Hashing as Tie-Aware Learning to Rank

We formulate the problem of supervised hashing, or learning binary embeddings of data, as a learning to rank problem. Specifically, we optimize two common ranking-based evaluation metrics, Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). Observing that ranking with the discrete Hamming distance naturally results in ties, we propose to use tie-aware versions of ranking metrics in both the evaluation and the learning of supervised hashing. For AP and NDCG, we derive continuous relaxations of their tie-aware versions, and optimize them using stochastic gradient ascent with deep neural networks. Our results establish the new state-of-the-art for tie-aware AP and NDCG on common hashing benchmarks.