Statistics – Applications
Scientific paper
2012-02-27
Annals of Applied Statistics 2011, Vol. 5, No. 4, 2403-2424
Statistics
Applications
Published in at http://dx.doi.org/10.1214/11-AOAS495 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins
Scientific paper
10.1214/11-AOAS495
Prototype methods seek a minimal subset of samples that can serve as a distillation or condensed view of a data set. As the size of modern data sets grows, being able to present a domain specialist with a short list of "representative" samples chosen from the data set is of increasing interpretative value. While much recent statistical research has been focused on producing sparse-in-the-variables methods, this paper aims at achieving sparsity in the samples. We discuss a method for selecting prototypes in the classification setting (in which the samples fall into known discrete categories). Our method of focus is derived from three basic properties that we believe a good prototype set should satisfy. This intuition is translated into a set cover optimization problem, which we solve approximately using standard approaches. While prototype selection is usually viewed as purely a means toward building an efficient classifier, in this paper we emphasize the inherent value of having a set of prototypical elements. That said, by using the nearest-neighbor rule on the set of prototypes, we can of course discuss our method as a classifier as well.
Bien Jacob
Tibshirani Robert
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