Unsupervised hashing has received extensive research focus on the past decade, which typically aims at preserving a predefined metric (i.e. Euclidean metric) in the Hamming space. To this end, the encoding functions of the existing hashing are typically quasi-isometric, which devote to reducing the quantization loss from the target metric space to the discrete Hamming space. However, it is indeed problematic to directly minimize such error, since such mentioned two metric spaces are heterogeneous, and the quasi-isometric mapping is non-linear. The former leads to inconsistent feature distributions, while the latter leads to problematic optimization issues. In this paper, we propose a novel unsupervised hashing method, termed Sparsity-Induced Generative Adversarial Hashing (SiGAH), to encode large-scale high-dimensional features into binary codes, which well solves the two problems through a generative adversarial training framework. Instead of minimizing the quantization loss, our key innovation lies in enforcing the learned Hamming space to have similar data distribution to the target metric space via a generative model. In particular, we formulate a ReLU-based neural network as a generator to output binary codes and an MSE-loss based auto-encoder network as a discriminator, upon which a generative adversarial learning is carried out to train hash functions. Furthermore, to generate the synthetic features from the hash codes, a compressed sensing procedure is introduced into the generative model, which enforces the reconstruction boundary of binary codes to be consistent with that of original features. Finally, such generative adversarial framework can be trained via the Adam optimizer. Experimental results on four benchmarks, i.e., Tiny100K, GIST1M, Deep1M, and MNIST, have shown that the proposed SiGAH has superior performance over the state-of-the-art approaches.

翻译：无监督哈希在过去十年中获得了广泛的研究关注，其典型目标是在汉明空间中保持预定义的度量（即欧几里得度量）。为此，现有哈希的编码函数通常为准等距映射，旨在减少从目标度量空间到离散汉明空间的量化损失。然而，直接最小化此类误差确实存在困难，因为所提及的两个度量空间是异质的，且准等距映射是非线性的。前者导致特征分布不一致，而后者导致优化问题复杂化。本文提出了一种新颖的无监督哈希方法，称为稀疏-诱导生成对抗哈希（SiGAH），用于将大规模高维特征编码为二进制码，该方法通过生成对抗训练框架很好地解决了上述两个问题。我们的关键创新点不在于最小化量化损失，而是通过生成模型迫使学习的汉明空间具有与目标度量空间相似的数据分布。具体而言，我们设计了一个基于ReLU的神经网络作为生成器以输出二进制码，并设计了一个基于MSE损失的自编码器网络作为判别器，在此基础上进行生成对抗学习以训练哈希函数。此外，为从哈希码生成合成特征，我们在生成模型中引入了一种压缩感知过程，该过程强制二进制码的重建边界与原始特征的重建边界保持一致。最后，该生成对抗框架可通过Adam优化器进行训练。在四个基准数据集（即Tiny100K、GIST1M、Deep1M和MNIST）上的实验结果表明，所提出的SiGAH方法在性能上优于最先进的方法。