A Systematic Review of Computational geometry algorithms for high-dimensional clustering analysis: Methods, Architectures, and Future Research Directions

Abstract

High-dimensional clustering has emerged as a critical challenge in modern data-driven systems, where traditional distance-based methods suffer from the curse of dimensionality and reduced discriminative power. Computational geometry provides a rigorous mathematical foundation for addressing these challenges through geometric structures, spatial partitioning, and efficient proximity search mechanisms. This paper presents a systematic review of computational geometry algorithms applied to high-dimensional clustering analysis, focusing on methods, architectures, and emerging research directions. The study synthesizes recent advances from 2018 to 2025, highlighting geometric indexing structures, approximate nearest neighbor search, manifold-aware clustering, and hybrid AI-driven approaches. The findings reveal a clear evolution from classical geometric constructs such as Voronoi diagrams and k-d trees toward scalable, probabilistic, and learning-augmented frameworks. Key contributions of this review include a unified analysis of algorithmic design principles, identification of scalability and robustness trade-offs, and the exploration of integration pathways with modern software engineering and AI ecosystems. The paper also outlines future directions emphasizing adaptive geometry-aware learning, distributed clustering architectures, and security-aware data clustering frameworks.