Multivariate data analysis on matrix manifolds (with Manopt) /

Multivariate data analysis on matrix manifolds (with Manopt) /

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Bibliographic Details
Author / Creator:	Trendafilov, N.T. (Nickolay T.), author.
Imprint:	Cham : Springer, [2021] ©2021
Description:	1 online resource : illustrations (chiefly color).
Language:	English
Series:	Springer series in the data sciences, 2365-5682 Springer series in the data sciences.
Subject:	Multivariate analysis. Multivariate analysis -- Computer programs. Manifolds (Mathematics) Manifolds (Mathematics) Multivariate analysis. Multivariate analysis -- Computer programs. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12659839

Hidden Bibliographic Details
Other authors / contributors:	Gallo, Michele, author.
ISBN:	9783030769741 3030769747 9783030769734 3030769739
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed September 27, 2021).
Summary:	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 of exercises 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. .
Other form:	Original 3030769739 9783030769734
Standard no.:	10.1007/978-3-030-76974-1

Table of Contents:

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.