The Majorization Approach to Multidimensional Scaling PDF Download

Author: Patrick J. F. Groenen
Publisher:
ISBN:
Category : Inequalities (Mathematics).
Languages : en
Pages : 178

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Author: Ingwer Borg
Publisher: Springer Science & Business Media
ISBN: 1475727119
Category : Mathematics
Languages : en
Pages : 469

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Book Description
Multidimensional scaling (MDS) is a technique for the analysis of similarity or dissimilarity data on a set of objects. Such data may be intercorrelations of test items, ratings of similarity on political candidates, or trade indices for a set of countries. MDS attempts to model such data as distances among points in a geometric space. The main reason for doing this is that one wants a graphical display of the structure of the data, one that is much easier to understand than an array of numbers and, moreover, one that displays the essential information in the data, smoothing out noise. There are numerous varieties of MDS. Some facets for distinguishing among them are the particular type of geometry into which one wants to map the data, the mapping function, the algorithms used to find an optimal data representation, the treatment of statistical error in the models, or the possibility to represent not just one but several similarity matrices at the same time. Other facets relate to the different purposes for which MDS has been used, to various ways of looking at or "interpreting" an MDS representation, or to differences in the data required for the particular models. In this book, we give a fairly comprehensive presentation of MDS. For the reader with applied interests only, the first six chapters of Part I should be sufficient. They explain the basic notions of ordinary MDS, with an emphasis on how MDS can be helpful in answering substantive questions.

Author: Trevor F. Cox
Publisher: CRC Press
ISBN: 9781420036121
Category : Mathematics
Languages : en
Pages : 332

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Book Description
Multidimensional scaling covers a variety of statistical techniques in the area of multivariate data analysis. Geared toward dimensional reduction and graphical representation of data, it arose within the field of the behavioral sciences, but now holds techniques widely used in many disciplines. Multidimensional Scaling, Second Edition extends the popular first edition and brings it up to date. It concisely but comprehensively covers the area, summarizing the mathematical ideas behind the various techniques and illustrating the techniques with real-life examples. A computer disk containing programs and data sets accompanies the book.

Author: J. M. Ortega
Publisher: Elsevier
ISBN: 1483276724
Category : Mathematics
Languages : en
Pages : 593

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Book Description
Computer Science and Applied Mathematics: Iterative Solution of Nonlinear Equations in Several Variables presents a survey of the basic theoretical results about nonlinear equations in n dimensions and analysis of the major iterative methods for their numerical solution. This book discusses the gradient mappings and minimization, contractions and the continuation property, and degree of a mapping. The general iterative and minimization methods, rates of convergence, and one-step stationary and multistep methods are also elaborated. This text likewise covers the contractions and nonlinear majorants, convergence under partial ordering, and convergence of minimization methods. This publication is a good reference for specialists and readers with an extensive functional analysis background.

Author: Ingwer Borg
Publisher: Springer Science & Business Media
ISBN: 3642318487
Category : Computers
Languages : en
Pages : 119

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Book Description
This book introduces MDS as a psychological model and as a data analysis technique for the applied researcher. It also discusses, in detail, how to use two MDS programs, Proxscal (a module of SPSS) and Smacof (an R-package). The book is unique in its orientation on the applied researcher, whose primary interest is in using MDS as a tool to build substantive theories. This is done by emphasizing practical issues (such as evaluating model fit), by presenting ways to enforce theoretical expectations on the MDS solution, and by discussing typical mistakes that MDS users tend to make. The primary audience of this book are psychologists, social scientists, and market researchers. No particular background knowledge is required, beyond a basic knowledge of statistics.

Author: Ingwer Borg
Publisher: Springer
ISBN: 3319734717
Category : Computers
Languages : en
Pages : 128

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Book Description
This book introduces multidimensional scaling (MDS) and unfolding as data analysis techniques for applied researchers. MDS is used for the analysis of proximity data on a set of objects, representing the data as distances between points in a geometric space (usually of two dimensions). Unfolding is a related method that maps preference data (typically evaluative ratings of different persons on a set of objects) as distances between two sets of points (representing the persons and the objects, resp.). This second edition has been completely revised to reflect new developments and the coverage of unfolding has also been substantially expanded. Intended for applied researchers whose main interests are in using these methods as tools for building substantive theories, it discusses numerous applications (classical and recent), highlights practical issues (such as evaluating model fit), presents ways to enforce theoretical expectations for the scaling solutions, and addresses the typical mistakes that MDS/unfolding users tend to make. Further, it shows how MDS and unfolding can be used in practical research work, primarily by using the smacof package in the R environment but also Proxscal in SPSS. It is a valuable resource for psychologists, social scientists, and market researchers, with a basic understanding of multivariate statistics (such as multiple regression and factor analysis).

Author: Gérard Govaert
Publisher: John Wiley & Sons
ISBN: 111861786X
Category : Mathematics
Languages : en
Pages : 265

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Book Description
The first part of this book is devoted to methods seeking relevant dimensions of data. The variables thus obtained provide a synthetic description which often results in a graphical representation of the data. After a general presentation of the discriminating analysis, the second part is devoted to clustering methods which constitute another method, often complementary to the methods described in the first part, to synthesize and to analyze the data. The book concludes by examining the links existing between data mining and data analysis.

Author: Hans-Hermann Bock
Publisher: Springer Science & Business Media
ISBN: 364246808X
Category : Business & Economics
Languages : en
Pages : 475

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Proceedings of the 17th Annual Conference of the Gesellschaft für Klassifikation e.V., University of Kaiserslautern, March 3 - 5, 1993

Author: Edwin Diday
Publisher: Springer Science & Business Media
ISBN: 3642511759
Category : Business & Economics
Languages : en
Pages : 695

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Book Description
The subject of this book is the analysis and processing of structural or quantitative data with emphasis on classification methods, new algorithms as well as applications in various fields related to data analysis and classification. The book presents the state of the art in world-wide research and application of methods from the fields indicated above and consists of survey papers as well as research papers.

Author: Wolfgang A. Gaul
Publisher: Springer Science & Business Media
ISBN: 364279999X
Category : Mathematics
Languages : en
Pages : 472

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Book Description
The subject of this book is the incorporation and integration of mathematical and statistical techniques and information science topics into the field of classification, data analysis, and knowledge organization. Readers will find survey papers as well as research papers and reports on newest results. The papers are a combination of theoretical issues and applications in special fields: Spatial Data Analysis, Economics, Medicine, Biology, and Linguistics.