# Linear Discriminant Analysis

Linear Discriminant Analysis （线性判别分析）的缩写也叫LDA，核心就是 $$J(w) = \frac{(\mu\_2 - \mu\_1)^2}{s\_1^2 + s\_2^2}$$ : 就是希望投影后的两类样本 的均值越远越好，但是各类别方差越小越好。

## kernel LDA

$$y = W^T X + \lambda \left | W \right |$$

[线性判别分析（二）——Bayes最优分类器的角度看LDA](https://blog.csdn.net/VictoriaW/article/details/78275394)

从bayes的角度看LDA很重要，因为QDA的train和predict一般实现就是从bayes角度实现的。而且和 NaiveBayes中的关联Gaussian Naive Bayes classifier 也是从这个角度的。

[高斯判别分析模型](https://www.cnblogs.com/fanyabo/p/4067295.html)

[MLAPP 读书笔记 - 04 高斯模型(Gaussian models)](https://github.com/Kivy-CN/MLAPP-CN/blob/master/04%20Gaussian%20models.md)

![](/files/-M7DePJoN5kahYXoVUxo)\
LDA假设各类别的协方差一样，而QDA没有该要求，所以更灵活。

一般看y=1的概率，但是也可以看log-probability ratios 。\
（此不作为重点，因为一般分类用AUC来评价）

![](/files/-M7DePJpUNakU3lOEDeO)从此式也可以看出是关于x的一次函数，所以是线性判别![](/files/-M7DePJqxNHUC9Do0_GQ)

### 参考佳文

[Linear Discriminant Analysis 线性判别分析](https://blog.csdn.net/matrix_space/article/details/51375691)

<https://mp.weixin.qq.com/s/AeLwfmM0N-b1dfxt3v4C-A>

[线性判别分析LDA详解](https://blog.csdn.net/qianhen123/article/details/39832951)\
[机器学习中的数学(4)-线性判别分析（LDA）, 主成分分析(PCA)](http://www.cnblogs.com/LeftNotEasy/archive/2011/01/08/lda-and-pca-machine-learning.html)

[正则化最小二乘线性判别分析算法](http://www.doc88.com/p-9793175171823.html)

<https://blog.csdn.net/VictoriaW/article/details/78275394>

<http://www.doc88.com/p-147667786401.html>


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