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Multidimensional Scaling

By: Joseph B. Kruskal, Myron Wish

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Paperback | 1 January 1978

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96 Pages

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21.59 x 13.97 x 0.58

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Outlines a set of techniques that enable a researcher to discuss the "hidden structure" of large data bases. These techniques use proximities, measures which indicate how similar or different objects are, to find a configuration of points which reflects the structure in the data.

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Non-Fiction Mathematics Probability & Statistics Applied Mathematics Sociology & Anthropology Sociology Social Research & Statistics Reference, Information & Interdisciplinary Subjects Research & Information Research Methods

Editor's Introduction	p. 5
Basic Concepts of Multidimensional Scaling	p. 7
Introduction	p. 7
Some Methods for Obtaining Proximities Data	p. 9
Relationship Between the Proximities and the Spatial Distances	p. 14
Notation and Terminology	p. 16
Different Types of MDS	p. 19
Defining an Objective Function	p. 23
Computational Procedure	p. 27
Looking at the Scatter Diagram	p. 28
Interpretation of the Configuration	p. 30
Application to Perceptions of Nations	p. 30
Linear Regression for Dimensional Interpretation	p. 35
Neighborhood Interpretation of MDS Configurations	p. 43
Embedding Other Information in the MDS Configuration	p. 45
Dimensionality	p. 48
Introduction	p. 48
Goodness-of-Fit	p. 49
Other Considerations Concerning Dimensionality	p. 56
Three-Way Multidimensional Scaling	p. 60
Introduction	p. 60
The INDSCAL Model	p. 61
INDSCAL Analysis of the Nation Similarities Data	p. 63
Fitting the Friendship Ratings into the Similarities Space	p. 69
INDSCAL Analysis of Profile Proximities	p. 70
Preparing the Input for Multidimensional Scaling	p. 73
Preprocessing of Data	p. 73
Metric Versus Nonmetric MDS, and Transformation of the Proximities	p. 76
Some Available Computer Programs for MDS	p. 78
Notes	p. 82
References	p. 83
Some Comments on Multiple Linear Regression	p. 87
Other Uses for Lines and the "Horseshoe" Phenomenon	p. 88
Statistical Guide to Dimensionality	p. 89
Relationship Between MDS Solutions in Different Dimensionalities	p. 92
Determining Meaningful Directions by INDSCAL and by Other Methods	p. 92
Table of Contents provided by Syndetics. All Rights Reserved.

Multidimensional Scaling

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