融合导数与几何特征,提升高维时序分类精度。
Enriched Functional Tree-Based Classifiers: A Novel Approach Leveraging Derivatives and Geometric Features
- 结合函数数据分析与树模型,提取导数和几何特征
- 在7个真实数据集上性能显著优于传统方法
- 适用于多种树模型,可扩展至其他分类器
本研究属于标量对函数分类领域,具有广泛的应用价值。提出一种新型集成方法——增强型函数树分类器(EFTCs),将函数数据分析(FDA)与树模型集成技术相结合,用于高维时序数据的监督分类。该方法通过引入导数和几何特征,利用集成方法的多样性提升预测准确率并降低方差。已在函数分类树(FCT)、函数K近邻(FKNN)、函数随机森林(FRF)、函数XGBoost(FXGB)、函数LightGBM(FLGBM)等模型上验证,具备良好泛化能力。通过在7个真实数据集和6个模拟场景上的大量实验,结果表明该方法在复杂高维学习任务中表现优异,为函数数据分析在实际问题中的应用提供了新思路。
原文摘要 · Abstract (English)
The positioning of this research falls within the scalar-on-function classification literature, a field of significant interest across various domains, particularly in statistics, mathematics, and computer science. This study introduces an advanced methodology for supervised classification by integrating Functional Data Analysis (FDA) with tree-based ensemble techniques for classifying high-dimensional time series. The proposed framework, Enriched Functional Tree-Based Classifiers (EFTCs), leverages derivative and geometric features, benefiting from the diversity inherent in ensemble methods to further enhance predictive performance and reduce variance. While our approach has been tested on the enrichment of Functional Classification Trees (FCTs), Functional K-NN (FKNN), Functional Random Forest (FRF), Functional XGBoost (FXGB), and Functional LightGBM (FLGBM), it could be extended to other tree-based and non-tree-based classifiers, with appropriate considerations emerging from this investigation. Through extensive experimental evaluations on seven real-world datasets and six simulated scenarios, this proposal demonstrates fascinating improvements over traditional approaches, providing new insights into the application of FDA in complex, high-dimensional learning problems.
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