高维数据 | R语言绘图基础之主成分分析
高维数据 | R语言绘图基础之主成分分析
黑妹的小屋
发布于 2020-08-06 15:05:15
发布于 2020-08-06 15:05:15
高维数据可视化之主成分分析
在视觉性方面,人类普遍能够感知的是二维和三维空间。对于高维数据的可视化是将高维数据投影到二维或三维空间，去掉冗余属性，同时保留高维空间的数据和特征。说白了，高维数据的可视化就是使用降维度方法，主要分成线性和非线性两大类，关于非线性的非度量多维尺度分析NMDS见往期文章非度量多维尺度分析（NMDS），关于线性的PCA方法，见往期文章PCA做图最佳搭档-ggbiplot，本文主要针对迷弥小粉丝关于绘制线性PCA图数据处理过程遇到的问题进行记录。
01
原始数据
#迷弥小可爱提供的原始数据，为保密具体数值，此处公布随机数生成部分数据截图如下：
原始数据来看，变量“处理组”和“时间”属于中文字符型，需要将其改成英文的字符型“Treament”和“Time”，用reader时才可被RStudio识别。
02
ggbiplot绘制
#数据的导入。
library(readr)
Enzyme <- read_csv("~/Desktop/主成分分析/Enzyme.csv")
#导入
View(Enzyme)#查看Enzyme，确保导入成功，不乱码。
#数据处理。
我们处理数据的目标是研究不同的Treament对MDA，LOX等指标的影响。
>df1<-Enzyme[,2:10]
#预处理,选取Enzyme数据框中2到10列的数据形成新的矩阵df1.
> df1
# A tibble: 36 x 9
Time MDA LOX APX PAL CAT POD PPO TPC
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 40 41 19 58 80 186. 40 20 965
2 40 42 20 55 155 172. 34 37 955
3 40 43 17 51 92 166. 30 36 937
4 40 30 23 57 208 163. 85 23 1261
5 40 34 24 58 180 146. 89 26 1249
6 40 38 24 52 99 167. 81 21 1269
7 40 40 27 55 150 70.7 81 16 1322
8 40 30 30 54 104 56.7 81 16 1312
9 40 43 29 55 167 73.7 82 22 1357
10 40 46 27 58 96 66.7 64 22 1080
# … with 26 more rows
>Enzyme1.pca <- prcomp(df1,scale. = TRUE)
#对给定的数据矩阵进行主成分分析，并将结果作为类prcomp的对象返回。
> Enzyme1.pca
Standard deviations (1, .., p=9):
[1] 2.0909293 1.1638511 1.0689045 0.9458037 0.7227202 0.6075112 0.5181985 0.2353166 0.1451410
Rotation (n x k) = (9 x 9):
PC1 PC2 PC3 PC4 PC5 PC6 PC7
Time 0.46315503 -0.04916147 0.03637764 0.162115952 0.09831722 -0.05605495 0.15384446
MDA 0.43051775 -0.04773755 -0.14795093 -0.069491134 -0.36795168 -0.34716366 -0.30304858
LOX -0.09369929 0.32940027 -0.72371726 -0.441381496 -0.08318472 -0.00732021 0.37465711
APX -0.08716532 -0.75858481 -0.10162202 -0.059575764 -0.45541633 0.34852207 0.26596939
PAL 0.18847050 -0.30570836 0.24096297 -0.784312315 0.43453792 -0.08163434 -0.03770386
CAT -0.37539362 -0.03778714 0.33391251 -0.026114784 -0.18066354 -0.69437542 0.46568301
POD 0.41870137 0.00242730 0.02591931 0.254736824 0.31195985 0.10630817 0.65436944
PPO 0.44279023 -0.08209132 -0.12802074 -0.008043973 -0.27235413 -0.34781106 -0.01258019
TPC -0.18960223 -0.45795031 -0.50603522 0.299564950 0.49765782 -0.36567563 -0.16354171
PC8 PC9
Time -0.423321246 0.73470281
MDA -0.488029855 -0.44691662
LOX -0.086060923 0.09687049
APX -0.054174793 0.02299334
PAL 0.013325895 -0.02694037
CAT -0.113141408 0.03184374
POD 0.038176838 -0.46993978
PPO 0.746837400 0.16634344
TPC -0.009080942 -0.01764606#ggbiplot绘图
> library(ggbiplot)
>ggbiplot(Enzyme1.pca,obs.scale = 1,var.scale = 1,
groups =Enzyme$Treament,ellipse = TRUE,circle = TRUE)
+scale_color_discrete(name="")
+theme(legend.direction = 'horizontal'
,legend.position = 'top')
03
fviz_pca_ind绘制-1
#数据处理。
df<-Enzyme[c(2,3,4,5,6,7,8,9,10)]
View(df)
> Enzyme.pca<-PCA(df,graph=FALSE)
> Enzyme.pca
