  Support vector machines (SVM) and other kernel techniques represent a family
of powerful statistical classification methods with high accuracy and broad
applicability. Because they use all or a significant portion of the training
data, however, they can be slow, especially for large problems. Piecewise
linear classifiers are similarly versatile, yet have the additional advantages
of simplicity, ease of interpretation and, if the number of component linear
classifiers is not too large, speed. Here we show how a simple, piecewise
linear classifier can be trained from a kernel-based classifier in order to
improve the classification speed. The method works by finding the root of the
difference in conditional probabilities between pairs of opposite classes to
build up a representation of the decision boundary. When tested on 17 different
datasets, it succeeded in improving the classification speed of a SVM for 12 of
them by up to two orders-of-magnitude. Of these, two were less accurate than a
simple, linear classifier. The method is best suited to problems with continuum
features data and smooth probability functions. Because the component linear
classifiers are built up individually from an existing classifier, rather than
through a simultaneous optimization procedure, the classifier is also fast to
train.
