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    Area of Science:

    • Artificial Intelligence
    • Data Science
    • Machine Learning

    Background:

    • Clustering graph-structured and empty graph-structured data is crucial for data analysis.
    • Existing methods struggle with data lacking explicit topology and often ignore spatial information.
    • Graph convolutional neural networks (GCNs) show promise but face challenges with topology-deficient data.

    Purpose of the Study:

    • To develop a generalizable clustering method for both graph and empty graph-structured data.
    • To address the limitations of shallow networks and the neglect of spatial information in current methods.
    • To enhance the interpretability and quality of similarity matrices in clustering.

    Main Methods:

    • Proposed a multigranularity deep GCN node clustering method (CMDGCN) leveraging spatial information.
    • Converted empty graph data to graph data using the k-nearest neighbor (k-nn) algorithm.
    • Constructed multigranularity graph structures and improved the self-expressiveness principle for enhanced similarity matrices.

    Main Results:

    • CMDGCN effectively handles both graph-structured and empty graph-structured data.
    • The method demonstrated superior performance across multiple datasets compared to existing techniques.
    • Achieved high-quality and interpretable similarity matrices by incorporating original graph structure.

    Conclusions:

    • The proposed CMDGCN offers a robust and effective solution for graph node clustering and empty graph-structured data analysis.
    • This work provides novel perspectives and tools for handling diverse graph data types.
    • The method's effectiveness and robustness were validated through extensive experiments.