**Results for the Principal Component Analysis (PCA)**
The analysis was performed on 36 individuals, described by 9 variables
*The results are available in the following objects:
name description
1 "$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$col.w" "weights for the variables" #fviz_pca_ind()绘图
> library(factoextra)
> library(FactoMineR)
> fviz_pca_ind(Enzyme.pca,geom.ind="point",pointsize=3,
pointshape=21,fill.ind=Enzyme$Treament,
palette=c("#00AFBB","#E7B800","#FC4E07","blue"),
addEllipses=TRUE,legend.titl="Groups",title="")
+theme_grey()
04
fviz_pca_ind绘制-2
#数据处理。
我们处理数据的目标是研究在不同的作用时间Time对MDA，LOX等指标的影响。若直接按照fviz_pca_ind绘制-1提供的方法绘制PCA，这时候会出现以下错误：
>fviz_pca_ind(Enzyme2.pca,geom.ind="point",pointsize=4,pointshape=21,fill.ind=Enzyme$Time,palette=c("#00AFBB","#E7B800","#FC4E07"),addEllipses=TRUE,legend.titl="Groups",title="")+theme_grey()
错误: Continuous value supplied to discrete scale这是什么原因呢？？？我们来查看数据框
>str(Enzyme$Time)
num [1:36] 40 40 40 40 40 40 40 40 40 40 ...
#查看数据框中某列的数值类型，你会发现是num数值型，
而fill.ind=Enzyme$Time这列数据需要因子向量型。
>as.character(Enzyme$Time)
[1] "40" "40" "40" "40" "40" "40" "40" "40" "40" "40" "40" "40" "80" "80" "80"
[16] "80" "80" "80" "80" "80" "80" "80" "80" "80" "120" "120" "120" "120" "120" "120"
[31] "120" "120" "120" "120" "120" "120"
#将Time所在列的数据转换为字符型的因子向量。
>Enzyme$Time<-as.character(Enzyme$Time)
#将数据框中的某列的数值转换为因子向量，变量名仍为Time
>str(Enzyme$Time)
chr [1:36] "40" "40" "40" "40" "40" "40" "40" "40" "40" "40" "40" "40" "80" "80" "80" "80" ...
#再次查看，Time的类型，发现修改成功，变成字符型chr了。#绘图
> library(factoextra)
> library(FactoMineR)
> df2<-Enzyme[,3:10]
> df2
# A tibble: 36 x 8
MDA LOX APX PAL CAT POD PPO TPC
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 41 19 58 80 186. 40 20 965
2 42 20 55 155 172. 34 37 955
3 43 17 51 92 166. 30 36 937
4 30 23 57 208 163. 85 23 1261
5 34 24 58 180 146. 89 26 1249
6 38 24 52 99 167. 81 21 1269
7 40 27 55 150 70.7 81 16 1322
8 30 30 54 104 56.7 81 16 1312
9 43 29 55 167 73.7 82 22 1357
10 46 27 58 96 66.7 64 22 1080
# … with 26 more rows
> Enzyme2.pca<-PCA(df2,graph=FALSE)
> Enzyme2.pca
**Results for the Principal Component Analysis (PCA)**
The analysis was performed on 36 individuals, described by 8 variables
*The results are available in the following objects:
name description
1 "$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$col.w" "weights for the variables"
> fviz_pca_ind(Enzyme2.pca,geom.ind="point",
pointsize=4,pointshape=21,fill.ind=Enzyme$Time,
palette=c("#00AFBB","#E7B800","#FC4E07"),
addEllipses=TRUE,legend.titl="Groups",title="")
+theme_grey()
小结
ggbiplot：是ggplot2中绘制主成分的bioplot
groups：指可选因素的变量，即观测值所属的组。
prcomp()：对给定的数据矩阵进行主成分分析，并将结果作为类prcomp的对象返回。
PCA()：是FactoMineR包中主成分分析函数，能够对数据进行降维处理。
fviz_pca_ind():是factoextra包中的函数，能够以散点的形式展现数据分析结果。
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原始发表：2020-04-27，如有侵权请联系 cloudcommunity@tencent.com 删除
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