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

Learning-based hashing methods are widely used for nearest neighbor
retrieval, and recently, online hashing methods have demonstrated good
performance-complexity trade-offs by learning hash functions from streaming
data. In this paper, we first address a key challenge for online hashing: the
binary codes for indexed data must be recomputed to keep pace with updates to
the hash functions. We propose an efficient quality measure for hash functions,
based on an information-theoretic quantity, mutual information, and use it
successfully as a criterion to eliminate unnecessary hash table updates. Next,
we also show how to optimize the mutual information objective using stochastic
gradient descent. We thus develop a novel hashing method, MIHash, that can be
used in both online and batch settings. Experiments on image retrieval
benchmarks (including a 2.5M image dataset) confirm the effectiveness of our
formulation, both in reducing hash table recomputations and in learning
high-quality hash functions.

本研究提出了一种互信息学习的哈希方法 MIHash，可以在在线和批处理设置中使用，有效地减少哈希表重新计算并学习具有高质量的哈希函数，在 2.5M 图像数据集上取得了良好的表现。