Real-world object classes appear in imbalanced ratios. This poses a significant challenge for classifiers which get biased towards frequent classes. We hypothesize that improving the generalization capability of a classifier should improve learning on imbalanced datasets. Here, we introduce the first hybrid loss function that jointly performs classification and clustering in a single formulation. Our approach is based on an affinity measure' in Euclidean space that leads to the following benefits: (1) direct enforcement of maximum margin constraints on classification boundaries, (2) a tractable way to ensure uniformly spaced and equidistant cluster centers, (3) flexibility to learn multiple class prototypes to support diversity and discriminability in feature space. Our extensive experiments demonstrate the significant performance improvements on visual classification and verification tasks on multiple imbalanced datasets. The proposed loss can easily be plugged in any deep architecture as a differentiable block and demonstrates robustness against different levels of data imbalance and corrupted labels.
@cite_30: 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.
@cite_18: My first exposure to Support Vector Machines came this spring when heard Sue Dumais present impressive results on text categorization using this analysis technique. This issue's collection of essays should help familiarize our readers with this interesting new racehorse in the Machine Learning stable. Bernhard Scholkopf, in an introductory overview, points out that a particular advantage of SVMs over other learning algorithms is that it can be analyzed theoretically using concepts from computational learning theory, and at the same time can achieve good performance when applied to real problems. Examples of these real-world applications are provided by Sue Dumais, who describes the aforementioned text-categorization problem, yielding the best results to date on the Reuters collection, and Edgar Osuna, who presents strong results on application to face detection. Our fourth author, John Platt, gives us a practical guide and a new technique for implementing the algorithm efficiently.
@cite_4: We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm).
@cite_53: 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.
@cite_43: Cross-entropy loss together with softmax is arguably one of the most common used supervision components in convolutional neural networks (CNNs). Despite its simplicity, popularity and excellent performance, the component does not explicitly encourage discriminative learning of features. In this paper, we propose a generalized large-margin softmax (L-Softmax) loss which explicitly encourages intra-class compactness and inter-class separability between learned features. Moreover, L-Softmax not only can adjust the desired margin but also can avoid overfitting. We also show that the L-Softmax loss can be optimized by typical stochastic gradient descent. Extensive experiments on four benchmark datasets demonstrate that the deeply-learned features with L-softmax loss become more discriminative, hence significantly boosting the performance on a variety of visual classification and verification tasks.
Margin-maximizing learning objectives have been traditionally used in machine learning. Hinge loss in Support vector machines is one of the pioneering max-margin learning framework @cite_18 . Some recent works aim to integrate max-margin learning with cross-entropy loss function. Among these, Large-margin soft-max @cite_43 enforces inter-class separability directly on the dot-product similarity while SphereFace @cite_53 and ArcFace @cite_30 enforce multiplicative and additive angular margins on the hypersphere manifold, respectively. The hypersphere assumption for feature space makes the resulting loss less generalizable to applications other than face recognition. Furthermore, enforcing margin based separation in angular domain is an ill-posed problem and either requires approximations or assumptions (e.g., unit sphere) @cite_4 . THis paper proposes a new flexible loss function which simultaneously performs clustering and classification, and enables direct enforcement of the max-margin constraints. We describe the proposed loss formulation next.