Directional Statistics-based Deep Metric Learning for Image Classification and Retrieval.

Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in the embedding space has been used to improve the performance of several DDML methods. However, the commonly used Euclidean distanceis no longer an accurate metric for $L2$-normalized embedding space, i.e., a hyper-sphere. Another challenge of current DDML methods is that their loss functionsare usually based on rigid data formats, such as the triplet tuple. Thus, an extra process is needed to prepare data in specific formats. In addition, their losses are obtained from a limited number of samples, which leads to a lack of the global view of the embedding space. In this paper, we replace the Euclidean distancewith the cosine similarityto better utilize the $L2$-normalization, which is able to attenuate the curseof dimensionality. More specifically, a novel loss functionbased on the von Mises-Fisher distributionis proposed to learn a compact hyper-spherical embedding space. Moreover, a new efficient learning algorithm is developed to better capture the global structure of the embedding space. Experiments for both classification and retrieval tasks on several standard datasets show that our method achieves state-of-the-art performance with a simpler training procedure. Furthermore, we demonstrate that, even with a small number of convolutional layers, our model can still obtain significantly better classification performance than the widely used softmax loss.