The problem of handling a class imbalanced problem by modifying decision tree algorithm has received widespread attention in recent years. A new splitting measure, called class overlapping-balancing entropy (OBE), is introduced in this paper that essentially pay attentions to all classes equally. Each step, the proportion of each class is balanced via the assigned weighted values. They not only depend on equalizing each class, but they also take into account the overlapping region between classes. The proportion of weighted values corresponding to each class is used as the component of Shannon's entropy for splitting the current dataset. From the experimental results, OBE significantly outperforms the conventional splitting measures like Gini index, gain ratio and DCSM, which are used in the well-known decision tree algorithms. It also exhibits superior performance compared to AE and ME that are designed for handling the class imbalanced problem specifically.

In recent years, a significant issue in classification is to handle a dataset containing imbalanced number of instances in each class. Classifier modification is one of the well-known techniques to deal with this particular issue. In this paper, the effective classification model based on an oblique decision tree is enhanced to work with an imbalanced dataset that is called oblique minority condensed decision tree (OMCT). Initially, it selects the best axis-parallel hyperplane based on the decision tree algorithm using the minority entropy of instances within the minority inner fence selection. Then it perturbs this hyperplane along each axis to improve its minority entropy. Finally, it stochastically perturbs this hyperplane to escape the local solution. From the experimental results, OMCT significantly outperforms six state-of-the-art decision tree algorithms that are CART, C4.5, OC1, AE, DCSM and ME on 18 real-world datasets from UCI in term of precision, recall and F1 score. Moreover, the size of a decision tree from OMCT is significantly smaller than others.

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