Dynamic Bernstein GCN for Pan-Cancer Subtype Classification Using RNA-Seq and CNV Data

Cancer subtype classification requires capturing complex multi-omics interactions that conventional machine learning models often struggle to represent effectively. Graph Convolutional Networks (GCNs) leverage biological topologies but typically rely on fixed propagation mechanisms, which limit adaptability to diverse graph structures. This study introduces the Dynamic Bernstein Graph Convolutional Network (DB-GCN), a novel architecture that employs adaptive spectral propagation using Bernstein polynomials to enable topology-aware learning without eigendecomposition. DB-GCN supports single-omics (RNA) and multi-omics (RNA+CNV) inputs within a graph-based framework that represents genes as nodes and interactions as edges derived from gene-gene, protein-protein, and Co-expression networks. A dual-stream design combines a Bernstein graph stream with an omics multilayer perceptron to capture both local and global features. In pan-cancer experiments on 28 TCGA subtypes, DB-GCN achieves 86.05% $\pm$ 0.83 on STRING, 85.86% $\pm$ 0.98 on BioGRID, and 85.88% $\pm$ 0.71 on Co-expression for the 2,000-gene multi-omics setting. SHAP-based analysis identifies putative biomarker genes such as KLK11, OR4F15, and UBE2DNL, and 12 of the top 50 genes map to KEGG cancer pathways. These results indicate that DB-GCN provides an accurate and interpretable graph-based framework for pan-cancer subtype classification and biomarker discovery in precision oncology.