Multidimensional scaling forn‐tuples
作者:
Trevor F. Cox,
Michael A. A. Cox,
Joao A. Branco,
期刊:
British Journal of Mathematical and Statistical Psychology
(WILEY Available online 1991)
卷期:
Volume 44,
issue 1
页码: 195-206
ISSN:0007-1102
年代: 1991
DOI:10.1111/j.2044-8317.1991.tb00955.x
出版商: Blackwell Publishing Ltd
数据来源: WILEY
摘要:
Wide use has been made of multidimensional scaling (MDS) techniques since the pioneering papers of Shepard and Kruskal. In the main, dissimilarities used in the various MDS techniques are derived for pairs of objects or stimuli. This is termed 2‐way, 1‐mode data, meaning pairs of objects within a single set are considered. Some MDS techniques are designed for 3‐way or even higher, and for 2‐mode, 3‐mode or more. One such example is the CANDECOMP model which can deal withn‐way,m‐mode data where 3≤n≤7 and 2≤m≤7. This model considersn‐tuples of objects at a time, selecting these from m different sets.To date there are no models which considern‐way, 1‐mode data, where n≥3. An attempt is made in this paper to cater for this situation by an extension of the Shepard‐Kruskal approach to non‐metric multidimensional scaling which deals with dissimilarities defined for three or more objects. A computer program has been written using the new model to produce a configuration in Euclidean space to represent the objects. Some historical voting data and some
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