Deep neural networks (DNNs) especially convolutional neural networks (CNNs) have achieved state-of-the-art performances in many applications, and they have been shown to be especially powerful in multi-class classification tasks. Existing DNNs and CNNs are typically trained with a soft-max cross-entropy loss which only considers the ground-truth class by maximizing the predicted probability of the correct label. This cross-entropy loss ignores the intricate inter-class relationships that exist in the data. In this work, we propose to use the exact squared Earth Mover's Distance (EMD) as a loss function for multi-class classification tasks. The squared EMD loss uses the predicted probabilities of all classes and penalizes the miss-predictions accordingly. In experiments, we evaluate our squared EMD loss in ordered-classes datasets such as age estimation and image aesthetic judgment. We also generalize the squared EMD loss to classification datasets with orderless-classes such as the ImageNet. Our results show that the squared EMD loss allows networks to achieve lower errors than the standard cross-entropy loss, and result in state-of-the-art performances on two age estimation datasets and one image aesthetic judgment dataset.

本研究提出将Wasserstein距离应用于单标签分类，以考虑现实任务中存在的类别间联系，并表明该方法在具有明显类间关系的数据集上表现出最新的最优结果。

基于平方地球移动距离的深度神经网络训练损失