[Paper Review] Image Hashing by Minimizing Discrete Component-wise Wasserstein Distance

Khoa D. Doan, Saurav Manchanda+2 more|arXiv (Cornell University)|Feb 29, 2020

Advanced Image and Video Retrieval Techniques33 references4 citations

TL;DR

This paper proposes Discrete Component-wise Wasserstein Autoencoder (DCW-AE), a novel adversarial autoencoder for image hashing that minimizes a more generalizable, component-wise variant of the Wasserstein distance. By exploiting discrete properties of hash codes, DCW-AE achieves significantly better sample complexity and computational efficiency, leading to state-of-the-art retrieval performance with up to 10% improvement over existing methods.

ABSTRACT

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).

Motivation & Objective

• To address the poor generalization and high computational cost of existing adversarial autoencoder-based hashing methods.
• To reduce the sample complexity of Wasserstein-based adversarial training in image hashing.
• To improve retrieval performance by learning a more stable and efficient divergence minimization framework.
• To eliminate heuristic constraints in hash code optimization through implicit distribution matching.
• To develop a scalable, efficient, and high-performing unsupervised image hashing model for large-scale applications.

Proposed method

• The method introduces a novel divergence estimation technique that computes the Wasserstein distance as the average of one-dimensional Wasserstein distances along directions where the source and target distributions are most dissimilar.
• It leverages the discrete nature of binary hash codes to construct a component-wise Wasserstein distance that is more generalizable and easier to optimize than standard Wasserstein distances.
• The model uses adversarial training to match the learned hash code distribution to a target discrete prior, implicitly learning a locality-preserving hash function without explicit constraints.
• The proposed distance estimate is computed efficiently using random projections, enabling faster convergence and stable gradients during training.
• The framework is implemented as a variational autoencoder with a GAN-style discriminator, trained via stochastic gradient descent with mini-batches.
• The method avoids the need for hyperparameter tuning of explicit regularization terms by relying on the intrinsic properties of the discrete Wasserstein distance.

Experimental results

Research questions

• RQ1 Can a more generalizable variant of the Wasserstein distance improve the sample efficiency and generalization of adversarial autoencoder-based image hashing?
• RQ2 Does component-wise averaging of one-dimensional Wasserstein distances lead to better convergence and stability in adversarial training for hashing?
• RQ3 Can the proposed method achieve superior retrieval performance with significantly reduced training time compared to existing Wasserstein-based adversarial hashing models?
• RQ4 How does the proposed distance estimate compare to standard Wasserstein distance and sliced Wasserstein distance in terms of gradient stability and optimization dynamics?
• RQ5 To what extent does the discrete structure of hash codes enable a more efficient and effective divergence estimation in latent space?

Key findings

• DCW-AE achieves up to 10% higher retrieval performance than the current state-of-the-art image hashing methods on multiple real-world datasets.
• The proposed method has an order-of-magnitude better sample complexity than existing adversarial hashing methods, enabling better generalization with fewer training samples.
• Training time per epoch is significantly reduced—DCW-AE trains much faster than OT-AE and WGAN-AE across CIFAR10, FlickR25K, and PLACE365 datasets.
• The distance estimates and gradient norms in DCW-AE are more stable during training compared to SWD, especially with low numbers of random projections.
• t-SNE visualization shows that DCW-AE learns a more structured and separable embedding space, effectively distinguishing similar digits like 4 and 9.
• The method outperforms non-adversarial baselines (ITQ, DistillHash) and other adversarial models (OT-AE, SWD-AE), particularly in terms of retrieval accuracy and robustness.