Multivariate Data Analysis on Matrix Manifolds

(with Manopt)

Nickolay Trendafilov, Michele Gallo (Autoren)

Buch | Softcover

XX, 450 Seiten

2022 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-76976-5 (ISBN)

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This graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number ofexercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization.

Nickolay T. Trendafilov is Reader of Computational Statistics in the School of Mathematics and Statistics, Open University, UK. He received MSc and PhD in the Department of Mathematics and Informatics, University of Sofia "St. Kl. Ohridski", and then joined the Laboratory of Computational Stochastic, Bulgarian Academy of Sciences. He held research and visiting positions in a number of universities in Belgium, Italy, Japan and USA. His interests are in the computational aspects of multivariate data analysis and interpretation. Other activities include elected memberships in the International Statistical Institute (ISI), the Royal Statistical Society's (RSS) Computing Section, and the Board of Directors, European Regional Section of the International Association for Statistical Computing (IASC).
Michele Gallo is Professor in the Department of Human and Social Sciences at the University of Naples - L'Orientale. He received his PhD degree in Total Quality Management from the University of Naples - Federico II, in 2000. His current research interest is in Multivariate Data Analysis, Compositional and Ordinal Data, Rasch Analysis. He has published more than 90 research articles. He is Associate-Editor of the journal Computational Statistics.

Introduction.- Matrix analysis and differentiation.- Matrix manifolds in MDA.- Principal component analysis (PCA).- Factor analysis (FA).- Procrustes analysis (PA).- Linear discriminant analysis (LDA).- Canonical correlation analysis (CCA).- Common principal components (CPC).- Metric multidimensional scaling (MDS) and related methods.- Data analysis on simplexes.

Erscheinungsdatum	17.09.2022
Reihe/Serie	Springer Series in the Data Sciences
Zusatzinfo	XX, 450 p. 6 illus., 5 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	718 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Constrained optimization of least squares • Data matrix factorizations • Data Science • Estimation of matrix parameters • Likelihood functions • Matrix arguments • Matrix Manifolds • Multivariate Data Analysis • Principal Component Analysis • Sparse multivariate methods
ISBN-10	3-030-76976-3 / 3030769763
ISBN-13	978-3-030-76976-5 / 9783030769765
Zustand	Neuware