Abstract
The different techniques used for Euclidean approximation of distances are discussed. In the special case of points in a Euclidean space, whose distances are biased due to measure errors, accepting negative eigenvalues may help in the interpretation of results that are less biased than those obtained through an additive constant solution. Numerical examples are given.
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References
Bénasséni, J. (1984). Partial Additive Constant, J. Stat. Comp. Simul., 49, 179–193.
Borg, J. & Lingoes, J. (1987). Multidimensional Similarity Structure Analysis, Springer Verlag, New York.
Cailliez, F. (1983). The Analytical Solution of the Additive Constant Problem, Psychometrika, 48, 2, 305–308.
Critchley, F. (1980). Optimal Norm Characterisations of Multidimensional Scaling Methods and some Related Data Analysis Problems, in: Data Analysis and Informatics, Diday, E. et al. (Eds.), Amsterdam, North-Holland, 209–229.
Gower, J.C. (1966). Some Distance Properties of Latent Root and Vector Methods used in Multivariate Analysis, Biometrika, 53, 325–338.
Gower, J.C. (1985). Properties of Euclidean and Non-Euclidean Distance Matrices, Linear Algebra and its Applications, 67, 81–95.
Joly, S. & Le Calvé, G. (1986). Etude des puissances d’une distance, Statistique et Analyse des données, 11, 3, 30–50.
Kruskal, J.B. (1964a). Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis, Psychometrika, 29, 1–27.
Kruskal, J.B. (1964b). Nonmetric Multidimensional Scaling: a Numerical Method, Psychometrika, 29, 115–129.
Lang, S. (1972). Linear Algebra, Addison-Wesley, Reading, Mass.
Le Calvé, G. (1976). Quelques remarques sur certains aspects de ?analyse fac-torielle, Lab. Analyse des Données, Université de Rennes II, Cahier n. 2.
Lingoes, J.C. (1971). Some Boundary Conditions for a Monotone Analysis of Symmetric Matrices, Psychometrika, 36, 195–203.
Mardia, K.V., Kent, J.T. & Bibby, J.M. (1979). Multivariate Analysis, Academic Press, London.
Messick, S.J. & Abelson, R.P. (1956). The Additive Constant Problem in Multidimensional Scaling, Psychometrika, 21, 1–15.
Saito, T. (1978). The Problem of the Additive Constant and Eigenvalues in Metric Multidimensional Scaling, Psychometrika, 43, 2, 193–201.
Seber, G.A.F. (1984). Multivariate Observations, J. Wiley & Sons, New York.
Torgerson, W.S. (1958). Theory and Methods of Scaling, J.Wiley & Sons, NewYork.
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© 1999 Springer-Verlag Berlin · Heidelberg
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Camiz, S. (1999). Comparison of Euclidean Approximations of non-Euclidean Distances. In: Vichi, M., Opitz, O. (eds) Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60126-2_18
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DOI: https://doi.org/10.1007/978-3-642-60126-2_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65633-3
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