Measure inducing classification and regression trees for functional data

We propose a tree-based algorithm (μCART) for classification and regression problems in the context of functional data analysis, which allows to leverage measure learning multiple splitting rules at node level, with objective reducing error while retaining interpretability tree. For each internal node, our main contribution is idea weighted space by means constrained convex optimization, then used extract integral features from predictors, order determine binary split. The approach designed manage predictors and/or responses, defining suitable loss functions that can depend on specific problem also be combined additional scalar categorical as tree grown original greedy CART algorithm. focus case scalar-valued defined unidimensional domains illustrate effectiveness method both tasks, through simulation study four real-world applications.