Block diagrams and splitting criteria for classification trees

Various aspects of the classification tree methodology of Breiman et al., (1984) are discussed. A method of displaying classification trees, called block diagrams, is developed. Block diagrams give a clear presentation of the classification, and are useful both to point out features of the particular data set under consideration and also to highlight deficiencies in the classification method being used. Various splitting criteria are discussed; the usual Gini-Simpson criterion presents difficulties when there is a relatively large number of classes and improved splitting criteria are obtained. One particular improvement is the introduction of adaptive anti-end-cut factors that take advantage of highly asymmetrical splits where appropriate. They use the number and mix of classes in the current node of the tree to identify whether or not it is likely to be advantageous to create a very small offspring node. A number of data sets are used as examples.