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| 判别分析——线性判别分析法 |
| 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——线性判别分析法 |
| 英文关键词:判别分析——线性判别分析法 |
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| 中文摘要: |
| 【】本文的目的是介绍与线性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“线性判别函数”“投影”“Fisher线性判别准则”“拉格朗日乘数法”和“广义特征值”；计算方法涉及“问题描述”“目标函数”“类内散布矩阵和类间散布矩阵”“拉格朗日乘数法求解权重系数”和“求解广义特征值”；两个实例中的资料分别是“七类鱼在6个定量指标上的测定结果”和“五类作物在4个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线性判别分析,进而分别给出回代判别和基于刀切法进行交叉验证的总误判率。 |
| 英文摘要: |
| 【】The purpose of this paper was to introduce the basic concepts, computational methods, two examples, and their implementation using SAS for linear discriminant analysis. The basic concepts included "the linear discriminant function," "projection," "Fisher"s linear discriminant criterion," "Lagrange multiplier method," and "generalized eigenvalues." The computational methods involved "problem description," "objective function," "within-class and between-class scatter matrices," "solving for weight coefficients using the Lagrange multiplier method," and "solving for generalized eigenvalues." The data in the two examples were "measurement results of seven types of fish on six quantitative indicators" and "measurement results of five types of crops on four quantitative indicators." Using SAS software, linear discriminant analysis was performed on the data from both examples, followed by providing the total misjudgment rate for resubstitution discriminant and cross-validation based on the jackknife method. |
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