For unsupervised data-dependent hashing, the two most important requirements are to preserve similarity in the low-dimensional feature space and to minimize the binary quantization loss. A well-established hashing approach is Iterative Quantization (ITQ), which addresses these two requirements in separate steps. In this paper, we revisit the ITQ approach and propose novel formulations and algorithms to the problem. Specifically, we propose a novel approach, named Simultaneous Compression and Quantization (SCQ), to jointly learn to compress (reduce dimensionality) and binarize input data in a single formulation under strict orthogonal constraint. With this approach, we introduce a loss function and its relaxed version, termed Orthonormal Encoder (OnE) and Orthogonal Encoder (OgE) respectively, which involve challenging binary and orthogonal constraints. We propose to attack the optimization using novel algorithms based on recent advance in cyclic coordinate descent approach. Comprehensive experiments on unsupervised image retrieval demonstrate that our proposed methods consistently outperform other state-of-the-art hashing methods. Notably, our proposed methods outperform recent deep neural networks and GAN based hashing in accuracy, while being very computationally-efficient.

对于无监督的依赖数据的哈希，两个最重要的要求是在低维特征空间中保持相似性，并最大程度地减少二进制量化损失。一种完善的哈希方法是迭代量化（ITQ），它可以在单独的步骤中满足这两个要求。在本文中，我们将重新审视ITQ方法，并针对该问题提出新颖的公式和算法。具体来说，我们提出了一种新颖的方法，称为同时压缩和量化（SCQ），共同学习在严格的正交约束下以单一公式压缩（减少维数）并将输入数据二值化。通过这种方法，我们引入了损失函数及其松弛版本，分别称为正交编码器（OnE）和正交编码器（OgE），它们涉及具有挑战性的二进制和正交约束。我们建议基于循环坐标下降法的最新进展，使用新颖的算法来攻击优化。无监督图像检索的综合实验表明，我们提出的方法始终优于其他最新的哈希方法。值得注意的是，我们提出的方法在准确性上优于最新的深度神经网络和基于GAN的散列，同时计算效率很高。