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Abstract: Few shot learning aims at identifying novel concepts with very little supervisory information. For remote sensing (RS) image few shot classification, the existing methods are often unable to achieve satisfactory accuracy because of ignoring the correlation information between samples. In order to improve the RS few shot classification accuracy, Multi Graph Convolutional Network (Multi-GCN) is proposed in this paper. The proposed method uses a graph to model the similarity of images in the feature space, and uses multi-graph convolutional operation to smooth the image features from the same class to enhance the discrimination of different class samples to improve classification accuracy. First, an adjacency matrix of the graph is computed by "KNN + radial basis function" method after the initial feature of each image being extracted by a pre-trained convolutional neural network. Then the proposed multi-graph convolutional operation is used to update image features, which can make images with the same class get more similar feature representation. Finally, the updated features are used to predict class labels of nodes by metric distance between the labeled and the unlabeled in feature space. Through spectral domain analysis, it is concluded that the proposed method can effectively suppress high-frequency components of the graph signals and significantly enhance the clustering coefficients of node features from the same class. In addition, the fine-tuning method is introduced in the training process, and the labeled data in the new class are used to train the last layer graph convolutional network for a small number of times, which can further improve the classification accuracy and enhance the transfer ability of the model. In order to validate the effectiveness of the proposed method, the Multi-GCN is compared with ProtoNet, GNN-FSL and two single graph based methods ProtoGCN and ProtoIGCN on three benchmark datasets AID, OPTIMAL31 and RSI-CB256. The experimental results demonstrate that the classification accuracy of the proposed method is significantly higher than that of ProtoNet and GNN-FSL when the number of labeled samples of each class is only 1,3,5,10 and also higher than the graph convolutional methods based on a single adjacency matrix such as ProtoGCN and ProtoIGCN. After use of fine-tuning training methods, the classification accuracy can be further improved by about 1%. A few shot classification method of RS scene images is proposed in this paper. In this method, the multi-graph convolutional network is introduced into the metric network to smooth the data features, which can make images from same class get more similar feature representation and improve the classification accuracy. Experimental results demonstrate that the proposed method can increase the clustering degree of similar data in feature space and can achieve higher classification accuracy compared with ProtoNet, GNN-FSL and methods based on single graph convolutional network. The conclusion of multi-graph convolutional operation and spectrum analysis in this paper can also be extended to other graph-based semi-supervised learning.