Spectral embedded hashing for scalable image retrieval.

We propose a new graph based hashing method called spectral embedded hashing (SEH) for large-scale image retrieval. We first introduce a new regularizer into the objective function of the recent work spectral hashing to control the mismatch between the resultant hamming embedding and the low-dimensional data representation, which is obtained by using a linear regression function. This linear regression function can be employed to effectively handle the out-of-sample data, and the introduction of the new regularizer makes SEH better cope with the data sampled from a nonlinear manifold. Considering that SEH cannot efficiently cope with the high dimensional data, we further extend SEH to kernel SEH (KSEH) to improve the efficiency and effectiveness, in which a nonlinear regression function can also be employed to obtain the low dimensional data representation. We also develop a new method to efficiently solve the approximate solution for the eigenvalue decomposition problem in SEH and KSEH. Moreover, we show that some existing hashing methods are special cases of our KSEH. Our comprehensive experiments on CIFAR, Tiny-580K, NUS-WIDE, and Caltech-256 datasets clearly demonstrate the effectiveness of our methods.