LDA与QDA

一般地，对于多分类问题，假设有 个判别函数

如果满足

则将 判别为 类

如果 服从多元正态分布

其中 ， 是一个协方差矩阵， 是协方差矩阵的行列式

则决策函数可以表示为：

得出 quadratic discriminant analysis(QDA)二次判别 的数学模型

The plot shows decision boundaries for Linear Discriminant Analysis and Quadratic Discriminant Analysis. The bottom row demonstrates that Linear Discriminant Analysis can only learn linear boundaries（variances are similar among classes and there are not enough data to accurately estimate the variances）, while Quadratic Discriminant Analysis can learn quadratic boundaries and is therefore more flexible(variances are very different between classes and there are enough observations to accurately estimate the variances).

海明距离：

欧氏距离：

personal.psu.edu/jol2/course/stat597e/notes2/ lda .pdf

机器学习 周志华