Modern multidimensional scaling: theory and applications
type: Item
instance of: scholarly article
title: Modern multidimensional scaling: theory and applications
zbMATH Open document ID: 0862.62052
author: Ingwer Borg
author: Patrick J. F. Groenen
published in: Springer Series in Statistics
publication date: 1997-02-18T00:00:00Z
review text: This book provides a comprehensive presentation of multidimensional scaling (MDS), a statistical technique for the analysis of similarity or dissimilarity data on a set of objects in multidimensional scale. MDS attempts to model data as distances among points in a geometric space of low dimensionality, which makes the data structure easier to understand than an array of numbers. The contents of the book are divided into five parts. Part I is sufficient for readers with applied interests only. It explains the basic notions of ordinary MDS and deals with some special models that are important in particular applications of MDS. Part II discusses technical aspects of MDS (matrix algebra for MDS, majorization algorithm for solving MDS problems, ordinal transformations of similiarity data, fit measures, classical scaling). Part III introduces the idea of unfolding and some variants of this model. Part IV treats the geometry of MDS as a substantive model (MDS as a psychological model, scalar products, mapping proximities into Euclidean distances). The last part, Part V, discusses some methods and models closely related to MDS (principal components analysis, models for asymmetric data, correspondence analysis). The first six chapters of Part I make up a complete introductory course to MDS that assumes only elementary knowledge of descriptive statistics. The book is also suited for various advanced courses on MDS oriented either to data analysis or to the psychology of similarity.
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 91C15
Mathematics Subject Classification ID: 62-01
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62P15
zbMATH DE Number: 979008
zbMATH Keywords: matrix algebra
zbMATH Keywords: principal components analysis
zbMATH Keywords: multidimensional scaling
zbMATH Keywords: MDS
zbMATH Keywords: majorization algorithm
zbMATH Keywords: ordinal transformations of similiarity data
zbMATH Keywords: fit measures
zbMATH Keywords: unfolding
zbMATH Keywords: psychological model
zbMATH Keywords: asymmetric data
zbMATH Keywords: correspondence analysis
reviewed by: Ivan Křivý
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 979008