# A Large-Class Few-Shot Learning Method Based on High-Dimensional Features
## 1 Introduction  
The problem of few-shot learning (FSL) attracted the attention of [PERSON] et al., in 2000 [1]. With the development of deep learning [2; 3; 4], since 2015, some few-shot learning methods based on deep features have been proposed, which have achieved remarkable results in fewer-class scenarios. In 2016, the matching network [5] proposed by [PERSON] et al. achieved a 98.9% recognition accuracy under an experimental setup using a 5-way 5-shot setting on Omniglot; the prototype network [6] proposed by [PERSON] et al., in 2017 achieved a 99.7% recognition accuracy with the same dataset and experimental settings. These methods were aimed at scenarios with a very small number of target classes (5 or 20 classes). The recognition accuracy declines significantly when the number of target classes increases. Under an experimental setup using a 2636-way 5-shot setting on Omniglot, the accuracy of the matching network and prototype network decreased to 68.04% and 69.90%, respectively [7]. However, there are a large number of categories in the real world, and it is difficult to achieve a practical level using the existing few-shot learning methods in large-class scenarios. Compared with a traditional few-shot learning task, large-class few-shot learning tasks contain hundreds or thousands of target classes, which is more challenging. This paper proposes a large-class few-shot learning method for an image recognition task. We use a global regularization strategy to make different classes of samples as orthogonal as possible. In addition, we apply AM-Softmax Loss to the final cost function in order to describe the relationships between samples distributed on a hypersphere.  
At present, little research for large-class few-shot learning has been performed. As far as we know, there are only a few studies [7; 8; 9; 10; 11]. Recently, theoretical research on few-shotlearning in a high-dimensional feature space has been carried out [11; 12; 13; 14; 15]. As reported by [11], with certain conditions, the precision of few-shot classification can improve as the number of classes grows. Ref. [15] conducted theoretical research on high-dimensional space and proved that as long as samples of different classes are scattered and samples of the same class are distributed compactly in high-dimensional space, a large-class FSL learner can achieve a better generalization ability. Inspired by this theory, this paper proposes a large-class few-shot learning method based on high-dimensional features. The basic idea is to use convolutional neural networks to extract high-dimensional features and unitize them to project samples onto a feature sphere. The global orthogonal regularization strategy is then used to make the samples in different categories as orthogonal as possible on the hypersphere, so as to achieve the purpose of compactness within the class and dispersion between classes in high-dimensional space. To describe the relationships between samples distributed on a sphere, we employ an angle metric-based loss function. Our source code is available at: [[https://github.com/jwdang/HF-FSL](https://github.com/jwdang/HF-FSL)]([https://github.com/jwdang/HF-FSL](https://github.com/jwdang/HF-FSL)) (accessed on 30 October 2023). The main contribution of this paper consists of two parts:  
1. A large-class few-shot learning method, HF-FSL, based on high-dimensional features is proposed. On the high-dimensional feature sphere, HF-FSL uses a regularization strategy to make different classes of samples as orthogonal as possible, so as to achieve the purpose of homogeneous compactness and heterogeneous dispersion. In addition, HF-FSL uses AM-Softmax Loss to describe the relationships between samples distributed on a hypersphere.
2. The experimental results from three public large-class few-shot datasets, Omniglot [16], Fungi, and ImageNet [17], show that HF-FSL can effectively improve the recognition accuracy of a large-class FSL task.