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 have a tendency to correlate classifier norm with the amount of training data for a given class. On the other hand, Prototype classifiers do not suffer from this shortcoming and can deliver promising results simply using Nearest-Class-Mean (NCM), a special case where prototypes are empirical centroids. However, the potential of Prototype classifiers as an alternative to softmax in LTR is relatively underexplored. In this work, we propose Prototype classifiers, which jointly learn prototypes that minimize average cross-entropy loss based on probability scores from distances to prototypes. We theoretically analyze the properties of Euclidean distance based prototype classifiers that leads to stable gradient-based optimization which is robust to outliers. We further enhance Prototype classifiers by learning channel-dependent temperature parameters to enable independent distance scales along each channel. Our analysis shows that prototypes learned by Prototype classifiers are better separated than empirical centroids. Results on four long-tailed recognition benchmarks show that Prototype classifier outperforms or is comparable to the state-of-the-art methods.

翻译：近年来，长尾识别（LTR）问题因现实世界中物体分布遵循基本幂律分布而受到关注。大多数近期LTR研究采用softmax分类器，这类分类器倾向于将分类器范数与特定类别的训练数据量相关联。相比之下，原型分类器不存在这一缺陷，且能通过最近类均值（NCM）这一特例（其中原型为经验质心）取得令人满意的结果。然而，原型分类器作为LTR中softmax替代方案的潜力尚未得到充分探索。本文提出原型分类器，通过联合学习原型，基于样本到原型距离的概率得分最小化平均交叉熵损失。我们从理论上分析了基于欧氏距离的原型分类器的性质，这种性质能够实现稳定的梯度优化，且对异常值具有鲁棒性。此外，我们通过学习通道相关温度参数增强原型分类器，使各通道独立调整距离尺度。分析表明，原型分类器学习的原型比经验质心具有更好的分离性。在四个长尾识别基准上的实验结果表明，原型分类器性能优于或可比拟现有最先进方法。