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Learning-based hashing algorithms are “hot topics” because they can greatly increase the scale at which existing methods operate. In this paper, we propose a new learning-based hashing method called “fast supervised discrete hashing” (FSDH) based on “supervised discrete hashing” (SDH). Regressing the training examples (or hash code) to the corresponding class labels is widely used in ordinary least squares regression. Rather than adopting this method, FSDH uses a very simple yet effective regression of the class labels of training examples to the corresponding hash code to accelerate the algorithm. To the best of our knowledge, this strategy has not previously been used for hashing. Traditional SDH decomposes the optimization into three sub-problems, with the most critical sub-problem - discrete optimization for binary hash codes - solved using iterative discrete cyclic coordinate descent (DCC), which is …