Multivariate Data Analysis on Matrix Manifolds: (with Manopt)

This textbook provides a unified presentation and solution of multivariate data analysis (MDA) techniques, treating them as optimization problems on matrix manifolds. It includes examples, Manopt codes, and software guides for direct application and problem-solving. Suitable for computational statistics, data analysis, data mining, and optimization.

Format: Hardback
Length: 450 pages
Publication date: 16 September 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook, designed for advanced students, offers a unified presentation and comprehensive solution of various commonly employed techniques for multivariate data analysis (MDA). Unlike similar texts, it treats MDA problems as optimization challenges on matrix manifolds defined by the MDA model parameters, enabling their efficient resolution through the use of free optimization software, Manopt. The book is enriched with numerous in-text examples, along with Manopt codes and software guides, which serve as practical tools for applying these techniques or as templates for solving similar and novel problems.

In the first two chapters, an overview and essential background are provided, covering the fundamental concepts and notations necessary for studying MDA. Subsequently, several sets of matrices commonly used in MDA are explored, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt completes the prerequisite knowledge for MDA.

The remaining chapters delve into individual MDA techniques in depth, providing comprehensive explanations and detailed examples. Each chapter includes a substantial number of exercises, complementing the main text with additional information and occasionally involving open and challenging research questions. This textbook is suitable for students and researchers in computational statistics, data analysis, data mining, data science, theoretical computer science, machine learning, and optimization. It is assumed that readers have a foundational understanding of MDA and some experience with matrix analysis, computing, and optimization.

Weight: 920g
Dimension: 163 x 241 x 29 (mm)
ISBN-13: 9783030769734
Edition number: 1st ed. 2021