R语言主成分分析(PCA)加“置信椭圆”

使用R语言为PCA散点图加置信区间的方法，我知道的有三种，分别是使用ggplot2,ggord,ggfortify三个包去绘制。后面两个R包是基于ggplot2的快捷返方法。

1.对数据集进行主成分分析

现在拿一组数据集为例，使用先R中的prcomp()基础函数完成主成分分析

查看数据类型，每一列代表一个样本，每一行代表一个基因（变量）
> head(a,3)
                X1_untreated X2_untreated X3_untreated X4_untreated    X1_Dex    X2_Dex
ENSG00000223972    -2.089725    -2.090478    -2.090475    -2.089265 -2.079351 -2.087724
ENSG00000227232     6.760110     6.892673     6.346646     6.739761  6.450597  6.749787
ENSG00000243485     0.000000     0.000000     0.000000     0.000000  0.000000  0.000000
                   X3_Dex    X4_Dex
ENSG00000223972 -2.091304 -2.089408
ENSG00000227232  6.623112  6.524621
ENSG00000243485  0.000000  0.000000
b <- t(a)#PCA分析需要将表达矩阵转置 
-----------------标准化处理--------------
R函数：scale(data, center=T/F, scale=T/F)或者scale(data)
参数：center (中心化)将数据减去均值，默认为T
参数：scale (标准化)在中心化后的数据基础上再除以数据的标准差,默认值F,建议改为T
c <- prcomp(b[ , which(apply(data, 2, var) != 0)], scale=TRUE)
summary(c)
可以看到pc1方差的解释率达23.05%，pc2的方差的解释率达18.8%，等等
Importance of components:
                           PC1     PC2     PC3     PC4     PC5      PC6      PC7       PC8
Standard deviation     86.1425 77.7838 71.9321 64.5281 59.7924 54.48867 53.27203 3.021e-12
Proportion of Variance  0.2305  0.1880  0.1607  0.1293  0.1111  0.09223  0.08816 0.000e+00
Cumulative Proportion   0.2305  0.4185  0.5792  0.7086  0.8196  0.91184  1.00000 1.000e+00
> 

2.使用ggplot2可视化

提取不同记录的PC1-PC8数值，即点的横纵坐标值
dt = c$x
> head(dt,3)
                   PC1        PC2       PC3         PC4       PC5        PC6      PC7
X1_untreated -70.89354   47.84633 -93.91127    3.457347 -32.08983 -72.516671 60.80422
X2_untreated -89.78212   14.29189  61.29232 -102.245406 -39.00539  59.352006 21.05424
X3_untreated -81.40448 -105.32841 -15.33420   19.990771 107.24132   9.986499  4.28529
                      PC8
X1_untreated 2.802701e-12
X2_untreated 2.715383e-12
X3_untreated 2.618101e-12
condition 
 condition
1   control
2   control
3   control
4   control
5     treat
6     treat
7     treat
8     treat
将condition列添加到dt中
dt = cbind(dt,condition)
> head(dt,3)
                   PC1        PC2       PC3         PC4       PC5        PC6      PC7
X1_untreated -70.89354   47.84633 -93.91127    3.457347 -32.08983 -72.516671 60.80422
X2_untreated -89.78212   14.29189  61.29232 -102.245406 -39.00539  59.352006 21.05424
X3_untreated -81.40448 -105.32841 -15.33420   19.990771 107.24132   9.986499  4.28529
                      PC8 condition
X1_untreated 2.802701e-12   control
X2_untreated 2.715383e-12   control
X3_untreated 2.618101e-12   control
生成坐标轴标题
summ = summary(c)
xlab = paste0("PC1(",round(summ$importance[2,1]*100,2),"%)")
ylab = paste0("PC2(",round(summ$importance[2,2]*100,2),"%)")
载入ggplot2包
library(ggplot2)
ggplot(data = dt,aes(x=PC1,y= PC2,color=condition))+stat_ellipse(aes(fill=condition),type="norm",geom="polygon",alpha=0.2,color=NA)+geom_point()+labs(x=xlab,y=ylab,color="")+guides(fill=F)

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