Modern Multidimensional Scaling: Theory and Applications

Modern Multidimensional Scaling: Theory and Applications

2005 | Ingwer Borg, Patrick J.F. Groenen
Modern Multidimensional Scaling (MDS) is a technique for analyzing similarity or dissimilarity data on a set of objects. It models such data as distances among points in a geometric space to provide a graphical display of the data structure, which is easier to understand than numerical arrays. MDS has various forms, distinguished by geometry, mapping functions, algorithms, error handling, and the ability to represent multiple similarity matrices. The book provides a comprehensive overview of MDS, covering its theoretical and practical aspects. It includes 24 chapters divided into five parts, with the first six chapters offering an introduction to MDS, focusing on its four main purposes: data exploration, testing structural hypotheses, discovering psychological dimensions, and modeling similarity judgments. Later chapters delve into specific models, technical aspects, and applications. The book also discusses unfolding, a special case of MDS, and explores various models for asymmetric data. It covers classical scaling, confirmatory MDS, and other advanced topics. The text includes detailed discussions on algorithms, fit measures, and software tools for MDS. The second edition expands on the first, adding new chapters and updating existing content to reflect recent developments in MDS. The book is intended for both theoretical and applied readers, with exercises and examples to aid understanding. It is a comprehensive resource for those interested in MDS, providing both foundational knowledge and advanced techniques.Modern Multidimensional Scaling (MDS) is a technique for analyzing similarity or dissimilarity data on a set of objects. It models such data as distances among points in a geometric space to provide a graphical display of the data structure, which is easier to understand than numerical arrays. MDS has various forms, distinguished by geometry, mapping functions, algorithms, error handling, and the ability to represent multiple similarity matrices. The book provides a comprehensive overview of MDS, covering its theoretical and practical aspects. It includes 24 chapters divided into five parts, with the first six chapters offering an introduction to MDS, focusing on its four main purposes: data exploration, testing structural hypotheses, discovering psychological dimensions, and modeling similarity judgments. Later chapters delve into specific models, technical aspects, and applications. The book also discusses unfolding, a special case of MDS, and explores various models for asymmetric data. It covers classical scaling, confirmatory MDS, and other advanced topics. The text includes detailed discussions on algorithms, fit measures, and software tools for MDS. The second edition expands on the first, adding new chapters and updating existing content to reflect recent developments in MDS. The book is intended for both theoretical and applied readers, with exercises and examples to aid understanding. It is a comprehensive resource for those interested in MDS, providing both foundational knowledge and advanced techniques.
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