In high-dimensional data spaces, most data are located at the edges of the high-dimensional space and distributed sparsely, resulting in the problem of "curse of dimensionality", which makes existing anomaly detection methods unable to ensure the accuracy of anomaly detection. To address this problem, an Angle-based Graph Neural Network(A-GNN) high-dimensional data anomaly detection method is proposed. First, the data used for training are expanded by uniformly sampling the data space and perturbing the initial training data. Second, the k-nearest neighbor relationship is used to construct a k-nearest neighbor relationship graph of the training data, and the variance of the k-nearest neighbor element distance weighted angle is used as the initial anomaly factor for the nodes in the k-nearest neighbor relationship graph. Finally, by training a GNN model, information exchange between nodes is achieved, enabling adjacent nodes to learn from each other and effectively evaluate anomalies. The A-GNN method is experimentally compared with nine typical anomaly detection methods on six natural datasets. The results demonstrate that A-GNN achieved the highest Area Under the Curve(AUC) value in five datasets, which can significantly improve the anomaly detection accuracy of various dimensions of data. On some true high-dimensional data, the AUC of anomaly detection increased by more than 40%. Compared with three k-nearest neighbor-based anomaly detection methods at different k values, A-GNN can effectively avoid the impact of k values on detection results by utilizing information exchange between GNN nodes, and the method has stronger robustness
