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Size and Power of Multivariate Outlier Detection Rules Read chapter Read first chapter

2013 | OriginalPaper | Chapter

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

Authors : Matthias Trendtel, Ali Ünlü

Published in: Algorithms from and for Nature and Life

Publisher: Springer International Publishing

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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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previous chapter Properties of a General Measure of Configuration Agreement
next chapter Principal Components Analysis for a Gaussian Mixture
Literature
Boyd, S., & Vandenberghe, L. (2009). Convex optimization. New York: Cambridge University Press.
Dattorro, J. (2009). Convex optimization & euclidean distance geometry. Palo Alto: Meboo.
Dzhafarov, E. N. (2002). Multidimensional Fechnerian scaling: pairwise comparisons, regular minimality, and nonconstant self-similarity. Journal of Mathematical Psychology, 46, 583–608.MathSciNetMATHCrossRef
Dzhafarov, E. N., & Colonius, H. (2006a). Reconstructing distances among objects from their discriminability. Psychometrika, 71, 365–386.MathSciNetCrossRef
Dzhafarov, E. N., & Colonius, H. (2006b). Regular minimality: a fundamental law of discrimination. In: H. Colonius & E. N. Dzhafarov (Eds.), Measurement and representation of sensations (pp. 1–46). Mahwah: Erlbaum.
Dzhafarov, E. N., & Colonius, H. (2007). Dissimilarity cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290–304.MathSciNetMATHCrossRef
Dzhafarov, E. N., Ünlü, A., Trendtel, M., & Colonius, H. (2011). Matrices with a given number of violations of regular minimality. Journal of Mathematical Psychology, 55, 240–250.MathSciNetMATHCrossRef
Ekeland, I., & Temam, R. (1999). Convex analysis and variational problems. Philadelphia: SIAM.MATHCrossRef
Goldfarb, D., & Idnani, A. (1983). A numerically stable dual method for solving strictly convex quadratic programs. Mathematical Programming, 27, 1–33MathSciNetMATHCrossRef
Hiriart-Urruty, J., & Lemaréchal, C. (2001). Fundamentals of convex analysis. Berlin: Springer.MATHCrossRef
Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling. Beverly Hills: Sage.
Roberts, A. W., & Varberg, D. E. (1973). Convex functions. New York: Academic.MATH
Trendtel, M., Ünlü, A., & Dzhafarov, E. N. (2010). Matrices satisfying Regular Minimality. Frontiers in Quantitative Psychology and Measurement, 1, 1–6.
Ünlü, A., & Trendtel, M. (2010). Testing for regular minimality. In A. Bastianelli & G. Vidotto (Eds.), Fechner Day 2010 (pp. 51–56). Padua: The International Society for Psychophysics.
Metadata
Title
Convex Optimization as a Tool for Correcting Dissimilarity Matrices for Regular Minimality
Authors
Matthias Trendtel
Ali Ünlü
Copyright Year
2013
Book
Algorithms from and for Nature and Life

Print ISBN: 978-3-319-00034-3

Electronic ISBN: 978-3-319-00035-0

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-319-00035-0_16

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