Convex optimization as a tool for correcting dissimilarity matrices for regular minimality

Matthias Trendtel; Ali Ünlü

doi:10.1007/978-3-319-00035-0_16

Convex optimization as a tool for correcting dissimilarity matrices for regular minimality

Matthias Trendtel, Ali Ünlü

Chair of Methods in Empirical Educational Research

Innovation and Development of Austrian School System (BIFIE)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Fechnerian scaling as developed by Dzhafarov and Colonius (e.g., Dzhafarov and Colonius, J Math Psychol 51:290-304, 2007) aims at imposing a metric on a set of objects based on their pairwise dissimilarities. A necessary condition for this theory is the law of Regular Minimality (e.g., Dzhafarov EN, Colonius H (2006) Regular minimality: A fundamental law of discrimination. In: Colonius H, Dzhafarov EN (eds) Measurement and representation of sensations. Erlbaum, Mahwah, pp. 1-46 ). In this paper, we solve the problem of correcting a dissimilarity matrix for Regular Minimality by phrasing it as a convex optimization problem in Euclidean metric space. In simulations, we demonstrate the usefulness of this correction procedure.

Original language	English
Title of host publication	Algorithms from and for Nature and Life
Subtitle of host publication	Classification and Data Analysis
Publisher	Kluwer Academic Publishers
Pages	165-174
Number of pages	10
ISBN (Print)	9783319000343
DOIs	https://doi.org/10.1007/978-3-319-00035-0_16
State	Published - 2013
Event	Joint Conf. of the 35th Annual Conf. on German Classification Society, GfKl 2011, 33rd Annual Symposium on German Association for Pattern Recognition, DAGM 2011, and the Symposium of the International Federation of Classification Societies, IFCS 2011 - Frankfurt am Main, Germany Duration: 30 Aug 2011 → 2 Sep 2011

Publication series

Name	Studies in Classification, Data Analysis, and Knowledge Organization
ISSN (Print)	1431-8814

Conference

Conference	Joint Conf. of the 35th Annual Conf. on German Classification Society, GfKl 2011, 33rd Annual Symposium on German Association for Pattern Recognition, DAGM 2011, and the Symposium of the International Federation of Classification Societies, IFCS 2011
Country/Territory	Germany
City	Frankfurt am Main
Period	30/08/11 → 2/09/11

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10.1007/978-3-319-00035-0_16

Cite this

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title = "Convex optimization as a tool for correcting dissimilarity matrices for regular minimality",

abstract = "Fechnerian scaling as developed by Dzhafarov and Colonius (e.g., Dzhafarov and Colonius, J Math Psychol 51:290-304, 2007) aims at imposing a metric on a set of objects based on their pairwise dissimilarities. A necessary condition for this theory is the law of Regular Minimality (e.g., Dzhafarov EN, Colonius H (2006) Regular minimality: A fundamental law of discrimination. In: Colonius H, Dzhafarov EN (eds) Measurement and representation of sensations. Erlbaum, Mahwah, pp. 1-46 ). In this paper, we solve the problem of correcting a dissimilarity matrix for Regular Minimality by phrasing it as a convex optimization problem in Euclidean metric space. In simulations, we demonstrate the usefulness of this correction procedure.",

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series = "Studies in Classification, Data Analysis, and Knowledge Organization",

publisher = "Kluwer Academic Publishers",

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booktitle = "Algorithms from and for Nature and Life",

note = "Joint Conf. of the 35th Annual Conf. on German Classification Society, GfKl 2011, 33rd Annual Symposium on German Association for Pattern Recognition, DAGM 2011, and the Symposium of the International Federation of Classification Societies, IFCS 2011 ; Conference date: 30-08-2011 Through 02-09-2011",

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Trendtel, M & Ünlü, A 2013, Convex optimization as a tool for correcting dissimilarity matrices for regular minimality. in Algorithms from and for Nature and Life: Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization, Kluwer Academic Publishers, pp. 165-174, Joint Conf. of the 35th Annual Conf. on German Classification Society, GfKl 2011, 33rd Annual Symposium on German Association for Pattern Recognition, DAGM 2011, and the Symposium of the International Federation of Classification Societies, IFCS 2011, Frankfurt am Main, Germany, 30/08/11. https://doi.org/10.1007/978-3-319-00035-0_16

Convex optimization as a tool for correcting dissimilarity matrices for regular minimality. / Trendtel, Matthias; Ünlü, Ali.
Algorithms from and for Nature and Life: Classification and Data Analysis. Kluwer Academic Publishers, 2013. p. 165-174 (Studies in Classification, Data Analysis, and Knowledge Organization).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Convex optimization as a tool for correcting dissimilarity matrices for regular minimality

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