  Image hashing is one of the fundamental problems that demand both efficient
and effective solutions for various practical scenarios. Adversarial
autoencoders are shown to be able to implicitly learn a robust,
locality-preserving hash function that generates balanced and high-quality hash
codes. However, the existing adversarial hashing methods are inefficient to be
employed for large-scale image retrieval applications. Specifically, they
require an exponential number of samples to be able to generate optimal hash
codes and a significantly high computational cost to train. In this paper, we
show that the high sample-complexity requirement often results in sub-optimal
retrieval performance of the adversarial hashing methods. To address this
challenge, we propose a new adversarial-autoencoder hashing approach that has a
much lower sample requirement and computational cost. Specifically, by
exploiting the desired properties of the hash function in the low-dimensional,
discrete space, our method efficiently estimates a better variant of
Wasserstein distance by averaging a set of easy-to-compute one-dimensional
Wasserstein distances. The resulting hashing approach has an order-of-magnitude
better sample complexity, thus better generalization property, compared to the
other adversarial hashing methods. In addition, the computational cost is
significantly reduced using our approach. We conduct experiments on several
real-world datasets and show that the proposed method outperforms the competing
hashing methods, achieving up to 10% improvement over the current
state-of-the-art image hashing methods. The code accompanying this paper is
available on Github (https://github.com/khoadoan/adversarial-hashing).
