Title: Improve distance metric learning by learning positions of class centers. Abstract: Deep metric learning aims at learning a deep neural network by letting similar samples have small distances while dissimilar samples have large distances. To achieve this goal, the current DML algorithms mainly focus on pulling similar samples in each class as closely as possible. However, pulling similar samples only considers the local distribution of the data samples and ignores the global distribution of the data set, i.e., the center positions of different classes. The global distribution helps the distance metric learning. For example, expanding the distance between centers can increase the discriminant ability of the extracted features. However, how to increase the distance between centers is a challenging task. In this paper, we design a genius function named the skewed mean function, which only considers the most considerable distances of a set of samples. So maximizing the value of the skewed mean function can make the largest distance larger. We also prove that the current energy functions used for uniformity regularization on centers are special cases of our skewed mean function. At last, we conduct extensive experiments to illustrate the superiority of our methods.