Geometry in Data Science: From Structure to Insight

Anjan Kumar Ojha

Abstract: Geometry—the study of shape, space, and structure—has become a cornerstone of modern data science. By capturing intrinsic relationships in high-dimensional and non-Euclidean datasets, geometric approaches enable deeper understanding of complex structures beyond conventional statistical methods. This paper explores the conceptual foundations of geometry in data science, discusses core methodologies including manifold learning, graph-based modeling, and topological data analysis, and examines applications across machine learning, computer vision, network analysis, and biology. Emphasis is placed on theoretical insights, ethical considerations, and the emerging paradigm of geometric deep learning.