Inducing safer oblique trees without costs

Decision tree induction has been has been widely studied and applied. In safety applications, such as determining whether a chemical process is safe, or whether a person has a medical condition, the cost of misclassification in one of the classes is significantly higher than the other class. Several authors have tackled this problem by developing cost-sensitive decision tree learning algorithms or suggested ways of changing the distribution of training examples to bias the decision tree learning process so as to take account of costs. A pre-requisite for applying such algorithms is the availability of costs of misclassification. Although this may be possible for some applications, in the area of safety, obtaining reasonable estimates of costs of misclassification is not easy. This paper presents a new algorithm for applications where the cost of misclassifications can not be quantified, though the cost of misclassification in one class is known to be significantly higher than another class. The algorithm utilises linear discriminant analysis to identify oblique relationships between continuous attributes and then carries out an appropriate modification to ensure that the resulting tree errs on the side of safety. The algorithm is evaluated with respect to ICET, one of the best known cost-sensitive algorithms, OC1 a well known oblique decision tree algorithm and an algorithm that utilises robust linear programming.