Topological Machine Learning for Nonlinear Biomarker Space Characterization: A Hybrid TDA-ML Framework for Ovarian Cancer Prediction
Chinmayee Nayak, Alakananda Tripathy, Manoranjan Parhi, Madhuchhanda TripathyIntroduction:
Nonlinear interactions among clinical biomarkers play a significant role in the biological progression of diseases and biomarker evolution.
Objectives:
This study aims to design and evaluate an integrated analytical framework that combines topological data analysis (TDA) with machine learning to identify nonlinear biomarker interactions and improve predictive modeling in ovarian cancer.
Methods:
The dataset comprised 349 patient samples and 47 clinical biomarkers. Persistent homology, Betti numbers, and Mapper graphs were employed to capture the underlying manifold geometry of the data. Topological invariants, such as long-lived H1 loops, were extracted using persistence images and persistence landscapes to generate topological feature embeddings. These embeddings were integrated with standard biochemical features and analyzed using supervised learning models, including Support Vector Machines (SVM), Random Forests (RF), and Multi-Layer Perceptrons (MLP). The proposed hybrid Topological Data Analysis–Machine Learning (TDA-ML) framework demonstrates strong potential for clinical decision-support systems and emerging patent-based medical diagnostic technologies.
Results:
The hybrid TDA-ML model achieved an AUC improvement of 96% compared with rawfeature baseline models, demonstrating the synergistic integration of geometric topology and datadriven learning. Discussion: The hybrid model outperformed the baseline models by effectively capturing nonlinear geometric relationships within the biomarker space.
Discussion:
This study demonstrates that the hybrid TDA-ML framework can reveal nonlinear geometric patterns in biomarker data that are often overlooked by traditional models. Consequently, the proposed hybrid approach provides enhanced feature discriminability and improved predictive performance compared with baseline SVM models.
Conclusion:
These findings highlight the potential of topology-based representations for developing computationally robust, reproducible, and clinically applicable diagnostic modeling frameworks for decision-support systems.