Current CNN-based deep feature learning methods for image classification are mainly focused on learning with two types of loss functions: the softmax loss and its variants with class-level labels, or the metric-learning losses with pairwise labels. The former regards the weight vectors of the last fully connected layer of CNNs as representations of the class centres and focuses on the similarity between a single feature and each weight vector. The latter aims at seeking appropriate distance metrics between features pairs to boost the CNNs by learning a discriminative embedding space. In this work, we propose a simple yet effective new loss function called angular joint loss (AJL) to exploit the best of both worlds. By integrating feature-weight angles with feature-feature angles, AJL inherits the simplicity of softmax loss and the power of pair-wise metric learning and enhances both the intra-class compactness and the inter-class separability. The proposed AJL is simple to implement and has no time-consuming mining of pair or triple samples. On some popular image classification datasets (CIFAR-10, CIFAR-100 and ImageNet), extensive experimental results show that the proposed AJL can achieve the state-of-the-art performance.
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