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Ordinal Network Representation: Representing Proximities by Graphs

Published online by Cambridge University Press:  01 January 2025

Karl Christoph Klauer
Karl Christoph Klauer*
Affiliation:
Freie Universitat Berlin
*
Requests for reprints should be sent to K. Christoph Klauer, FU Berlin, Institut für Psychologie, Habelschwerdter Allee 45, 1000 Berlin 33, FRG.
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Abstract

Ordinal network representations are graph-theoretic representations of proximity data. They seek to provide parsimonious representations of the ordinal (nonmetric) information in observed proximity data by means of the minimum-path-length distance of a connected and weighted graph. In contrast to traditional tree-based graph-theoretic approaches, ordinal network representation is not limited to but includes the representation by trees. Asymmetry in the proximity data and violations of zero-minimality are allowed for. The paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations. A simple strategy for handling the problem of errors in the data is described and illustrated.

Keywords

proximitygraph-theoretic representationaddtreesextended similarity treeshierarchical clustering
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 4 , December 1989 , pp. 737 - 750
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

This work was supported by grant Fe 75/20-2 of the Deutsche Forschungsgemeinschaft. The author is indebted to Hubert Feger for many inspiring discussions.

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