A Lower Bound of Hash Codes' Performance

Xiaosu Zhu, Jingkuan Song, Yu Lei, Lianli Gao, Hengtao Shen

Keywords: Learning to hash, Compact representation, Fast retrieval, Hamming space metric learning

Abstract: As a crucial approach for compact representation learning, hashing has achieved great success in effectiveness and efficiency. Numerous heuristic Hamming space metric learning objectives are designed to obtain high-quality hash codes. Nevertheless, a theoretical analysis of criteria for learning good hash codes remains largely unexploited. In this paper, we prove that inter-class distinctiveness and intra-class compactness among hash codes determine the lower bound of hash codes' performance. Promoting these two characteristics could lift the bound and improve hash learning. We then propose a surrogate model to fully exploit the above objective by estimating the posterior of hash codes and controlling it, which results in a low-bias optimization. Extensive experiments reveal the effectiveness of the proposed method. By testing on a series of hash-models, we obtain performance improvements among all of them, with an up to $26.5\%$ increase in mean Average Precision and an up to $20.5\%$ increase in accuracy. Our code is publicly available at https://github.com/VL-Group/LBHash.

TL;DR: We propsoe a lower bound of hash codes' performance and a posterior estimation surrogate model over hash codes to improve hash learning.

Community Implementations: [ 2 code implementations](https://www.catalyzex.com/paper/arxiv:2210.05899/code)