Oblique decision trees have attracted attention due to their potential for improved classification performance over traditional axis-aligned decision trees. However, methods that rely on exhaustive search to find oblique splits face computational challenges. As a result, they have not been widely explored. We introduce a novel algorithm, Classification and Regression Tree - Exhaustive Linear Combinations (CART-ELC), for inducing oblique decision trees that performs an exhaustive search on a restricted set of hyperplanes. We then investigate the algorithm's computational complexity and its predictive capabilities. Our results demonstrate that CART-ELC consistently achieves competitive performance on small datasets, often yielding statistically significant improvements in classification accuracy relative to existing decision tree induction algorithms, while frequently producing shallower, simpler, and thus more interpretable trees.

本研究针对传统轴对齐决策树的分类性能不足问题，提出了一种新颖的算法CART-ELC，该算法能够通过在限制的超平面集合上进行穷举搜索来诱导斜决策树。研究表明，CART-ELC在小型数据集上始终能够达到具有竞争力的性能，且相比于现有算法，在分类准确性方面常常显著提升，同时生成的决策树更加简洁易懂。

CART-ELC：通过穷举搜索诱导斜决策树