Weisfeiler-Lehman Kernel Augmented Product Representation for Queries on Large-Scale BIM Scenes

To achieve efficient querying of BIM products in large-scale virtual scenes, this study introduces a Weisfeiler-Lehman (WL) kernel augmented representation for Building Information Modeling(BIM) products based on Product Attributed Graphs (PAGs). Unlike conventional data-driven approaches that demand extensive labeling and preprocessing, our method directly processes raw BIM product data to extract stable semantic and geometric features. Initially, a PAG is constructed to encapsulate product features. Subsequently, a WL kernel enhanced multi-channel node aggregation strategy is employed to integrate BIM product attributes effectively. Leveraging the bijective relationship in graph isomorphism, an unsupervised convergence mechanism based on attribute value differences is established. Experiments demonstrate that our method achieves convergence within an average of 3 iterations, completes graph isomorphism testing in minimal time, and attains an average query accuracy of 95%. This approach outperforms 1-WL and 3-WL methods, especially in handling products with topologically isomorphic but oppositely attributed spaces.