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.

翻译：许多传统的统计和机器学习方法在直接应用于高维时间观测数据时面临挑战。近几十年来，函数型数据分析作为对本质上为时间域函数的数进行建模与分析的一种框架，已得到广泛普及。尽管监督分类在近几十年的函数型数据分析文献中已被广泛探索，但函数型分类器的集成学习直到最近才成为一个备受关注的研究课题。因此，后者从多种统计学视角呈现出未探索的方面与挑战。本文的焦点在于函数型数据的集成学习领域，旨在展示如何利用不同的函数型数据表征来训练集成成员，以及如何通过多数投票组合基模型预测结果。我们提出所谓的函数投票分类器，以展示导致多样性增强的不同函数型表征如何提高预测精度。来自多个领域的众多真实数据集被用于证明，与个体模型相比，函数投票分类器能够显著提升性能。所提出的框架为函数型数据的投票集成奠定了基础，并能在函数型数据分析领域激发极具前景的研究方向。