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| 判别分析¾多类Fisher二次型判别分析法 |
| Discriminant analysis¾ Multiple-Class Fisher Quadratic Discriminant AnalysisHu Chunyan1,Liu Huigang2,Hu Liangping1,3* |
| 投稿时间：2025-04-25 修订日期：2025-04-25 |
| DOI： |
| 中文关键词: 多类判别分析 二次型判别函数 正则化 维数灾难 降维策略 |
| 英文关键词:Multiclass Discriminant Analysis Quadratic Discriminant Function Regularization Dimensionality Disaster Dimension Reduction Strategies |
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| 中文摘要: |
| 本文目的是介绍与多类Fisher二次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。基本概念包括协方差矩阵齐性检验、标准化或归一化、正则化、维数灾难和降维策略。计算方法涉及问题设定、判别准则、构建二次型判别函数和分类规则。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了多类Fisher二次型判别分析,对SAS输出结果给出了解释。 |
| 英文摘要: |
| This paper aimed to introduce the basic concepts, computational methods, two examples, and their implementation using SAS for multiclass Fisher"s quadratic discriminant analysis. The fundamental concepts included covariance matrix homogeneity tests, standardization or normalization, regularization, dimensionality disaster, and dimension reduction strategies. The computational methods involved problem setup, discriminant criteria, constructing quadratic discriminant functions, and classification rules. The data in the two examples were "measurement results of seven classes of fish on six quantitative indicators" and "measurement results of five classes of crops on four quantitative indicators". Using SAS software, multiclass Fisher"s quadratic discriminant analysis was performed on the data from the two examples, and the output results from SAS were interpreted. |
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