Hashing, or learning binary embeddings of data, is frequently used in nearest neighbor retrieval. In this paper, we develop learning to rank formulations for hashing, aimed at directly optimizing ranking-based evaluation metrics such as Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). We first observe that the integer-valued Hamming distance often leads to tied rankings, and propose to use tie-aware versions of AP and NDCG to evaluate hashing for retrieval. Then, to optimize tie-aware ranking metrics, we derive their continuous relaxations, and perform gradient-based optimization with deep neural networks. Our results establish the new state-of-the-art for image retrieval by Hamming ranking in common benchmarks.

翻译：在近邻的检索中,经常使用散列或学习数据二进制嵌入。在本文中,我们发展了对散列配方进行排序的学习,目的是直接优化基于排名的评价指标,如平均精度(AP)和标准化折扣累积收益(NDCG ) 。 我们首先观察到,整数值仓储距离往往导致捆绑排名,并提议使用AP和NDCG的带线识别版本来评估仓储检索。 然后,为了优化对齐的排名,我们不断获得它们的放松,并且与深层神经网络进行基于梯度的优化。 我们的结果建立了用于Hamming排名图像检索的新的最新水平。