TDA in Machine Learning: Methods, Applications and Future Directions

Topological Data Analysis (TDA) offers a robust framework for enhancing machine learning (ML) through shape-aware, multiscale, and noise-resistant techniques. This paper examines important TDA techniques, including Mapper, Wasserstein, and persistent homology, and how they can be used to machine learning tasks including time-series analysis, anomaly detection, and classification. We showcase new developments such as explainability tools, topological regularization, and TDA-based neural layers, showcasing their efficacy in domains like computer vision, finance, and bioinformatics. Additionally, the study describes new directions such as benchmarking frameworks, quantum-TDA, and topology-guided AutoML. Through the integration of abstract topology and practical data issues, TDA is positioned to emerge as a fundamental element of interpretable and robust AI systems.