PSMEKL: Positional and structural multiple empirical kernel learning for node embedding

Graph Neural Networks (GNNs) are powerful for processing graph-structured data, where nodes are linked through edges. Generally, incorporating positional and structural information into node embeddings can capture distribution characteristics of nodes. However, traditional GNNs struggle to perfectly capture both types of information simultaneously. Moreover, existing node embedding methods struggle to handle both attributed and non-attributed graphs simultaneously. To this end, we propose Positional and Structural Multiple Empirical Kernel Learning (PSMEKL), a method that enhances node feature representations by incorporating positional and structural information. PSMEKL integrates kernel mapping and community detection to capture both positional relationships and global graph structures, optimizing a dedicated criterion function to generate effective node embeddings for both attributed and non-attributed graphs. This approach enhances the distinction between nodes with different structures while ensuring that nodes with similar connectivity patterns share similar embedding features. Extensive experiments confirm that preprocessing node features with PSMEKL significantly improves GNN performance. The code for PSMEKL is available at https://github.com/ZonghaiZhu/PSMEKL.