High Dimensional Data Analysis: An Interpoint Distance Approach

This book presents a rigorous and unified treatment of the analysis of high-dimensional data through the lens of distance-based methodology. It synthesizes recent advances in the field by framing them within a coherent paradigm: proximity-driven, nonparametric approaches for exploration and inference in complex multivariate spaces. Within this framework, interpoint distances serve as fundamental primitives, enabling the reduction of intricate, high-dimensional relationships to analytically tractable one-dimensional representations. Designed for graduate students, advanced undergraduates, and researchers with training in matrix theory and mathematical statistics, the text assumes no prior exposure to high-dimensional techniques. Familiarity with classical multivariate analysis, while not required, will deepen appreciation of the material. The exposition balances theoretical development with practical insight, pairing formal proofs with illustrative examples and providing implementations in the R programming language to support hands-on engagement. Key Features: Incorporates real-world data applications to ground theoretical concepts. More than 180 exercises, with solutions, available on the publisher’s website. Provides accompanying R code for computational exploration.