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Dimension Reduction with Linear Discriminant Functions Based on an Odds Ratio Parameterization
Author(s) -
Linde Angelika
Publication year - 2003
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2003.tb00218.x
Subject(s) - mathematics , contingency table , statistics , linear discriminant analysis , covariance , combinatorics , multidimensional scaling
Summary The association of two random elements with positive joint probability density function is given by an odds ratio function. The covariance is an adequate description only in the case of two jointly Gaussian variables. The impact of the association structure on the set‐up and solution of problems of linear discrimination is investigated, and the results are related to standard techniques of multivariate analysis, particularly to canonical correlation analysis, analysis of contingency tables, discriminant analysis and multidimensional scaling . Résumé L'association entre deux éléments aléatoires ayant une densité conjointe positive est donnée par l'odds ratio fonction. La covariance n'est une description adéquate que dans le cas gaussien. L'impact de ce résultat en termes de réduction de la dimension et en terme de discrimination est examinée et les résultats sont rapportés aux techniques traditionelles de l'analyse discriminante et du scaling multidimensional.