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Differential Ordering of Objects and Attributes

Published online by Cambridge University Press:  01 January 2025

J. P. Sutcliffe
J. P. Sutcliffe*
Affiliation:
University of Sydney
*
Requests for reprints should be sent to J. P. Sutcliffe, Department of Psychology, University of Sydney, Sydney, 2006, N.S.W., AUSTRALIA.
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Abstract

By reference to nominated attributes, a genus, being a population of objects of one specified kind, may be partitioned into species, being subpopulations of different kinds. A prototype is an object representative of its species within the genus. Using this framework, the paper describes how objects can be relatively differentiated with respect to attributes, and how attributes can be relatively differentiating with respect to objects. Methods and rationale for such differential ordering of objects and attributes are presented by example, formal development, and application.

For a genus Ω comprising n species of object there is a subset P ofn distinct prototypes. With respect to m nominated attributes, each object in Ω has an m-element characterization. Together these determine an n × m objects × attributes matrix, the rows of which are the characterizations of the prototypical objects. Over then species in Ω, an associated relative frequency vector gives the distribution of objects (and of their characterizations). The matrix and vector associate the objects in Ω with points in a metric space (P, δ); and it is with respect to various sums of distances in this attribute space that one can differentially order objects and attributes.

The definition of the distance function δ is generalized across kinds of difference, types of characterization, scale-types of measurement, Minkowski index ≧ 1, and any form of distribution of objects over species. Explanatory and taxonomic applications in psychology and other fields are discussed, with focus on classification, identification, recognition, and search. The Braille code and the identification of its characters provide illustration.

Keywords

numerical taxonomyinformation storage and retrievalclassificationidentificationrecognitionsearchgenusspeciesprototypeobject × attribute matrixdatumMinkowski metricdistancesimilaritydifferentiationdistinguishing featuretreekeyBraille
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 2 , June 1986 , pp. 209 - 240
Copyright
Copyright © 1986 The Psychometric Society

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Footnotes

An anticipation and some preliminary indications were given in Sutcliffe and Bristow (1966), Sutcliffe (1972, 1973), and Nowakowska (1975). Subsequently the ideas have been extended and their applications realized in a computer program which, in its development, has so far gone through many minor and three major revisions to its present form in Sutcliffe (1985). The foregoing provided the foundation for the empirical applications and for the presentation in this paper of the ideas in their general form. the research has been supported by funds from the University of Sydney Research Grant and from the Australian Research Grants Scheme. In the working out and exposition of the ideas I have very much benefited from constructive critical comment given by C. R. Latimer, J. B. Michell, G. Oliphant, and E. Seneta, and from the professional programming skills of Michael Wilson and David Shillito. I am grateful for the invitation and the facilities for writing extended during 1983 by Georges Noizet, Laboratoire de Psychologie Expérimentale, Université René Descartes, Paris V, and by Samuel Messick, Vice President for Research, E.T.S. Princeton, N.J. Finally, I acknowledge the improvements in presentation of this paper which have arisen from the editor's and reviewers' comments.

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