T-vMF Similarity for Regularizing Intra-Class Feature Distribution

Deep convolutional neural networks (CNNs) leverage large-scale training dataset to produce remarkable performance on various image classification tasks. It, however, is difficult to effectively train the CNNs on some realistic learning situations such as regarding class imbalance, small-scale and label noises. Regularizing CNNs works well on learning with such deteriorated training datasets by mitigating overfitting issues. In this work, we propose a method to effectively impose regularization on feature representation learning. By focusing on the angle between a feature and a classifier which is embedded in cosine similarity at the classification layer, we formulate a novel similarity beyond the cosine based on von Mises-Fisher distribution of directional statistics. In contrast to the cosine similarity, our similarity is compact while having heavy tail, which contributes to regularizing intra-class feature distribution to improve generalization performance. Through the experiments on some realistic learning situations such as of imbalance, small-scale and noisy labels, we demonstrate the effectiveness of the proposed method for training CNNs, in comparison to the other regularization methods. Codes are available at https://github.com/tk1980/tvMF.