Topological Methods in Data Analysis: Applications in Machine Learning

Abstract

Topological methods offer powerful tools for analyzing complex and high-dimensional datasets, providing insights into their underlying structure and relationships. the applications of topological methods in data analysis, with a focus on their relevance to machine learning tasks. We begin by introducing key concepts from algebraic topology, such as simplicial complexes, homology, and persistent homology, and discuss how these concepts can be applied to represent and analyze data.various applications of topological methods in machine learning, including dimensionality reduction, clustering, classification, and anomaly detection. By leveraging topological descriptors such as persistent homology, researchers can capture important features of the data that are not easily detected by traditional methods. We illustrate these concepts with real-world examples and demonstrate their effectiveness in uncovering hidden structures and patterns in diverse datasets.