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Geometric Models of Similarity

Johannesson, Mikael LU (2002) In Lund University Cognitive Studies 90.
Abstract
This dissertation examines and discusses some phenomena related to the geometric representation of similarity. It takes its inspiration from the existing body of empirical research within the fields of perceptual and cognitive psychology, but also connects to certain areas of machine learning.



The problems discussed concern the modelling of information integration behavior when concepts like asymmetry, integrality, separability and familiarity are taken into account. The dissertation investigates how these phenomena can be modelled using geometric representations in order to increase the descriptive power of the models.



The main conclusions that can be drawn from this dissertation are that the... (More)
This dissertation examines and discusses some phenomena related to the geometric representation of similarity. It takes its inspiration from the existing body of empirical research within the fields of perceptual and cognitive psychology, but also connects to certain areas of machine learning.



The problems discussed concern the modelling of information integration behavior when concepts like asymmetry, integrality, separability and familiarity are taken into account. The dissertation investigates how these phenomena can be modelled using geometric representations in order to increase the descriptive power of the models.



The main conclusions that can be drawn from this dissertation are that the descriptive powers of geometric models can be increased in a number of ways: a) By augmenting traditional geometric models with parameters of prominence they can reflect asymmetric similarity at least as well as previously known asymmetric models which include more parameters. b) Some specific metric, for instance, the Euclidean metric, should not be used merely by tradition. If there is reason to believe that there are groupings of dimensions such that the most descriptive metric differs between groups, the distance may be better described with a combination rule adding the contribution of each group/subspace together. c) Aspects of familiarity with stimuli should be taken into consideration, even for familiarity built up during a short period of time. When taking familiarity into consideration it may be possible to describe information integration over time with a finer granularity. Furthermore, by focusing on the part of the phenomenological data that reflect a more stable behavior, which seems to occur first when subjects are sufficiently familiar with the stimuli, the more stable behavior can be more accurately described. (Less)
Abstract (Swedish)
Popular Abstract in Swedish

Även om vi kanske inte tänker på det så ofta så är vår förmåga att bedöma likhet av stor vikt, inte minst då det gäller begreppsbildning och generalisering.



Denna avhandling handlar om likhet, speciellt geometriska modeller av likhet. I sådana modeller representeras objekt som punkter i abstrakta rum, och likhet svarar (omvänt) mot avstånd i rummen.



Avhandlingen tar upp två av de problem geometriska modeller har vad gäller att beskriva människors sätt att bedöma likhet. Ett representativt exempel på det första problemet är att man har funnit att människor ofta bedömer Mexiko som mer likt USA än tvärtom. Det här problemet rör hur likhet kan modelleras... (More)
Popular Abstract in Swedish

Även om vi kanske inte tänker på det så ofta så är vår förmåga att bedöma likhet av stor vikt, inte minst då det gäller begreppsbildning och generalisering.



Denna avhandling handlar om likhet, speciellt geometriska modeller av likhet. I sådana modeller representeras objekt som punkter i abstrakta rum, och likhet svarar (omvänt) mot avstånd i rummen.



Avhandlingen tar upp två av de problem geometriska modeller har vad gäller att beskriva människors sätt att bedöma likhet. Ett representativt exempel på det första problemet är att man har funnit att människor ofta bedömer Mexiko som mer likt USA än tvärtom. Det här problemet rör hur likhet kan modelleras geometriskt men ändå vara asymmetrisk, dvs det faktum att likhet mellan två objekt inte bara beror på de aspekter i vilka objekten är jämförbara, utan också på riktningen av jämförelsen. Eftersom likhet svarar mot avstånd i geometriska modeller är det inte trivialt att modellera asymmetri: avståndet mellan två punkter definieras normalt som detsamma oavsett riktningen.



Det andra problemet rör hur vi integrerar information utifrån olika aspekter till ett enda mått och hur detta kan beskrivas med hjälp av geometriska modeller. Ett exempel skulle kunna vara hur vi jämför äpplen och apelsiner. Äpplen och apelsiner är jämförbara på ett antal olika sätt. De har, exempelvis, båda form, färg, yta och smak. Något förenklat skulle processen att bedöma likheten mellan ett äpple och en apelsin kunna beskrivas som att betraktaren först jämför dem med avseende på de egenskaper som känns relevanta och därefter att resultaten av jämförelserna slås samman till ett resultat.



