Augmented Functional Random Forests: Classifier Construction and Unbiased Functional Principal Components Importance through Ad-Hoc Conditional Permutations

TL;DR

This paper presents augmented functional random forests that improve classification accuracy for high-dimensional functional data and introduces an unbiased importance measure for functional principal components using ad-hoc permutations.

Contribution

It develops augmented functional classification trees and random forests with a new unbiased importance measure for functional principal components, addressing correlation issues.

Findings

Enhanced classification accuracy on real and simulated datasets.

Effective unbiased importance measure for correlated functional features.

Improved predictive power over existing functional classifiers.

Abstract

This paper introduces a novel supervised classification strategy that integrates functional data analysis (FDA) with tree-based methods, addressing the challenges of high-dimensional data and enhancing the classification performance of existing functional classifiers. Specifically, we propose augmented versions of functional classification trees and functional random forests, incorporating a new tool for assessing the importance of functional principal components. This tool provides an ad-hoc method for determining unbiased permutation feature importance in functional data, particularly when dealing with correlated features derived from successive derivatives. Our study demonstrates that these additional features can significantly enhance the predictive power of functional classifiers. Experimental evaluations on both real-world and simulated datasets showcase the effectiveness of the proposed methodology, yielding promising results compared to existing methods.