Biometrika Advance Access originally published online on April 1, 2009
Biometrika 2009 96(2):469-478; doi:10.1093/biomet/asp007
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Article |
Scale adjustments for classifiers in high-dimensional, low sample size settings
Department of Mathematics and Statistics, The University of Melbourne, Parkville, Victoria 3010, Australia y.chan{at}ms.unimelb.edu.au P.Hall{at}ms.unimelb.edu.au
Received for publication 1 October 2007.
Revision received 1 September 2008.
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Abstract |
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Distance-based classifiers are generally considered to be effective at discriminating between populations that differ in location. Indeed, nearest-neighbour methods and the support vector machine are frequently used in very high-dimensional problems involving gene expression data, where it is believed that elevated levels of expression convey much of the information for classification. However, one problem inherent to distance-based classifiers is that scale differences can mask location differences. In consequence, such classifiers can have poor performance if the information for classification accumulates through a large number of relatively small location differences in data components, rather than via large differences. In this paper, we show that a simple adjustment for scale, applicable to a variety of distance-based classifiers, can remedy the problem. For some classifiers, such as those based on the support vector machine or the centroid method, scale corrections are important primarily in the case of small training-sample sizes. However, for other classifiers, including those based on nearest-neighbour and average-distance methods, scale adjustments are helpful more generally.
Key Words: Average-distance classifier • Centroid method • Distance-based classifier • Location difference • Nearest-neighbour method • Support vector machine