Multigranularity Deep Graph Convolutional Neural Network Node Clustering Leveraging Spatial Information.

In the era of information explosion, clustering analysis of graph-structured data and empty graph-structured data is of great significance for extracting the intrinsic value of data. From the perspective of spatial information, empty graph-structured data and graph-structured data are essentially the same type of data, both containing rich spatial information. However, there is currently no general clustering method that can handle both types of data, and the clustering methods applicable to empty graph-structured data pay little attention to the spatial information they contain. Meanwhile, graph convolutional neural networks (GCN) have made significant progress in processing graph-structured data, but applying them to empty graph-structured data still faces challenges because the latter lacks an explicit topological structure. To address these problems, this study proposes a multigranularity deep GCN node clustering method leveraging spatial information (CMDGCN). It converts empty graph-structured data into graph-structured data using the $k$ -nearest neighbor (k-nn) algorithm and constructs multigranularity graph structures based on feature segmentation to extend the network depth to deep layers, thereby addressing the issue of shallow network layers in traditional GCN models. In addition, this study improves the self-expressiveness principle, ensuring that the learned similarity matrix not only depends on the node embedding representation but also incorporates the original structural information of the graph, resulting in a high-quality and interpretable similarity matrix. Furthermore, through experimental verification on multiple graph-structured datasets and empty graph-structured datasets, our method outperforms existing methods in several key indicators, proving its effectiveness and robustness. This achievement not only provides new methods and perspectives for graph node clustering but also offers new effective tools for processing empty graph-structured data.