Enhance Learning Efficiency of Oblique Decision Tree via Feature Concatenation

TL;DR

This paper introduces FC-ODT, an improved oblique decision tree method that uses feature concatenation to transmit linear projections along decision paths, leading to faster learning and better generalization especially for shallow trees.

Contribution

The paper proposes FC-ODT, a novel method that enhances oblique decision trees by enabling feature transformation transmission, improving learning efficiency and generalization.

Findings

FC-ODT outperforms state-of-the-art decision trees at limited depths.

Theoretically, FC-ODT has a faster consistency rate with respect to tree depth.

Experiments confirm improved performance of FC-ODT on various datasets.

Abstract

Oblique Decision Tree (ODT) separates the feature space by linear projections, as opposed to the conventional Decision Tree (DT) that forces axis-parallel splits. ODT has been proven to have a stronger representation ability than DT, as it provides a way to create shallower tree structures while still approximating complex decision boundaries. However, its learning efficiency is still insufficient, since the linear projections cannot be transmitted to the child nodes, resulting in a waste of model parameters. In this work, we propose an enhanced ODT method with Feature Concatenation (\texttt{FC-ODT}), which enables in-model feature transformation to transmit the projections along the decision paths. Theoretically, we prove that our method enjoys a faster consistency rate w.r.t. the tree depth, indicating that our method possesses a significant advantage in generalization performance, especially for shallow trees. Experiments show that \texttt{FC-ODT} can outperform the other state-of-the-art decision trees with a limited tree depth.