Geometric-structural multi-label learning for non-invasive prediction of breast cancer biomarkers

Accurate profiling of molecular biomarkers, including ER, PR, HER2, and Ki-67, is pivotal for tailoring therapeutic strategies in breast cancer management. However, conventional determination relies on invasive tissue biopsies, which are costly, time-consuming, and often limited by intratumoral heterogeneity. To address these challenges, this study proposes a non-invasive framework termed Geometric-Structural Multi-Label Learning (GSMLL) for predicting biomarker profiles using routine hematological and clinical features. Central to our approach is the Manifold-Regularized Ensemble of Classifier Chains (M-ECC) algorithm, which synergistically models high-order biological correlations among biomarkers while preserving the intrinsic geometric structure of the patient data via graph Laplacian regularization. Notably, the proposed framework admits a closed-form solution, ensuring a globally optimal solution under convexity assumption and computational efficiency, in contrast to iterative deep learning approaches. Comprehensive experiments on a clinical cohort of 151 patients demonstrate that M-ECC significantly outperforms state-of-the-art baselines, achieving an Average Precision of 0.9416 and a Ranking Loss of 0.1176. These findings suggest that the proposed geometrically aware ensemble framework offers a reliable and cost-effective pathway for developing liquid-biopsy-based decision support systems in oncology.