Penalised Optimal Soft Trees for Functional Data

47/2025

Penalised Optimal Soft Trees for Functional Data

Wednesday 13th August 2025

Gimenez Zapiola, A.; Consolo, A.; Amaldi, E.; Vantini, S.

We propose a new tree-based classifier for Functional Data. A novel objective function for Suárez and Lutsko (1999)’s globally-optimised Soft Classification Trees is proposed to adapt it to the Functional Data Analysis setting when using an FPCA basis. It consists of a supervised and an unsupervised term, with the latter working as a penalisation for heterogeneity in the leaf nodes of the tree. Experiments on benchmark data sets and two case studies demonstrate that the penalisation and proposed initialisation heuristics work synergically to increase model performance both in the train and test data set. In particular, including the unsupervised term shows to aid the supervised term to reach better objective function values. The case studies specifically illustrate how the unsupervised term yields adaptiveness to different problems, by using custom criteria of homogeneity in the leaf nodes. The interpretability of the splitting functions at the internal nodes is also discussed.