  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 time-consuming.
However, FSDH has a closed-form solution and only requires a single rather than
iterative hash code-solving step, which is highly efficient. Furthermore, FSDH
is usually faster than SDH for solving the projection matrix for least squares
regression, making FSDH generally faster than SDH. For example, our results
show that FSDH is about 12-times faster than SDH when the number of hashing
bits is 128 on the CIFAR-10 data base, and FSDH is about 151-times faster than
FastHash when the number of hashing bits is 64 on the MNIST data-base. Our
experimental results show that FSDH is not only fast, but also outperforms
other comparative methods.
