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Convex Optimization as a Tool for Correcting Dissimilarity Matrices for Regular Minimality

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Algorithms from and for Nature and Life

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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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Acknowledgements

We are deeply indebted to Professor Ehtibar N. Dzhafarov for introducing us to this topic.

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Authors and Affiliations

  1. Division for Methodology and Statistics, Federal Institute for Educational Research, Innovation & Development of the Austrian School System (BIFIE), Salzburg, Austria

    Matthias Trendtel

  2. Chair for Methods in Empirical Educational Research, TUM School of Education, Technische Universität München, München, Germany

    Ali Ünlü

Authors
  1. Matthias Trendtel
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  2. Ali Ünlü
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Corresponding author

Correspondence to Matthias Trendtel .

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Editors and Affiliations

  1. University of Essex Department of Mathematical Sciences, Colchester, United Kingdom

    Berthold Lausen

  2. Ghent University Department of Marketing, Ghent, Belgium

    Dirk Van den Poel

  3. University of Marburg Databionics, FB 12, Marburg, Germany

    Alfred Ultsch

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© 2013 Springer International Publishing Switzerland

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Trendtel, M., Ünlü, A. (2013). Convex Optimization as a Tool for Correcting Dissimilarity Matrices for Regular Minimality. In: Lausen, B., Van den Poel, D., Ultsch, A. (eds) Algorithms from and for Nature and Life. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-00035-0_16

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