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Exact and approximate algorithms for variable selection in linear discriminant analysis

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  • Brusco, Michael J.
  • Steinley, Douglas

Abstract

Variable selection is a venerable problem in multivariate statistics. In the context of discriminant analysis, the goal is to select a subset of variables that accomplishes one of two objectives: (1) the provision of a parsimonious, yet descriptive, representation of group structure, or (2) the ability to correctly allocate new cases to groups. We present an exact (branch-and-bound) algorithm for variable selection in linear discriminant analysis that identifies subsets of variables that minimize Wilks' [Lambda]. An important feature of this algorithm is a variable reordering scheme that greatly reduces computation time. We also present an approximate procedure based on tabu search, which can be implemented for a variety of objective criteria designed for either the descriptive or allocation goals associated with discriminant analysis. The tabu search heuristic is especially useful for maximizing the hit ratio (i.e., the percentage of correctly classified cases). Computational results for the proposed methods are provided for two data sets from the literature.

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  • Brusco, Michael J. & Steinley, Douglas, 2011. "Exact and approximate algorithms for variable selection in linear discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 123-131, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:123-131
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    References listed on IDEAS

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    9. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 249-270, June.
    10. Michael Brusco & Renu Singh & Douglas Steinley, 2009. "Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 705-726, December.
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