Direct variable selection for discrimination among several groups
Journal of Multivariate Analysis
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Variable selection is an important technique for reducing the dimensionality in multivariate predictive discriminant analysis and classification. In the past, direct evaluation of the subsets by means of a classifier has been computationally too expensive, rendering necessary the use of heuristic measures of class separation, such as Wilk's $\Lambda$ or the Mahalanobis distance between class means. We present new fast algorithms for stepwise variable selection based on quadratic and linear classifiers with time complexities which, to within a constant, are the same as those applying measures of class separation. Comparing the new algorithms to previous implementations of classifier-based variable selection, we show that dramatic speed-ups are achieved.