Journal ArticleDOI
Modern Multidimensional Scaling: Theory and Applications
TLDR
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.read more
Citations
More filters
Journal ArticleDOI
Representational Similarity Analysis – Connecting the Branches of Systems Neuroscience
TL;DR: A new experimental and data-analytical framework called representational similarity analysis (RSA) is proposed, in which multi-channel measures of neural activity are quantitatively related to each other and to computational theory and behavior by comparing RDMs.
Book
Methods and Data Analysis for Cross-Cultural Research
TL;DR: This comprehensive guide, which covers all major issues in the field, presents cross-cultural methodology in a practical light and discusses the design and analysis of quasi-experiments - the dominant framework for cross- cultural research.
Proceedings ArticleDOI
Localization from mere connectivity
TL;DR: An algorithm that uses connectivity information who is within communications range of whom to derive the locations of the nodes in the network is presented, based on multidimensional scaling, a data analysis technique that takes O(n3) time for a network of n nodes.
Posted Content
Computational Optimal Transport
Gabriel Peyré,Marco Cuturi +1 more
TL;DR: This short book reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications.
Journal ArticleDOI
Random-Walk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation
TL;DR: The model, which nicely fits into the so-called "statistical relational learning" framework, could also be used to compute document or word similarities, and could be applied to machine-learning and pattern-recognition tasks involving a relational database.
References
More filters
Journal ArticleDOI
Analysis of individual differences in multidimensional scaling via an n-way generalization of 'eckart-young' decomposition
J. Douglas Carroll,Jih-Jie Chang +1 more
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.
Introduction to Multidimensional Scaling
TL;DR: This introductory volume covers the design, execution, and analysis of multidimensional scaling experiments and includes detailed descriptions and examples of six major MDS computer programs: MINISSA, POLYCON, KYST, INDSCAL/SINDSCal, ALSCAL and MULTISCALE.
Book
Multidimensional Scaling: History, Theory, and Applications
Forrest W. Young,Robert M. Hamer +1 more
TL;DR: Young as discussed by the authors used the Generalized Euclidian Model to study ideological shifts in the U.S. Senate in the 1970s and 1980s, and applied it to Auditory Pattern Perception.
Journal ArticleDOI
Multidimensional scaling: Combining observations when individuals have different perceptual structures
TL;DR: The authors showed that the usual methods of combining observations to give interpoint distance estimates based on interstimulus differences lead to a distortion of the stimulus configuration unless all individuals in a group perceive the stimuli in perceptual spaces which are essentially the same.
Related Papers (5)
A global geometric framework for nonlinear dimensionality reduction.
Nonlinear dimensionality reduction by locally linear embedding.
Sam T. Roweis,Lawrence K. Saul +1 more