# Supervised Discrete Hashing with Relaxation

## TL;DR

This paper introduces SDHR, a novel supervised hashing method that optimizes the regression target for improved classification accuracy and retrieval efficiency in high-dimensional data, outperforming previous SDH.

## Contribution

The paper proposes a new supervised discrete hashing method called SDHR that optimizes the regression target, enhancing flexibility and accuracy over traditional SDH.

## Key findings

- SDHR outperforms SDH on CIFAR-10, MNIST, and FRGC datasets.
- SDHR demonstrates improved retrieval accuracy and efficiency.
- Experimental results confirm SDHR's effectiveness in large-scale datasets.

## Abstract

Data-dependent hashing has recently attracted attention due to being able to support efficient retrieval and storage of high-dimensional data such as documents, images, and videos. In this paper, we propose a novel learning-based hashing method called "Supervised Discrete Hashing with Relaxation" (SDHR) based on "Supervised Discrete Hashing" (SDH). SDH uses ordinary least squares regression and traditional zero-one matrix encoding of class label information as the regression target (code words), thus fixing the regression target. In SDHR, the regression target is instead optimized. The optimized regression target matrix satisfies a large margin constraint for correct classification of each example. Compared with SDH, which uses the traditional zero-one matrix, SDHR utilizes the learned regression target matrix and, therefore, more accurately measures the classification error of the regression model and is more flexible. As expected, SDHR generally outperforms SDH. Experimental results on two large-scale image datasets (CIFAR-10 and MNIST) and a large-scale and challenging face dataset (FRGC) demonstrate the effectiveness and efficiency of SDHR.