Geometric Prior Guided Feature Representation Learning for Long-Tailed Classification

Real-world data are long-tailed, the lack of tail samples leads to a significant limitation in the generalization ability of the model. Although numerous approaches of class re-balancing perform well for moderate class imbalance problems, additional knowledge needs to be introduced to help the tail class recover the underlying true distribution when the observed distribution from a few tail samples does not represent its true distribution properly, thus allowing the model to learn valuable information outside the observed domain. In this work, we propose to leverage the geometric information of the feature distribution of the well-represented head class to guide the model to learn the underlying distribution of the tail class. Specifically, we first systematically define the geometry of the feature distribution and the similarity measures between the geometries, and discover four phenomena regarding the relationship between the geometries of different feature distributions. Then, based on four phenomena, feature uncertainty representation is proposed to perturb the tail features by utilizing the geometry of the head class feature distribution. It aims to make the perturbed features cover the underlying distribution of the tail class as much as possible, thus improving the model's generalization performance in the test domain. Finally, we design a three-stage training scheme enabling feature uncertainty modeling to be successfully applied. Experiments on CIFAR-10/100-LT, ImageNet-LT, and iNaturalist2018 show that our proposed approach outperforms other similar methods on most metrics. In addition, the experimental phenomena we discovered are able to provide new perspectives and theoretical foundations for subsequent studies.