Applications of Topological Data Analysis in Machine Learning Algorithms

Abstract

Topology-based techniques have proven useful to provide meaningful structural information from complex and high dimensional data, and to support machine learning techniques in new ways. Topological Data Analysis (TDA) is a mathematical method that aims to capture the underlying shape, connectivity, and geometry of data that are not captured by traditional statistical or computational methods. The paper reviews the uses of TDA in machine learning algorithms and how TDA has been used to enhance data representation, feature extraction, dimensionality reduction, clustering, classification, anomaly detection, and predictive modelling. The study follows a comprehensive review methodology where the literature, theory and practical applications of recent studies in various fields like healthcare, finance, image processing, cyber-security, bioinformatics and social network analysis are analyzed. The review elucidates the complementarity between the use of tools like persistent homology, simplicial complexes, Mapper algorithms, and persistence diagrams to traditional machine learning models, which they are able to capture some robust topological properties that are stable even in the presence of noisy data. The results show that the proposed approach of combining topological information along with supervised and unsupervised learning algorithms contributes to the interpretability of the model, prediction accuracy and robustness against data variability. However, the computational complexity, parameter selection, scalability and lack of topologic methods awareness are still blocking the popularization of this technology. Finally, the paper argues that TDA is a promising interdisciplinary technique that can overcome some of the drawbacks of traditional machine learning techniques, especially when dealing with complex, high-dimensional data. Further, future work should go into the development of scalable computational frameworks, making more software accessible, and adopting topological methods combined with new AI models to inform and assist more efficient, explainable, and robust machine learning systems.