Bloomy decision tree for multi-objective classification

This paper presents a novel decision-tree induction for a multi-objective data set, i.e. a data set with a multi-dimensional class. Inductive decision-tree learning is one of the frequently-used methods for a single-objective data set, i.e. a data set with a single-dimensional class. However, in a real data analysis, we usually have multiple objectives, and a classifier which explains them simultaneously would be useful and would exhibit higher readability. A conventional decision-tree inducer requires transformation of a multi-dimensional class into a singledimensional class, but such a transformation can considerably worsen both accuracy and readability. In order to circumvent this problem we propose a bloomy decision tree which deals with a multi-dimensional class without such transformations. A bloomy decision tree has a set of split nodes each of which splits examples according to their attribute values, and a set of flower nodes each of which predicts a class dimension of examples. A flower node appears not only at the fringe of a tree but also inside a tree. Our pruning is executed during tree construction, and evaluates each class dimension based on Cramér’s V. The proposed method has been implemented as D3-B (Decision tree in Bloom), and tested with eleven data sets. The experiments showed that D3-B has higher accuracies in nine data sets than C4.5 and tied with it in the other two data sets. In terms of readability, D3-B has a smaller number of split nodes in all data sets, and thus outperforms C4.5.