Randomized Spline Trees for Functional Data Classification: Theory and Application to Environmental Time Series

TL;DR

This paper introduces Randomized Spline Trees, a novel ensemble method that uses randomized functional representations to improve classification accuracy on environmental time series data, demonstrating significant performance gains.

Contribution

It proposes a new algorithm combining randomized spline-based functional data representations with ensemble learning, enhancing accuracy and theoretical understanding in environmental time series classification.

Findings

RST outperforms standard Random Forests and Gradient Boosting on most datasets.

Classification accuracy improves by up to 14%.

Theoretical analysis links functional diversity to reduced generalization error.

Abstract

Functional data analysis (FDA) and ensemble learning can be powerful tools for analyzing complex environmental time series. Recent literature has highlighted the key role of diversity in enhancing accuracy and reducing variance in ensemble methods.This paper introduces Randomized Spline Trees (RST), a novel algorithm that bridges these two approaches by incorporating randomized functional representations into the Random Forest framework. RST generates diverse functional representations of input data using randomized B-spline parameters, creating an ensemble of decision trees trained on these varied representations. We provide a theoretical analysis of how this functional diversity contributes to reducing generalization error and present empirical evaluations on six environmental time series classification tasks from the UCR Time Series Archive. Results show that RST variants outperform standard Random Forests and Gradient Boosting on most datasets, improving classification accuracy by up to 14\%. The success of RST demonstrates the potential of adaptive functional representations in capturing complex temporal patterns in environmental data. This work contributes to the growing field of machine learning techniques focused on functional data and opens new avenues for research in environmental time series analysis.