线性回归模型中响应值的选取对二分类问题的影响

The Effects of Different Response Values in Linear Regression Model on Binary Classification

摘要: 我们利用多元线性回归模型处理两个总体的分类问题，首先对响应变量按一定的规则赋值，并在最小二乘法的基础上构建判别函数及判别准则，进而论证了响应值的选取对平衡及不平衡数据二分类问题的影响。此外，我们将此判别方法与经典判别分析方法如：经典马氏距离判别法、Bayes判别法进行比较，并得到它们之间的内在联系及优缺点。

Abstract: We use the multiple linear regression model to deal with the classification problem of two popula-tions. Firstly, we assign the response variables and some corresponding values with certain rules, and then construct discriminant function and criterion via least square method. On this basis, we discuss the effects of different response values on classification for balanced and unbalanced data in linear model. In addition, we compare the mentioned discriminant method above with classic discriminant methods including the classical Mahalanobis distance discriminant and Bayes dis-criminant. At last, we find the inner relation between these methods as well as their advantages and disadvantages.