Summary
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.
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Acknowledgment
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.
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Röhl, M.C., Weihs, C. & Theis, W. Direct Minimization of Error Rates in Multivariate Classification. Computational Statistics 17, 29–46 (2002). https://doi.org/10.1007/s001800200089
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DOI: https://doi.org/10.1007/s001800200089