Advanced deep learning methods, especially graph neural networks (GNNs), are increasingly expected to learn from brain functional network data and identify the functional connections between brain disorder and health. In this paper, we proposed a novel Transformer and snowball encoding networks (TSEN) for brain functional network classification, which introduced Transformer architecture with graph snowball connection into GNNs for learning whole-graph representation. TSEN combined graph snowball connection with graph Transformer by snowball encoding layers, which enhanced the power to capture multi-scale information and global patterns of brain functional networks. TSEN also introduced snowball graph convolution as position embedding in Transformer structure, which was a simple yet effective method for capturing local patterns naturally. We evaluated the proposed model by two large-scale brain functional network datasets, and the results demonstrated that TSEN outperformed the state-of-the-art GNN models and the graph-transformer based GNN models.
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