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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.
The von Mises-Fisher distribution is one of the most widely used probability distributions to describe directional data. Finite mixtures of von Mises-Fisher distributions have found numerous applications. However, the likelihood function for the fini
Robust estimation of location and concentration parameters for the von Mises-Fisher distribution is discussed. A key reparametrisation is achieved by expressing the two parameters as one vector on the Euclidean space. With this representation, we fir
In recent years, visible-spectrum face verification systems have been shown to match expert forensic examiner recognition performance. However, such systems are ineffective in low-light and nighttime conditions. Thermal face imagery, which captures b
Face super-resolution (FSR), also known as face hallucination, which is aimed at enhancing the resolution of low-resolution (LR) face images to generate high-resolution (HR) face images, is a domain-specific image super-resolution problem. Recently,
Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the