Deep Hashing via Householder Quantization

TL;DR

This paper introduces a novel two-stage deep hashing method using Householder transformations that improves quantization without sacrificing similarity performance, achieving state-of-the-art results in image retrieval.

Contribution

It proposes a new quantization approach with orthogonal transformations, enhancing existing deep hashing algorithms without additional hyperparameters or performance loss.

Findings

Achieves state-of-the-art image retrieval performance.

Provides consistent improvements over existing deep hashing methods.

Efficiently leverages Householder matrices for orthogonal transformations.

Abstract

Hashing is at the heart of large-scale image similarity search, and recent methods have been substantially improved through deep learning techniques. Such algorithms typically learn continuous embeddings of the data. To avoid a subsequent costly binarization step, a common solution is to employ loss functions that combine a similarity learning term (to ensure similar images are grouped to nearby embeddings) and a quantization penalty term (to ensure that the embedding entries are close to binarized entries, e.g., -1 or 1). Still, the interaction between these two terms can make learning harder and the embeddings worse. We propose an alternative quantization strategy that decomposes the learning problem in two stages: first, perform similarity learning over the embedding space with no quantization; second, find an optimal orthogonal transformation of the embeddings so each coordinate of the embedding is close to its sign, and then quantize the transformed embedding through the sign function. In the second step, we parametrize orthogonal transformations using Householder matrices to efficiently leverage stochastic gradient descent. Since similarity measures are usually invariant under orthogonal transformations, this quantization strategy comes at no cost in terms of performance. The resulting algorithm is unsupervised, fast, hyperparameter-free and can be run on top of any existing deep hashing or metric learning algorithm. We provide extensive experimental results showing that this approach leads to state-of-the-art performance on widely used image datasets, and, unlike other quantization strategies, brings consistent improvements in performance to existing deep hashing algorithms.