  A number of pattern recognition tasks, \textit{e.g.}, face verification, can
be boiled down to classification or clustering of unit length directional
feature vectors whose distance can be simply computed by their angle. In this
paper, we propose the von Mises-Fisher (vMF) mixture model as the theoretical
foundation for an effective deep-learning of such directional features and
derive a novel vMF Mixture Loss and its corresponding vMF deep features. The
proposed vMF feature learning achieves the characteristics of discriminative
learning, \textit{i.e.}, compacting the instances of the same class while
increasing the distance of instances from different classes. Moreover, it
subsumes a number of popular loss functions as well as an effective method in
deep learning, namely normalization. We conduct extensive experiments on face
verification using 4 different challenging face datasets, \textit{i.e.}, LFW,
YouTube faces, CACD and IJB-A. Results show the effectiveness and excellent
generalization ability of the proposed approach as it achieves state-of-the-art
results on the LFW, YouTube faces and CACD datasets and competitive results on
the IJB-A dataset.
