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.

本文提出了一种新的基于监督离散哈希（SDH）的学习型哈希方法，称为快速监督离散哈希（FSDH）。FSDH 使用一种简单但有效的回归方法来加速算法，具有封闭的解决方案，只需要单个哈希代码求解步骤，非常高效。作者的实验结果表明，FSDH 不仅快速，而且优于其他比较方法。

快速监督离散哈希

Fast Supervised Discrete Hashing

Data-dependent hashing has recently attracted attention due to being able to
support efficient retrieval and storage of high-dimensional data such as
documents, images, and videos. In this paper, we propose a novel learning-based
hashing method called "Supervised Discrete Hashing with Relaxation" (SDHR)
based on "Supervised Discrete Hashing" (SDH). SDH uses ordinary least squares
regression and traditional zero-one matrix encoding of class label information
as the regression target (code words), thus fixing the regression target. In
SDHR, the regression target is instead optimized. The optimized regression
target matrix satisfies a large margin constraint for correct classification of
each example. Compared with SDH, which uses the traditional zero-one matrix,
SDHR utilizes the learned regression target matrix and, therefore, more
accurately measures the classification error of the regression model and is
more flexible. As expected, SDHR generally outperforms SDH. Experimental
results on two large-scale image datasets (CIFAR-10 and MNIST) and a
large-scale and challenging face dataset (FRGC) demonstrate the effectiveness
and efficiency of SDHR.

本文提出了一种基于学习的哈希方法，称为 “带松弛的监督离散哈希”（SDHR），它在传统监督离散哈希的基础上优化了回归目标矩阵，并满足每个示例的正确分类的大边界约束。SDHR 相对于传统的离散哈希方法具有更高的分类精度和更好的灵活性，并在图像和人脸数据集上得到了有效和高效的结果。