Keywords: decision tree, functional data, functional logistic regression, random forest, supervised learning
Functional data occur frequently in various fields of application and many standard tools for data analysis already have their functional counterparts tailored to the specific properties of such data. Specifically, there is a growing interest in classification methods that are designed for functional data and allow to utilize information about appearance and shape of the functional observations. Most of the procedures available, however, are rather inspired by "classical" statistical methods than machine learning approaches. Here we propose a novel classification tree designed to deal with functional predictors. Partitioning for a chosen predictor in a specific node of the tree is based on comparing each observational curve in that node to the class-specific mean curves. A metric suitable for functional data is used to measure the "amount of closeness/similarity" of an observed curve to each of the class-specific mean curves. A curve under consideration is assigned to the class to whose mean curve it is closest in terms of the chosen metric. To choose a predictor for the next split in the current node, common node impurity measures such as the misclassification rate or the Gini index are employed. The proposed functional classification tree may be used as a self-contained approach, but also as a base learner for an ensemble learning method such as a random forest or boosting. The performance of the functional classification tree is investigated on real as well as on simulated data and compared to alternative procedures such as a functional logistic regression model.