Completion time requirements are often imposed on a classification task. In practice, the desired completion time for classifying a subject may depend on its label (target) value. For example, a timely diagnosis is important for an illness that requires immediate medical attention. It is common in medical diagnoses, therefore, to set completion times based on the severity level of the illness. In this study, we use “label-dependent” completion time requirements to formulate a new classification problem for cost-sensitive decision tree induction by adding “late constraints” to control the rate of tardy classifications for each label value. Adding the late constraints generalizes and enriches the decision tree induction problem, but also poses a challenge to developing an efficient solution algorithm because the conventional approach based on the “divide-and-conquer” strategy cannot be used. We develop a novel algorithm that relaxes the late constraints and iteratively solves a series of cost-sensitive decision tree problems under systematically-generated late penalties. The results of an extensive numerical experiment show that the proposed algorithm is effective in finding the optimal or a near-optimal solution.

Structured continuous-label classification is a variety of classification in which the label is continuous in the data, but the goal is to classify data into classes that are a set of predefined ranges and can be organized in a hierarchy. In the hierarchy, the ranges at the lower levels are more specific and inherently more difficult to predict, whereas the ranges at the upper levels are less specific and inherently easier to predict. Therefore, both prediction specificity and prediction accuracy must be considered when building a decision tree (DT) from this kind of data. This paper proposes a novel classification algorithm for learning DT classifiers from data with structured continuous labels. This approach considers the distribution of labels throughout the hierarchical structure during the construction of trees without requiring discretization in the preprocessing stage. We compared the results of the proposed method with those of the C4.5 algorithm using eight real data sets. The empirical results indicate that the proposed method outperforms the C4.5 algorithm with regard to prediction accuracy, prediction specificity, and computational complexity.

In traditional decision (classification) tree algorithms, the label is assumed to be a categorical (class) variable. When the label is a continuous variable in the data, two possible approaches based on existing decision tree algorithms can be used to handle the situations. The first uses a data discretization method in the preprocessing stage to convert the continuous label into a class label defined by a finite set of nonoverlapping intervals and then applies a decision tree algorithm. The second simply applies a regression tree algorithm, using the continuous label directly. These approaches have their own drawbacks. We propose an algorithm that dynamically discretizes the continuous label at each node during the tree induction process. Extensive experiments show that the proposed method outperforms the preprocessing approach, the regression tree approach, and several nontree-based algorithms.