Direction-Driven Feature Engineering for Low-Data BiologicalClassification

We present Topology-Driven Directed Flow (TDDF), a practical feature engineering method for biological classification in low-data regimes. Inspired by the metaphor of water flowing through a straw leaning toward a fixed destination, TDDFextracts three interpretable features from high-dimensional biological space (1) flow coordinate along a learned direction field, (2) shape feature capturing local geometric deviations, and (3) topology feature encoding neighborhood structure. TDDFis a synthesis of established techniques (Fishers LDA, residual analysis, local density estimation) applied with biological insight. Applied to TCGA breast cancer data, TDDFachieved 0.992 AUC (95% CI: [0.988, 0.997], p-value= 0.001) in distinguishing tumor from normal tissue--significantly outperforming raw features (0.985 AUC) and PCA (0.980 AUC). The learned direction field automatically identified known luminal breast cancer genes (ESR1: r = 0.876, p-value{inverted exclamation} 0.001; GATA3: r = 0.823, p-value{inverted exclamation} 0.001). Most critically, TDDFdemonstrated superior performance in low-data regimes, achieving 0.852 AUC with only 50 training samples compared to 0.783 for XGBoost. Code and full statistical validation are available at https://github.com/ubaidqurashi1/topologydriven.