High Dimensional Data Analysis

An Interpoint Distance Approach
1. Auflage 2026
ISBN: 978-1-041-32194-1
Verlag: Taylor & Francis Ltd

Buch, Englisch, 696 Seiten, Format (B × H): 178 mm x 254 mm

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.

Zielgruppe

Academic

Autoren/Hrsg.

Modarres, Reza

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Author Glossary of Symbols 1 Introduction 2 Interpoint Distances 3 High Dimensional Dissimilarity Indices 4 High Dimensional Graphics 5 Testing the Equality of High Dimensional Distributions 6 High Dimensional Classification of Categorical Data 7 IPD of Multivariate Power Series Distributions 8 General Notation of Data Depth 9 Hotelling T 2 Test and Wilks Outlier Method 10 High Dimensional Outlier Detection Methods 11 High Dimensional Tests of Independence 12 High Dimensional Change Point Detection Methods 13 High Dimensional Clustering Methods 14 Analysis of Distance Matrices 15 Testing Multivariate Symmetry Bibliography Index

Über Autor(innen)

Prof. Reza Modarres graduated from the American University with a B.S. in Mathematics and Computer Science. He later earned an M.S. in Computer Science and a Ph.D. in Statistics from the American University. His thesis focused on the analysis of correlation matrices. Upon graduation, Dr. Modarres worked as a post-doctoral fellow before joining George Washington University. Dr. Modarres is an elected member of the International Statistical Institute and has published more than 100 research articles on Statistics, Computer Science, and their interface. His research includes high-dimensional analysis, statistical computing, multivariate nonparametric analysis, and environmental statistics.