A non-alternating graph hashing algorithm for large-scale image search

In the era of big data, methods for improving memory and computational efficiency have become crucial for the successful deployment of technology. Hashing is one of the most effective approaches to deal with the computational limitations associated with big data. One natural way to formulate this problem is spectral hashing, which directly incorporates an affinity to learning binary codes. However, owing to the binary constraints, the optimization becomes intractable. To mitigate this challenge, different relaxation approaches have been proposed to reduce the computational load required to obtain binary codes and still attain a good solution. The problem with all existing relaxation methods involves the use of one or more additional auxiliary variables to attain high-quality binary codes while relaxing the problem. The existence of auxiliary variables leads to the coordinate descent approach, which increases the computational complexity. We argue that the introduction of these variables is unnecessary. To this end, we propose a novel relaxed formulation for spectral hashing that adds no additional variables to the problem. Furthermore, instead of solving the problem in the original space where the number of variables is equal to the data points, we solve the problem in a much smaller space and retrieve the binary codes from this solution. This technique reduces both the memory and computational complexity simultaneously. We apply two optimization techniques, namely, the projected gradient and optimization on the manifold, to obtain the solution. Using comprehensive experiments on four public datasets, we show that the proposed efficient spectral hashing (ESH) algorithm achieves a highly competitive retrieval performance compared with the state-of-the-art algorithms at low complexity.