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Optimizing the approximation of Average Precision (AP) has been widelystudied for image retrieval. Limited by the definition of AP, such methodsconsider both negative and positive instances ranking before each positiveinstance. However, we claim that only penalizing negative instances beforepositive ones is enough, because the loss only comes from these negativeinstances. To this end, we propose a novel loss, namely Penalizing Negativeinstances before Positive ones (PNP), which can directly minimize the number ofnegative instances before each positive one. In addition, AP-based methodsadopt a fixed and sub-optimal gradient assignment strategy. Therefore, wesystematically investigate different gradient assignment solutions viaconstructing derivative functions of the loss, resulting in PNP-I withincreasing derivative functions and PNP-D with decreasing ones. PNP-I focusesmore on the hard positive instances by assigning larger gradients to them andtries to make all relevant instances closer. In contrast, PNP-D pays lessattention to such instances and slowly corrects them. For most real-world data,one class usually contains several local clusters. PNP-I blindly gathers theseclusters while PNP-D keeps them as they were. Therefore, PNP-D is moresuperior. Experiments on three standard retrieval datasets show consistentresults with the above analysis. Extensive evaluations demonstrate that PNP-Dachieves the state-of-the-art performance. Code is available athttps://github.com/interestingzhuo/PNPloss

Rethinking the Optimization of Average Precision: Only Penalizing Negative Instances before Positive Ones is Enough