The problem of long-tailed recognition (LTR) has received attention in recent years due to the fundamental power-law distribution of objects in the real-world. Most recent works in LTR use softmax classifiers that are biased in that they correlate classifier norm with the amount of training data for a given class. In this work, we show that learning prototype classifiers addresses the biased softmax problem in LTR. Prototype classifiers can deliver promising results simply using Nearest-Class- Mean (NCM), a special case where prototypes are empirical centroids. We go one step further and propose to jointly learn prototypes by using distances to prototypes in representation space as the logit scores for classification. Further, we theoretically analyze the properties of Euclidean distance based prototype classifiers that lead to stable gradient-based optimization which is robust to outliers. To enable independent distance scales along each channel, we enhance Prototype classifiers by learning channel-dependent temperature parameters. Our analysis shows that prototypes learned by Prototype classifiers are better separated than empirical centroids. Results on four LTR benchmarks show that Prototype classifier outperforms or is comparable to state-of-the-art methods. Our code is made available at https://github.com/saurabhsharma1993/prototype-classifier-ltr.

翻译：长尾识别（LTR）问题近年来因现实世界中物体服从基本幂律分布而受到关注。现有大多数LTR方法使用softmax分类器，但其存在偏差——分类器范数与特定类别的训练数据量相关。本文证明，学习原型分类器可解决LTR中的softmax偏差问题。原型分类器仅通过最近类均值（NCM，一种原型为经验质心的特例）即可取得优异结果。我们进一步提出联合学习原型：将表示空间中与原型之间的距离直接作为分类logit得分。此外，我们从理论上分析了基于欧氏距离的原型分类器特性，其具有鲁棒于异常值的稳定梯度优化能力。为支持各通道的独立距离尺度，我们通过学习通道相关的温度参数增强原型分类器。分析表明，本文学习的原型相较于经验质心具有更好的分离性。在四个LTR基准上的实验结果显示，原型分类器性能优于或媲美现有最优方法。代码已开源至https://github.com/saurabhsharma1993/prototype-classifier-ltr。