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.

翻译：传统决策树受限于轴正交划分，当真实决策边界为斜向时性能往往不佳。虽然斜决策树方法解决了这一局限，但通常面临计算成本高、多类分类困难以及缺乏有效特征选择等问题。本文提出了LDATree与FoLDTree两种新颖框架，将不相关线性判别分析（ULDA）与前向ULDA集成到决策树结构中。这些方法能够实现高效的斜划分，处理缺失值，支持特征选择，并提供类别标签与概率作为模型输出。通过对模拟数据集和真实数据集的评估，LDATree与FoLDTree在性能上持续优于轴正交及其他斜决策树方法，其准确度达到与随机森林相当的水平。结果表明这些框架具备成为传统单树方法强健替代方案的潜力。