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

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.

Random Survival Forest for Censored Functional Data

This paper introduces a Random Survival Forest (RSF) method for functional data. The focus is specifically on defining a new functional data structure, the Censored Functional Data (CFD), for dealing with temporal observations that are censored due to study limitations or incomplete data collection. This approach allows for precise modelling of functional survival trajectories, leading to improved interpretation and prediction of survival dynamics across different groups. A medical survival study on the benchmark SOFA data set is presented. Results show good performance of the proposed approach, particularly in ranking the importance of predicting variables, as captured through dynamic changes in SOFA scores and patient mortality rates.

Supervised Learning via Ensembles of Diverse Functional Representations: the Functional Voting Classifier

Many conventional statistical and machine learning methods face challenges when applied directly to high dimensional temporal observations. In recent decades, Functional Data Analysis (FDA) has gained widespread popularity as a framework for modeling and analyzing data that are, by their nature, functions in the domain of time. Although supervised classification has been extensively explored in recent decades within the FDA literature, ensemble learning of functional classifiers has only recently emerged as a topic of significant interest. Thus, the latter subject presents unexplored facets and challenges from various statistical perspectives. The focal point of this paper lies in the realm of ensemble learning for functional data and aims to show how different functional data representations can be used to train ensemble members and how base model predictions can be combined through majority voting. The so-called Functional Voting Classifier (FVC) is proposed to demonstrate how different functional representations leading to augmented diversity can increase predictive accuracy. Many real-world datasets from several domains are used to display that the FVC can significantly enhance performance compared to individual models. The framework presented provides a foundation for voting ensembles with functional data and can stimulate a highly encouraging line of research in the FDA context.

Clustering of functional boxplots for multiple streaming time series

In this paper we introduce a micro-clustering strategy for Functional Boxplots. The aim is to summarize a set of streaming time series splitted in non overlapping windows. It is a two step strategy which performs at first, an on-line summarization by means of functional data structures, named Functional Boxplot micro-clusters; then it reveals the final summarization by processing, off-line, the functional data structures. Our main contribute consists in providing a new definition of micro-cluster based on Functional Boxplots and, in defining a proximity measure which allows to compare and update them. This allows to get a finer graphical summarization of the streaming time series by five functional basic statistics of data. The obtained synthesis will be able to keep track of the dynamic evolution of the multiple streams.