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：长尾识别（LTR）问题近年来因现实世界中对象的幂律分布特性而受到关注。近期的LTR研究大多采用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。而原型分类器不存在这一缺陷，仅通过最近类均值（NCM）即可取得显著效果——该方法是原型作为经验质心的特例。然而，原型分类器作为softmax替代方案在LTR中的应用潜力尚未充分探索。本文提出一种原型分类器，通过联合学习原型，基于样本与原型间距离计算概率得分，从而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，其梯度优化具有稳定性且对异常值鲁棒。通过引入通道相关温度参数，我们使各通道独立调节距离尺度，进一步增强了原型分类器性能。分析表明，原型分类器学得的原型较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显示，原型分类器性能优于或可比肩当前最优方法。