## 1 Introduction
[PERSON] [16] calculated the reconstruction error between the support sample and the query sample as the similarity score. DN4 [17] and Deep EMD [18] obtain rich similarity measures directly from local features. Recent studies have indicated that the FSC of the transfer-learning method can attain comparable performance to that of the meta-learning method with complex episodic training. Such methods typically combine pre-trained feature extractors on all base-class datasets with arbitrary traditional classifiers to make classification decisions for query samples of unknown classes. It has been shown that pre-training the entire base class dataset using the cross-entropy loss function followed by fine-tuning the pre-trained model using support samples of the visible class can provide a powerful baseline for FSC tasks [19]. Since then, several efforts have been proposed to improve the representation performance of feature extractors. For example, [PERSON] [20] proposed the use of the non-negative interval Cosine loss function to optimize the model, thereby increasing the distance between the training sample and its corresponding parametric prototype, which can effectively improve the generalization performance of the model. [PERSON] [21] used manifold mixing as an effective regularization method to improve the generalization performance of the model. Refs. [22, 23] used rotation prediction and mirror prediction as self-supervised tasks to add to the pre-training process, and experimental results showed that self-supervised tasks are effective methods to improve feature representation performance. In the pursuit of high-accuracy classification performance, many studies tend to employ highly complex networks to enhance the representation of features. As a result, deploying these methods in real-world applications often requires significant computing resources (such as storage space and computing power) and leads to significant time delays. However, power inspection heavily relies on intelligent mobile devices, including inspection robots and UAVs. Considering the limited storage capacity of these devices, it is essential to ensure that the classification model's size is not excessively large[PERSON] Therefore, in this study, we utilize a knowledge distillation-based model compression algorithm to achieve few-shot image classification, aiming to reduce the number of model parameters. Knowledge distillation [24, 25] is one of the most effective model compression methods and has garnered significant research interest in both industry and academia due to its simple training strategy and effective performance[PERSON] It leverages the knowledge acquired by a teacher network to guide the training of a small-scale student network, enabling the latter to achieve comparable performance despite having fewer parameters. In order to make better use of the knowledge information contained in the teacher network, [PERSON] [26] proposed to take the spatial attention of the hidden layer features of the teacher network as knowledge and instruct the student network to imitate its attention feature map. [PERSON] [27] proposed a relational knowledge distillation method, which used distance and angle to measure the relationship between sample features, as a valid type of knowledge during distillation. [PERSON] et al. [28] used the kernel function to obtain higher-order relationships between the features of samples as effective distillation knowledge. Although the model compression methods based on feature relation knowledge mentioned above can effectively improve the performance of small-capacity student networks, the current work only focuses on the local relationship between individual sample features, ignoring the global relationship between the features of samples. Therefore, this paper proposes a method based on global and local knowledge distillation and applies it to the task of FSC for electrical equipment images. In this paper, we propose three main contributions:  
1.