Hashing as Tie-Aware Learning to Rank
  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.
