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From: enat@zeus.bris.ac.uk (A. Tocatlidou)
Subject: Re:Seeking help on Similarity Measurement
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Similarity was at first defined/used within the framework of
data analysis and imnterpretation => multidimensional scaling.

Therefore until mid 70s the similarity measures in use
were distance based, more or less variants of Minkowski
metrics.
(As E. Rosch remarked the availability of existing methods
determined to an extend the research path, i.e. similarity
judgement was assumed to obey the metric axioms)

See for example:
R. N. Shepard, The Analysis of Proximities:
 Multidimentional Scaling with an Unknown Distance Function. II.,
 Psychometrika, (27)( 1962,  pp. 210-246.

H. Eisler and E. E. Roskam (1977) "Multidimensional Similarity:
An Experimental and Theoretical Comparison of Vector,
 Distance, and Set Theoretical Models:
II. Multidimensional Analyses: The Subjective Space" ,
 Acta Psychologica, 41,  pp. 335-363.

WW. S. Torgerson (1965) "Multidimensional Scaling of Similarity"
Psychometrika, 30,  pp. 379-393.
In 1977 a paper by Tversky questioned (theoretical and experimentaly)
these metric assumptions
  A. Tversky, Features of Similarity.,
Psychological Review, (84)( 1977,  pp. 327-352.

in which a featural model of similarity was proposed.
Later some "hybrid" models appeared as well (e.g the distance, density
model proposed by Krumhansl in
C. L. Krumhansl (1978) "Concerning the Applicability
of Geometric Models to Similarity Data:
The Interrelationship Between Similarity and Spatial Density" ,
Psychological Review, 85,  pp. 445-463.

The mentioned paper by Goldstone contains in part a reply
to philosophical conscerns and "accusations" against similarity(!!)
by N. Goodman in
N. Goodman,  "Seven Strictures on Similarity",
in Problems and Projects. 1972,
the Bobbs-Merlrill Company, Inc.: p. 437-446.

A similar attempt is in
D. L. Medin, R. L. Goldstone and D. Gentner (1993)
"Respects for Similarity"
Psychological Review, 100,  pp. 254-278.

Some other proposals relate similarity to  structural
mapping (D. Gentner,  "The Mechanisms of Analogical Learning",
 in Similarity and Analogical Reasoning,
S. Vosniadou and A. Ortony, Editors. 1989, Cambridge University Press:
p. 199-241.)


A useful overview of similarity measures is in

E. E. Smith,  "Categorization",
in An Invitation to Cognitive Science: Vol.3 Thinking,
D. N. Osherson and E. E. Smith, Editors. 1990,
The MIT Press: Cambridge, Massachussets. p. 33-53.

and a good collection of papers in

Similarity and Analogical Reasoning,
S. Vosniadou and A. Ortony, Editors. 1989,
 Cambridge University Press

The only comparative analysis and testing of similarity measures
(as far as I am aware, being my area of research )
 is within fuzzy sets theory in 
 
R. Zwick, E. Carlstein and D. V. Budesku (1987)
 "Measures of Similarity Among Fuzzy Concepts:
 A Comparative Analysis"
International Journal of Approximate Reasoning, 1,
  pp. 221-242.


I hope these might help


Athena Tocatlidou
A.I. Group
Dept. of Eng.Maths
University of Bristol
BS8 1UK BRISTOL  ENGLAND
