GraphSC: Deep Graph Learning With Spectral Clustering for Flexible Gene Co-Expression Module Detection Across Pan-Cancer.

Identifying gene co-expression (GCE) modules from transcriptomic data is critical for understanding cellular functions and disease mechanisms. Traditional methods often rely on rigid assumptions to detect modules with specific topologies (e.g., spherical clusters or fully connected cliques), limiting their ability to capture the complex and heterogeneous co-expression patterns across different cancer types. Graph convolutional networks (GCNs) have been shown to encode topological structures and node content of networks, which provide a promising direction for more flexible gene co-expression modeling. However, directly applying naïve GCNs to detect GCE modules poses several challenges: sensitivity to expression data noise, lack of explicit mechanisms to obtain arbitrary-shaped modules, and lack of biological ground-truth for supervision. In this study, we propose GraphSC, a graph-based semi-supervised framework for flexible GCE module detection across pan-cancers. To reduce noise sensitivity, GraphSC adopts a graph attention-based encoder-decoder GCN for simultaneous gene embedding learning and expression data reconstruction. GraphSC also integrates a graph-theoretic spectral clustering to organize embeddings into flexible modules without shape constraints. Moreover, we design three loss functions to jointly optimize GraphSC: an unsupervised reconstruction loss for denoising, a structure preservation loss to retain local topology, and a phenotype-supervised module eigengene significance loss to ensure biological relevance. Experiments on eight TCGA datasets demonstrate that GraphSC outperforms state-of-the-art methods in both clustering quality and biological significance. Interpretability analyses further show that GraphSC identifies topologically diverse GCE modules enriched with cancer-specific functions, suggesting its potential for biomarker discovery in different cancers.