Asian Journal of Pure and Applied Mathematics

The Integration of Topological Data Analysis (TDA) with Learning (ML) algorithms provides a welcoming approach for the improvement of feature representation and predictive performance. TDA applies concepts from algebraic topology, specifically persistent homology, to capture the intrinsic shape and connectivity of complex datasets, producing noise-resistant and invariant features. This study reviews core TDA methods, examines their data descriptors, and evaluates their strengths and limitations in comparison with traditional approaches. A structured methodology is developed, encompassing step-by-step TDA feature extraction, ML model selection, and a unified integration workflows. Using both synthetic and real-world datasets, performance is assessed for TDA only, ML only, and integrated TDA–ML pipelines. Implementations are carried out in Python, with models compared on accuracy and computational efficiency. Finally, Results show that TDA–ML integration often outperforms traditional ML, particularly in high-dimensional or noisy environments where topological structure is informative. While computational complexity and parameter sensitivity pose challenges, the Integration of TDA with ML algorithms offers a reproducible framework for practical applications in domains such as bioinformatics, image recognition, and network analysis.Using synthetic datasets generated with known geometric and topological structures, TDA, specifically Persistent Homology  was applied to extract shape-based features, which were then combined with standard ML features for training Support Vector Machines (SVM), Random Forests (RF), and K-Nearest Neighbour (K-NN) models. The study showed that models augmented with TDA features significantly outperformed those relying solely on geometric data. Accuracy improved from 0.79 to 0.95, with similar gains in precision, recall, and F1-score. This confirmed that TDA captures structural patterns missed by conventional feature engineering, thereby enabling more effective and interpretable machine learning models.