用ULDA提升决策树的斜向切分效率与特征选择能力
FoLDTree: A ULDA-Based Decision Tree Framework for Efficient Oblique Splits and Feature Selection
- 引入ULDA构建斜向切分，突破轴对齐限制
- 在真实与模拟数据上准确率媲美随机森林
- 支持缺失值处理和概率输出，适合多场景应用
传统决策树受限于轴对齐切分，在真实决策边界为斜向时表现不佳。尽管已有斜向决策树方法，但普遍存在计算开销大、多分类困难及特征选择不足的问题。本文提出LDATree与FoLDTree两个新框架，将无相关线性判别分析（ULDA）与前向ULDA融入决策树结构，实现高效斜向切分，支持缺失值处理、特征选择，并输出类别标签与概率。在模拟及真实数据集上的评估表明，该方法在准确率上持续优于轴对齐及其他斜向决策树方法，性能接近随机森林，展现出作为传统单棵树方法可靠替代方案的潜力。
原文摘要 · Abstract (English)
Traditional decision trees are limited by axis-orthogonal splits, which can perform poorly when true decision boundaries are oblique. While oblique decision tree methods address this limitation, they often face high computational costs, difficulties with multi-class classification, and a lack of effective feature selection. In this paper, we introduce LDATree and FoLDTree, two novel frameworks that integrate Uncorrelated Linear Discriminant Analysis (ULDA) and Forward ULDA into a decision tree structure. These methods enable efficient oblique splits, handle missing values, support feature selection, and provide both class labels and probabilities as model outputs. Through evaluations on simulated and real-world datasets, LDATree and FoLDTree consistently outperform axis-orthogonal and other oblique decision tree methods, achieving accuracy levels comparable to the random forest. The results highlight the potential of these frameworks as robust alternatives to traditional single-tree methods.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。