HHCART：一种斜决策树
HHCART: An Oblique Decision Tree
摘要：
决策树是统计数据分类中的一种流行技术。它们递归地将特征空间划分为不相交的子区域，直到每个子区域相对于特定的类变得均匀。基本的分类和回归树（CART）算法使用轴平行分裂来划分特征空间。当真正的决策边界与特征轴不对齐时，这种方法会产生复杂的边界结构。斜决策树使用斜决策边界来潜在地简化边界结构。这种方法的主要局限性是树归纳算法计算量大。在这篇文章中，我们提出了一个新的决策树算法，称为HHCART。该方法利用一系列Householder矩阵来反映树构建过程中每个节点处的训练数据。每个反射基于来自每个类别的协方差阵的特征向量的方向。在反射的训练数据中考虑轴平行分裂提供了在未反射的训练数据中找到倾斜分裂的有效方式。实验结果表明，HHCART树的精度和大小与文献中的一些基准方法相当。HHCART的吸引人的特点是，它可以处理定性和定量的特点，在同一斜分裂。
英文摘要：
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using axis parallel splits. When the true decision boundaries are not aligned with the feature axes, this approach can produce a complicated boundary structure. Oblique decision trees use oblique decision boundaries to potentially simplify the boundary structure. The major limitation of this approach is that the tree induction algorithm is computationally expensive. In this article we present a new decision tree algorithm, called HHCART. The method utilizes a series of Householder matrices to reflect the training data at each node during the tree construction. Each reflection is based on the directions of the eigenvectors from each classes' covariance matrix. Considering axis parallel splits in the reflected training data provides an efficient way of finding oblique splits in the unreflected training data. Experimental results show that the accuracy and size of the HHCART trees are comparable with some benchmark methods in the literature. The appealing feature of HHCART is that it can handle both qualitative and quantitative features in the same oblique split.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
