FoLDTree: A ULDA-Based Decision Tree Framework for Efficient Oblique Splits and Feature Selection

TL;DR

This paper introduces LDATree and FoLDTree, innovative decision tree frameworks utilizing ULDA for efficient oblique splits, feature selection, and improved accuracy, addressing limitations of traditional and existing oblique decision trees.

Contribution

The paper presents novel ULDA-based frameworks that enable efficient oblique splits, feature selection, and handle missing data, outperforming existing methods in accuracy and computational efficiency.

Findings

Outperform axis-orthogonal and other oblique decision trees in accuracy.

Achieve comparable accuracy to random forests.

Effectively handle missing values and support feature selection.

Abstract

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.