Direct Minimization of Error Rates in Multivariate Classification
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We propose a computer intensive method for linear dimension reduction that minimizes the classification error directly. Simulated annealing (Bohachevsky et al. 1986), a modern optimization technique, is used to solve this problem effectively. This approach easily allows user preferences to be incorporated by means of penalty terms. Simulations and a real world example demonstrate the superiority of this optimal classification to classical discriminant analysis (McLachlan 1992). Special emphasis is given to the case when discriminant analysis collapses.
Keywordsclassification discriminant analysis error rate simulated annealing user preferences
This work has been supported by the Collaborative Research Centre “Reduction of Complexity in Multivariate Data Structures” (SFB 475) of the German Research Foundation (DFG). We particularly thank Dipl. Stat. D. Steuer for his constructive criticism. We also thank two unknown referees for their helpful comments.
- U. Heilemann and H. J. Münch, West German Business Cycles 1963–1994: A Multivariate Discriminant Analysis, CIRET-Conference in Singapore, CIRET-Studien 50 (1996)Google Scholar
- R. E. Lucas, Understanding business cycles, in: Studies in Business-Cycle Theory, Cambridge, Mass. and London, 215–240 (1983)Google Scholar
- G. J. McLachlan, Discriminant Analysis and Statistical Pattern Recognition, John Wiley & Sons (1992).Google Scholar
- M. C. Röhl and C. Weihs, Optimal vs. Classical Linear Dimension Reduction, in: W. Gaul, H. Locarek-Junge (eds.), Classification in the Information Age, Studies in Classification, Data Analysis, and Knowledge Organization, Springer, 252–259 (1999)Google Scholar