A topology-based framework for robust cancer-associated gene signature identification from scRNA-seq data.

Cancer transcriptomics faces a fundamental challenge: conventional gene selection methods capture statistical variance but fail to decode the intrinsic geometric architecture of high-dimensional single-cell RNA sequencing data, leaving critical cancer-specific signals obscured by noise and biological heterogeneity. We present a topology-guided framework that harnesses persistent homology to extract structurally invariant, cancer-associated gene signatures from scRNA-seq data - moving beyond gene-level statistics toward shape-aware biological discovery. The framework integrates highly variable feature selection and dimensionality reduction with Vietoris-Rips filtration-based gene correlation topology, followed by a dual-stage stability-driven classification strategy that identifies samples exhibiting reproducible cancer-specific topological patterns. Topologically significant genes are rigorously validated through differential expression analysis, ROC/AUC evaluation, KEGG pathway enrichment, protein-protein interaction network analysis, and literature evidence. Against conventional HVF+PCA-based selection, the TDA framework delivers markedly superior discriminative power, substantially higher literature-supported biological relevance, and dramatically more focused cancer-specific pathway enrichment - while converging to compact, functionally coherent gene sets that conventional approaches cannot achieve. In breast cancer, the framework reveals a dominant mitotic regulatory module centered on cell cycle dysregulation, while colorectal cancer is characterized by extracellular matrix remodeling and tumor microenvironment-driven mechanisms - demonstrating cancer-type-specific biological fidelity. Critically, the framework identifies computationally prioritized novel candidate biomarkers absent from standard pathway databases yet exhibiting topological and statistical significance. This work establishes persistent homology as a transformative paradigm for transcriptomic biomarker discovery, offering a principled, structure-aware foundation for precision oncology and next-generation cancer diagnostics.