Hypersphere

About: Hypersphere is a research topic. Over the lifetime, 1393 publications have been published within this topic receiving 26777 citations. The topic is also known as: n-sphere & sphere.

ArcFace: Additive Angular Margin Loss for Deep Face Recognition

Abstract: One of the main challenges in feature learning using Deep Convolutional Neural Networks (DCNNs) for large-scale face recognition is the design of appropriate loss functions that can enhance the discriminative power. Centre loss penalises the distance between deep features and their corresponding class centres in the Euclidean space to achieve intra-class compactness. SphereFace assumes that the linear transformation matrix in the last fully connected layer can be used as a representation of the class centres in the angular space and therefore penalises the angles between deep features and their corresponding weights in a multiplicative way. Recently, a popular line of research is to incorporate margins in well-established loss functions in order to maximise face class separability. In this paper, we propose an Additive Angular Margin Loss (ArcFace) to obtain highly discriminative features for face recognition. The proposed ArcFace has a clear geometric interpretation due to its exact correspondence to geodesic distance on a hypersphere. We present arguably the most extensive experimental evaluation against all recent state-of-the-art face recognition methods on ten face recognition benchmarks which includes a new large-scale image database with trillions of pairs and a large-scale video dataset. We show that ArcFace consistently outperforms the state of the art and can be easily implemented with negligible computational overhead. To facilitate future research, the code has been made available.

SphereFace: Deep Hypersphere Embedding for Face Recognition

Abstract: This paper addresses deep face recognition (FR) problem under open-set protocol, where ideal face features are expected to have smaller maximal intra-class distance than minimal inter-class distance under a suitably chosen metric space. However, few existing algorithms can effectively achieve this criterion. To this end, we propose the angular softmax (A-Softmax) loss that enables convolutional neural networks (CNNs) to learn angularly discriminative features. Geometrically, A-Softmax loss can be viewed as imposing discriminative constraints on a hypersphere manifold, which intrinsically matches the prior that faces also lie on a manifold. Moreover, the size of angular margin can be quantitatively adjusted by a parameter m. We further derive specific m to approximate the ideal feature criterion. Extensive analysis and experiments on Labeled Face in the Wild (LFW), Youtube Faces (YTF) and MegaFace Challenge 1 show the superiority of A-Softmax loss in FR tasks.

SphereFace: Deep Hypersphere Embedding for Face Recognition

Abstract: This paper addresses deep face recognition (FR) problem under open-set protocol, where ideal face features are expected to have smaller maximal intra-class distance than minimal inter-class distance under a suitably chosen metric space. However, few existing algorithms can effectively achieve this criterion. To this end, we propose the angular softmax (A-Softmax) loss that enables convolutional neural networks (CNNs) to learn angularly discriminative features. Geometrically, A-Softmax loss can be viewed as imposing discriminative constraints on a hypersphere manifold, which intrinsically matches the prior that faces also lie on a manifold. Moreover, the size of angular margin can be quantitatively adjusted by a parameter $m$. We further derive specific $m$ to approximate the ideal feature criterion. Extensive analysis and experiments on Labeled Face in the Wild (LFW), Youtube Faces (YTF) and MegaFace Challenge show the superiority of A-Softmax loss in FR tasks. The code has also been made publicly available.

ArcFace: Additive Angular Margin Loss for Deep Face Recognition

Abstract: One of the main challenges in feature learning using Deep Convolutional Neural Networks (DCNNs) for large-scale face recognition is the design of appropriate loss functions that enhance discriminative power. Centre loss penalises the distance between the deep features and their corresponding class centres in the Euclidean space to achieve intra-class compactness. SphereFace assumes that the linear transformation matrix in the last fully connected layer can be used as a representation of the class centres in an angular space and penalises the angles between the deep features and their corresponding weights in a multiplicative way. Recently, a popular line of research is to incorporate margins in well-established loss functions in order to maximise face class separability. In this paper, we propose an Additive Angular Margin Loss (ArcFace) to obtain highly discriminative features for face recognition. The proposed ArcFace has a clear geometric interpretation due to the exact correspondence to the geodesic distance on the hypersphere. We present arguably the most extensive experimental evaluation of all the recent state-of-the-art face recognition methods on over 10 face recognition benchmarks including a new large-scale image database with trillion level of pairs and a large-scale video dataset. We show that ArcFace consistently outperforms the state-of-the-art and can be easily implemented with negligible computational overhead. We release all refined training data, training codes, pre-trained models and training logs, which will help reproduce the results in this paper.

Clustering on the Unit Hypersphere using von Mises-Fisher Distributions

Abstract: Several large scale data mining applications, such as text categorization and gene expression analysis, involve high-dimensional data that is also inherently directional in nature. Often such data is L2 normalized so that it lies on the surface of a unit hypersphere. Popular models such as (mixtures of) multi-variate Gaussians are inadequate for characterizing such data. This paper proposes a generative mixture-model approach to clustering directional data based on the von Mises-Fisher (vMF) distribution, which arises naturally for data distributed on the unit hypersphere. In particular, we derive and analyze two variants of the Expectation Maximization (EM) framework for estimating the mean and concentration parameters of this mixture. Numerical estimation of the concentration parameters is non-trivial in high dimensions since it involves functional inversion of ratios of Bessel functions. We also formulate two clustering algorithms corresponding to the variants of EM that we derive. Our approach provides a theoretical basis for the use of cosine similarity that has been widely employed by the information retrieval community, and obtains the spherical kmeans algorithm (kmeans with cosine similarity) as a special case of both variants. Empirical results on clustering of high-dimensional text and gene-expression data based on a mixture of vMF distributions show that the ability to estimate the concentration parameter for each vMF component, which is not present in existing approaches, yields superior results, especially for difficult clustering tasks in high-dimensional spaces.