Tree-Structured Classification Via Generalized Discriminant Analysis
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通过广义判别分析构造树形分类规则
- 研究问题
- 如何利用含缺失协变量的已标注样本构造分类树，并同时处理分裂选择、树规模、变量排序与不同误分类成本？
- 方法与思路
- 作者递归使用线性判别分析，结合方差分析、典型判别和主成分分析，构造多种分裂形式并通过估计处理缺失值。
- 材料陈述的贡献
- 摘要称新方法允许多分支及不同分裂形式，计算更快；所述模拟显示其分类准确率与CART相近，而非全面占优。
- 阅读关注点
- 应核对缺失值估计、直接停止规则、成本和先验概率的作用，以及与CART比较时的计算环境、模拟设计和评价指标。
- 阅读边界
- 仅据版本未注明的OpenAlex索引摘要；速度与准确率结论限于所述比较，模拟细节未给出，不能推断普遍优势。
原文摘要
The problem of constructing classification rules that can be represented as decision trees is considered. Each object to be classified has an associated x vector containing possibly incomplete covariate information. Tree construction is based on the information provided in a “learning sample” of objects with known class identities. The x vectors in the learning sample may have missing values as well. Procedures are proposed for each of the components of classifier construction, such as split selection, tree-size determination, treatment of missing values, and ranking of variables. The main idea is recursive application of linear discriminant analysis, with the variables at each stage being appropriately chosen according to the data and the type of splits desired. Standard statistical techniques used as basic building blocks include analysis of variance, linear and canonical discriminant analysis, and principal component analysis. A new method of tree-structured classification is obtained by assembling the pieces. This method can accommodate prior probabilities as well as unequal misclassification costs and can yield trees with univariate, linear combination, or linear combination with polar coordinate splits. The method is compared with the CART method of Breiman, Friedman, Olshen, and Stone (1984). Some of the operational differences are that the new method (a) can have multiple splits per node, (b) is nonrandomized, (c) uses a direct stopping rule, (d) handles missing values by estimation, (e) allows both ordered and unordered variables in the same linear combination split, (f) is not invariant of monotone transformations of the individual variables, and (g) is computationally faster. Simulation experiments suggest that the two methods have comparable classification accuracy. The Boston housing data are analyzed in a classification context for illustration.