Topic
Multidimensional scaling
About: Multidimensional scaling is a research topic. Over the lifetime, 2541 publications have been published within this topic receiving 106756 citations. The topic is also known as: MDS.
Papers published on a yearly basis
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Papers
TL;DR: The fundamental hypothesis is that dissimilarities and distances are monotonically related, and a quantitative, intuitively satisfying measure of goodness of fit is defined to this hypothesis.
Abstract: Multidimensional scaling is the problem of representingn objects geometrically byn points, so that the interpoint distances correspond in some sense to experimental dissimilarities between objects. In just what sense distances and dissimilarities should correspond has been left rather vague in most approaches, thus leaving these approaches logically incomplete. Our fundamental hypothesis is that dissimilarities and distances are monotonically related. We define a quantitative, intuitively satisfying measure of goodness of fit to this hypothesis. Our technique of multidimensional scaling is to compute that configuration of points which optimizes the goodness of fit. A practical computer program for doing the calculations is described in a companion paper.
7,696 citations
TL;DR: VEGAN adds vegetation analysis functions to the general-purpose statistical program R, and implements several ordination methods, including Canonical Correspondence Analysis and Non-metric Multidimensional Scaling, vector fitting of environmental variables, randomization tests, and various other analyses of vegetation data.
Abstract: VEGAN adds vegetation analysis functions to the general-purpose statistical program R. Both R and VEGAN can be downloaded for free. VEGAN implements several ordination methods, including Canonical Correspondence Analysis and Non-metric Multidimensional Scaling, vector fitting of environmental variables, randomization tests, and various other analyses of vegetation data. It can be used for large data. Graphical output can be customized using the R language's extensive graphics capabilities. VEGAN is appropriate for routine and research use, if you are willing to learn some R. Abbreviation: MDS = Multidimensional Scaling.
5,337 citations
TL;DR: The numerical methods required in the approach to multi-dimensional scaling are described and the rationale of this approach has appeared previously.
Abstract: We describe the numerical methods required in our approach to multi-dimensional scaling. The rationale of this approach has appeared previously.
5,052 citations
TL;DR: In this paper, an individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common "psychological space" and a corresponding method of analyzing similarities data is proposed, involving a generalization of Eckart-Young analysis to decomposition of three-way (or higher-way) tables.
Abstract: An individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common “psychological space”. A corresponding method of analyzing similarities data is proposed, involving a generalization of “Eckart-Young analysis” to decomposition of three-way (or higher-way) tables. In the present case this decomposition is applied to a derived three-way table of scalar products between stimuli for individuals. This analysis yields a stimulus by dimensions coordinate matrix and a subjects by dimensions matrix of weights. This method is illustrated with data on auditory stimuli and on perception of nations.
5,038 citations
TL;DR: The four Purposes of Multidimensional Scaling, Special Solutions, Degeneracies, and Local Minima, and Avoiding Trivial Solutions in Unfolding are explained.
Abstract: Fundamentals of MDS.- The Four Purposes of Multidimensional Scaling.- Constructing MDS Representations.- MDS Models and Measures of Fit.- Three Applications of MDS.- MDS and Facet Theory.- How to Obtain Proximities.- MDS Models and Solving MDS Problems.- Matrix Algebra for MDS.- A Majorization Algorithm for Solving MDS.- Metric and Nonmetric MDS.- Confirmatory MDS.- MDS Fit Measures, Their Relations, and Some Algorithms.- Classical Scaling.- Special Solutions, Degeneracies, and Local Minima.- Unfolding.- Unfolding.- Avoiding Trivial Solutions in Unfolding.- Special Unfolding Models.- MDS Geometry as a Substantive Model.- MDS as a Psychological Model.- Scalar Products and Euclidean Distances.- Euclidean Embeddings.- MDS and Related Methods.- Procrustes Procedures.- Three-Way Procrustean Models.- Three-Way MDS Models.- Modeling Asymmetric Data.- Methods Related to MDS.
4,145 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 37 |
| 2024 | 74 |
| 2023 | 119 |
| 2022 | 154 |
| 2021 | 68 |