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 rankingbased 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.