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| 判别分析——典型判别分析法 |
| Liu Huigang1,Hu Chunyan2, Hu Liangping2,3*(1. School of Basic Medical Sciences, Capital Medical University, Beijing 100069,China; |
| 投稿时间：2025-02-20 修订日期：2025-02-20 |
| DOI： |
| 中文关键词: 判别分析——典型判别分析法 |
| 英文关键词:判别分析——典型判别分析法 |
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| 中文摘要: |
| 【】本文目的是介绍与典型判别分析有关的基本概念、计算方法、两个实例及其用SAS实现计算的方法。基本概念包括“类内散布矩阵”“类间散布矩阵”“典型判别变量与典型判别分析”“奇异矩阵与非奇异矩阵”和“回代判别”；计算方法涉及“计算类内散布矩阵”“计算类间散布矩阵”“求解广义特征值”“选择典型判别变量”和“投影到典型判别变量空间”；两个实例中的资料分别是“三类鸢尾属植物在4项定量指标上的测定结果”和“七种鱼在6项定量指标上的测定结果”；借助SAS软件,对两个实例中的数据进行典型判别分析,基于典型判别变量推测各样品的类别归属,并判定其与各样品的实际类别吻合情况,进而算出各实例的总误判率。 |
| 英文摘要: |
| 【】The purpose of this paper was to introduce the basic concepts, computational methods, and two examples related to Canonical Discriminant Analysis (CDA), as well as the method for implementing calculations using SAS. The basic concepts included "Within-class Scatter Matrix," "Between-class Scatter Matrix," "Canonical Discriminant Variables and Canonical Discriminant Analysis," "Singular Matrices and Non-singular Matrices," and "Resubstitution Discrimination"; the computational methods involved "Computing the Within-class Scatter Matrix," "Computing the Between-class Scatter Matrix," "Solving the Generalized Eigenvalue," "Selecting Canonical Discriminant Variables," and "Projecting onto Canonical Discriminant Variable Space." The data from two examples were "Measurement results of three types of Iris plants on four quantitative indicators" and "Measurement results of seven types of fish on six quantitative indicators." Using SAS software, CDA was performed on the data from these two examples to infer the category membership of each sample based on the canonical discriminant variables, determine their agreement with the actual categories of each sample, and calculate the overall misclassification rate for each example. |
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