PCA：principal component analysis，主成分分析。将n个维度，通过线性转换为新的n个线性无关的按方差解释度排序的主成分(principal component, PC)。
核心函数：
prcomp()princomp()FactoMineR::PCA()
由于基础函数画出的图相对比较单一，因此就有大神针对针对这个问题开发了R包：FactoMineR和factoextra。
# data为表达矩阵，prcomp默认带有数据标准化功能，如果已标准化，center=F, scale=F)
res.pca <- prcomp(data, center=F, scale=F)
下面以factoextra包自带的decathlon2数据集为例：
decathlon2是27名运动员，在Decastar和OlympicG两项运动会，十项全能运动的成绩。(其中4名为替补队员)
注意：PCA的输入数据，需要进行
归一化让数据间具有可比性。
参数解读：
PCA(X, scale.unit = TRUE, ncp = 5, graph = TRUE)
- X：数据框
- scale.unit：a logical value. If TRUE, the data are scaled to unit variance before the analysis. This standardization to the same scale avoids some variables to become dominant just because of their large measurement units. It makes variable comparable.
- ncp：最终降维后，输出的维度数目。
- graph：是否画图展示。
1.基础版
res.pca <- prcomp(decathlon2.active,scale. = T)
> res.pca
Standard deviations (1, .., p=10):
[1] 2.0308159 1.3559244 1.1131668 0.9052294 0.8375875 0.6502944 0.5500742 0.5238988
[9] 0.3939758 0.3492435
Rotation (n x k) = (10 x 10):
PC1 PC2 PC3 PC4 PC5 PC6
X100m -0.418859080 0.13230683 -0.27089959 0.03708806 -0.2321476 0.054398099
Long.jump 0.391064807 -0.20713320 0.17117519 -0.12746997 0.2783669 -0.051865558
Shot.put 0.361388111 -0.06298590 -0.46497777 0.14191803 -0.2970589 -0.368739186
High.jump 0.300413236 0.34309742 -0.29652805 0.15968342 0.4807859 -0.437716883
X400m -0.345478567 -0.21400770 -0.25470839 0.47592968 0.1240569 -0.075796432
X110m.hurdle -0.376265119 0.01824645 -0.40325254 -0.01866477 0.2676975 0.004048005
Discus 0.365965721 -0.03662510 -0.15857927 0.43636361 -0.4873988 0.305315353
Pole.vault -0.106985591 -0.59549862 -0.08449563 -0.37447391 -0.2646712 -0.503563524
Javeline 0.210864329 -0.28475723 -0.54270782 -0.36646463 0.2361698 0.556821016
X1500m 0.002106782 -0.57855748 0.19715884 0.49491281 0.3142987 0.064663250
PC7 PC8 PC9 PC10
X100m -0.16604375 -0.19988005 -0.76924639 0.12718339
Long.jump -0.28056361 -0.75850657 -0.13094589 0.08509665
Shot.put -0.01797323 0.04649571 0.12129309 0.62263702
High.jump 0.05118848 0.16111045 -0.28463225 -0.38244596
X400m 0.52012255 -0.44579641 0.20854176 -0.09784197
X110m.hurdle -0.67276768 -0.01592804 0.41058421 -0.04475363
Discus -0.25946615 -0.07550934 0.03391600 -0.49418361
Pole.vault -0.01889413 0.06282691 -0.06540692 -0.39288155
Javeline 0.24281145 0.10086127 -0.10268134 -0.01103627
X1500m -0.20245828 0.37119711 -0.25950868 0.17991689
提取PC矩阵的两种方法
res.pca1 <- res.pca$x
res.pca2 <- predict(res.pca)
2.进阶版
2.1 示例数据
rm(list = ls())
library(FactoMineR)
decathlon2.active <- decathlon2[1:23,1:10]
res.pca <- PCA(decathlon2.active,graph = F)
res.pca
## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 23 individuals, described by 10 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"
2.2 可视化及注释
核心函数：
get_eigenvalue(res.pca)fviz_eig(res.pca)-
get_pca_ind(res.pca),get_pca_var(res.pca) -
fviz_pca_ind(res.pca),fviz_pca_var(res.pca) fviz_pca_biplot(res.pca)
library(factoextra)
eig.val <- get_eigenvalue(res.pca)
eig.val
## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 4.124 41.24 41.2
## Dim.2 1.839 18.39 59.6
## Dim.3 1.239 12.39 72.0
## Dim.4 0.819 8.19 80.2
## Dim.5 0.702 7.02 87.2
## Dim.6 0.423 4.23 91.5
## Dim.7 0.303 3.03 94.5
## Dim.8 0.274 2.74 97.2
## Dim.9 0.155 1.55 98.8
## Dim.10 0.122 1.22 100.0
epigenes可视化
fviz_eig(res.pca,addlabels = T)
Colors by groups
var <- get_pca_var(res.pca)
set.seed(123)
res.km <- kmeans(var$coord,centers = 3,nstart = 25)
grp <- as.factor(res.km$cluster)
fviz_pca_var(res.pca,col.var = grp,
palette = c("#0073C2FF", "#EFC000FF", "#868686FF"),
legend.title = "Cluster")
3. 实用版
以iris数据集为例，添加cluster及分组信息。
iris.pca <- PCA(iris[,-5],graph = F)
fviz_pca_ind(iris.pca,
geom = "point",
col.ind = iris$Species,
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # Concentration ellipses
legend.title = "Groups")
加上小箭头
fviz_pca_biplot(iris.pca,
col.ind = iris$Species, palette = "jco",
addEllipses = TRUE, label = "var",
col.var = "black", repel = TRUE,
legend.title = "Species")
ggplot2版
iris.pca1 <-prcomp(iris[,-5])
pcapredict <- predict(iris.pca1)
rt <- data.frame(PC1=pcapredict[,1],PC2=pcapredict[,2],group=iris[,5])
library(ggsci)
ggplot(rt,aes(PC1,PC2))+
geom_point(aes(color=group))+
scale_color_lancet()+
theme_bw()+
theme(plot.margin = unit(rep(1.5,4),"lines"),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank())
参考链接：
A COMPLETE GUIDE TO PRINCIPAL COMPONENT ANALYSIS – PCA IN MACHINE LEARNING
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