Ett sätt att bygga en geometrisk modell över mänsklig likhetsbedömning skulle kunna vara att definiera operationer (liknande den som beskrevs ovan) som "arbetar på" den geometriska representationen. Ett problem i sammanhanget är dock att ingen vet hur sammanslagningen av information egentligen går till, åtminstone inte då fler än två egenskaper är involverade.



Utöver de två problemen diskuteras också en fråga som berör det andra problemet, nämligen hur ökad erfarenhet verkar påverka sammanslagningen av information. Avhandlingen visar - hur geometriska modeller kan reflektera asymmetrisk likhet - baserat på empiri, hur sammanslagning av information då det gäller fler än två egenskaper kan hanteras i geometriska modeller - att, och hur, "familjariteten" som byggts upp under kort tid verkar påverka sammanslagningen av information. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Michalski, Ryszard
organization
publishing date
type
Thesis
publication status
published
subject
keywords
symmetry, similarity, separable dimensions, prominence, multidimensional scaling, Minkowski metric, machine learning, integral dimensions, familiarity, geometric models, distance metric, asymmetry, conceptual spaces, Computer science, numerical analysis, systems, control, Datalogi, numerisk analys, system, kontroll, Geometry, algebraic topology, Geometri, algebraisk topologi
in
Lund University Cognitive Studies
volume
90
pages
171 pages
publisher
Department of Computer Science, Lund University
defense location
Sal 104, Kungshuset
defense date
2002-05-29 10:00:00
external identifiers
  • other:ISRN: LUHFDA/HFKO-1009-SE
ISSN
1101-8453
ISBN
91-628-5197-7
language
English
LU publication?
yes
id
0809d7d6-f0c4-46e6-b69e-f2a4412b0583 (old id 20807)
date added to LUP
2016-04-01 16:13:36
date last changed
2019-05-21 20:40:20
@phdthesis{0809d7d6-f0c4-46e6-b69e-f2a4412b0583,
  abstract     = {{This dissertation examines and discusses some phenomena related to the geometric representation of similarity. It takes its inspiration from the existing body of empirical research within the fields of perceptual and cognitive psychology, but also connects to certain areas of machine learning.<br/><br>
<br/><br>
The problems discussed concern the modelling of information integration behavior when concepts like asymmetry, integrality, separability and familiarity are taken into account. The dissertation investigates how these phenomena can be modelled using geometric representations in order to increase the descriptive power of the models.<br/><br>
<br/><br>
The main conclusions that can be drawn from this dissertation are that the descriptive powers of geometric models can be increased in a number of ways: a) By augmenting traditional geometric models with parameters of prominence they can reflect asymmetric similarity at least as well as previously known asymmetric models which include more parameters. b) Some specific metric, for instance, the Euclidean metric, should not be used merely by tradition. If there is reason to believe that there are groupings of dimensions such that the most descriptive metric differs between groups, the distance may be better described with a combination rule adding the contribution of each group/subspace together. c) Aspects of familiarity with stimuli should be taken into consideration, even for familiarity built up during a short period of time. When taking familiarity into consideration it may be possible to describe information integration over time with a finer granularity. Furthermore, by focusing on the part of the phenomenological data that reflect a more stable behavior, which seems to occur first when subjects are sufficiently familiar with the stimuli, the more stable behavior can be more accurately described.}},
  author       = {{Johannesson, Mikael}},
  isbn         = {{91-628-5197-7}},
  issn         = {{1101-8453}},
  keywords     = {{symmetry; similarity; separable dimensions; prominence; multidimensional scaling; Minkowski metric; machine learning; integral dimensions; familiarity; geometric models; distance metric; asymmetry; conceptual spaces; Computer science; numerical analysis; systems; control; Datalogi; numerisk analys; system; kontroll; Geometry; algebraic topology; Geometri; algebraisk topologi}},
  language     = {{eng}},
  publisher    = {{Department of Computer Science, Lund University}},
  school       = {{Lund University}},
  series       = {{Lund University Cognitive Studies}},
  title        = {{Geometric Models of Similarity}},
  volume       = {{90}},
  year         = {{2002}},
}