On piecewise-linear classification

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Abstract
The authors make use of a real data set containing 9-D measurements of fine needle aspirates of a patient's breast for the purpose of classifying a tumor's malignancy for which early stopping in the generation of the separating hyperplanes is not appropriate. They compare a piecewise-linear classification method with classification based on a single linear separator. A precise methodology for comparing the relative efficacy of two classification methods for a particular task is described and is applied to the comparison on the breast cancer data of the relative performances of the two versions of the piecewise-linear classifier and the classification based on an optimal linear separator. It is found that for this data set, the piecewise-linear classifier that uses all the hyperplanes needed to separate the training set outperforms the other two methods and that these differences in performance are significant at the 0.001 level. There is no statistically significant difference between the performance of the other two methods. The authors discuss the relevance of these results for this and other applications.

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