Optimization of Rank Losses for Image Retrieval

In image retrieval, standard evaluation metrics rely on score ranking, e.g. average precision (AP), recall at k (R@k), normalized discounted cumulative gain (NDCG). In this work, we introduce a general framework for robust and decomposable rank losses optimization. It addresses two major challenges for end-to-end training of deep neural networks with rank losses: non-differentiability and non-decomposability. First, we propose a general surrogate for ranking operator, SupRank, that is amenable to stochastic gradient descent. It provides an upperbound for rank losses and ensures robust training. Second, we use a simple yet effective loss function to reduce the decomposability gap between the averaged batch approximation of ranking losses and their values on the whole training set. We apply our framework to two standard metrics for image retrieval: AP and R@k. Additionally, we apply our framework to hierarchical image retrieval. We introduce an extension of AP, the hierarchical average precision $\mathcal {H}{\mathrm -AP}$, and optimize it as well as the NDCG. Finally, we create the first hierarchical landmarks retrieval dataset. We use a semi-automatic pipeline to create hierarchical labels, extending the large scale Google Landmarks v2 dataset.