Reversed Spectral Hashing.

Hashing is emerging as a powerful tool for building highly efficient indices in large-scale search systems. In this paper, we study spectral hashing (SH), which is a classical method of unsupervised hashing. In general, SH solves for the hash codes by minimizing an objective function that tries to preserve the similarity structure of the data given. Although computationally simple, very often SH performs unsatisfactorily and lags distinctly behind the state-of-the-art methods. We observe that the inferior performance of SH is mainly due to its imperfect formulation; that is, the optimization of the minimization problem in SH actually cannot ensure that the similarity structure of the high-dimensional data is really preserved in the low-dimensional hash code space. In this paper, we, therefore, introduce reversed SH (ReSH), which is SH with its input and output interchanged. Unlike SH, which estimates the similarity structure from the given high-dimensional data, our ReSH defines the similarities between data points according to the unknown low-dimensional hash codes. Equipped with such a reversal mechanism, ReSH can seamlessly overcome the drawback of SH. More precisely, the minimization problem in our ReSH can be optimized if and only if similar data points are mapped to adjacent hash codes, and mostly important, dissimilar data points are considerably separated from each other in the code space. Finally, we solve the minimization problem in ReSH by multilayer neural networks and obtain state-of-the-art retrieval results on three benchmark data sets.