexed by binary codes whose Hamming distances are small. Learning hash functions from data has recently been recognized as a promising approach to approximate nearest neighbor search for high dimensional data. Most of ´learning to hash´ methods resort to either unsupervised or supervised learning to determine hash functions. Recently semi-supervised learning approach was introduced in hashing where pair wise constraints (must link and cannot-link) using labeled data are leveraged while unlabeled data are used for regularization to avoid over-fitting. In this paper we base our semi-supervised hashing on linear discriminant analysis, where hash functions are learned such that labeled data are used to maximize the separability between binary codes associated with different classes while unlabeled data are used for regularization as well as for balancing condition and pair wise decor relation of bits. The resulting method is referred to as semi-supervised discriminant hashing (SSDH). Numerical experiments on MNIST and CIFAR-10 datasets demonstrate that our method outperforms existing methods, especially in the case of short binary codes.