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

  • Matthias Trendtel
  • Ali Ünlü
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


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.



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


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Division for Methodology and Statistics, Federal Institute for Educational ResearchInnovation & Development of the Austrian School System (BIFIE)SalzburgAustria
  2. 2.Chair for Methods in Empirical Educational Research, TUM School of EducationTechnische Universität MünchenMünchenGermany

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