Elliptical cost-sensitive decision tree algorithm (ECSDT)

Cost-sensitive multiclass classification problems, in which the task of assessing the impact of the costs associated with different misclassification errors, continues to be one of the major challenging areas for data mining and machine learning. The literature reviews in this area show that most of the cost-sensitive algorithms that have been developed during the last decade were developed to solve binary classification problems where an example from the dataset will be classified into only one of two available classes. Much of the research on cost-sensitive learning has focused on inducing decision trees, which are one of the most common and widely used classification methods, due to the simplicity of constructing them, their transparency and comprehensibility. A review of the literature shows that inducing nonlinear multiclass cost-sensitive decision trees is still in its early stages and further research could result in improvements over the current state of the art. Hence, this research aims to address the following question: How can non-linear regions be identified for multiclass problems and utilized to construct decision trees so as to maximize the accuracy of classification, and minimize misclassification costs? This research addresses this problem by developing a new algorithm called the Elliptical Cost-Sensitive Decision Tree algorithm (ECSDT) that induces cost-sensitive non-linear (elliptical) decision trees for multiclass classification problems using evolutionary optimization methods such as particle swarm optimization (PSO) and Genetic Algorithms (GAs). In this research, ellipses are used as non-linear separators, because of their simplicity and flexibility in drawing non-linear boundaries by modifying and adjusting their size, location and rotation towards achieving optimal results. The new algorithm was developed, tested, and evaluated in three different settings, each with a different objective function. The first considered maximizing the accuracy of classification only; the second focused on minimizing misclassification costs only, while the third considered both accuracy and misclassification cost together. ECSDT was applied to fourteen different binary-class and multiclass data sets and the results have been compared with those obtained by applying some common algorithms from Weka to the same datasets such as J48, NBTree, MetaCost, and the CostSensitiveClassifier. The primary contribution of this research is the development of a new algorithm that shows the benefits of utilizing elliptical boundaries for cost-sensitive decision tree learning. The new algorithm is capable of handling multiclass problems and an empirical evaluation shows good results. More specifically, when considering accuracy only, ECSDT performs better in terms of maximizing accuracy on 10 out of the 14 datasets, and when considering minimizing misclassification costs only, ECSDT performs better on 10 out of the 14 datasets, while when considering both accuracy and misclassification costs, ECSDT was able to obtain higher accuracy on 10 out of the 14 datasets and minimize misclassification costs on 5 out of the 14 datasets. The ECSDT also was able to produce smaller trees when compared with J48, LADTree and ADTree.