Interpreting PCA Results

问题

I am doing a principal component analysis on 5 variables within a dataframe to see which ones I can remove.

df <-data.frame(variableA, variableB, variableC, variableD, variableE)

prcomp(scale(df))
summary(prcomp)

gives the following results

                          PC1    PC2    PC3     PC4     PC5
Proportion of Variance 0.5127 0.2095 0.1716 0.06696 0.03925

My issue is that if I change the order of the variabes in the dataframe, I get the same results

df <-data.frame(variableC, variableF, variableA, variableE, variableB)

prcomp(scale(df))
summary(prcomp)

                          PC1    PC2    PC3     PC4     PC5
Proportion of Variance 0.5127 0.2095 0.1716 0.06696 0.03925

How do I know which of the 5 variables is related to PC1, which to PC2 etc?

回答1:

Here is an approach to identify the components explaining up to 85% variance, using the spam data from the kernlab package.

library(kernlab)
data(spam)
# log transform independent variables, ensuring all values above 0
princomp <- prcomp(log10(spam[,-58]+1))
stats <- summary(princomp)
# extract variable importance and list items explaining up to 85% variance
importance <- stats$importance[3,]
importance[importance <= 0.85]

...and the output:

> importance[importance <= 0.85]
    PC1     PC2     PC3     PC4     PC5     PC6     PC7     PC8     PC9    PC10    PC11 
0.49761 0.58021 0.63101 0.67502 0.70835 0.73188 0.75100 0.76643 0.78044 0.79368 0.80648 
   PC12    PC13    PC14 
0.81886 0.83046 0.84129 
>

We can obtain the factor scores for the first 14 components as follows.

resultNames <- names(importance[importance <= 0.85])
# return factor scores 
x_result <- as.data.frame(princomp$x[,resultNames])
head(x_result)

...and the output:

> head(x_result)
         PC1         PC2          PC3          PC4          PC5         PC6         PC7
1  0.7364988  0.19181730  0.041818854 -0.009236399  0.001232911  0.03723833 -0.01144332
2  1.3478167  0.22953561 -0.149444409  0.091569400 -0.148434128 -0.01923707 -0.07119210
3  2.0489632 -0.02668038  0.222492079 -0.107120738 -0.092968198 -0.06400683 -0.07078830
4  0.4912016  0.20921288 -0.002072148  0.015524007 -0.002347262 -0.14519336 -0.09238828
5  0.4911676  0.20916725 -0.002122664  0.015467369 -0.002373622 -0.14517812 -0.09243136
6 -0.2337956 -0.10508875  0.187831101 -0.335491660  0.099445713  0.09516875  0.11234080
          PC8          PC9        PC10        PC11        PC12         PC13        PC14
1 -0.08745771  0.079650230 -0.14450436  0.15945517 -0.06490913 -0.042909658  0.05739735
2  0.00233124 -0.091471125 -0.10304536  0.06973190  0.09373344  0.003069536  0.02892939
3 -0.10888375  0.227437609 -0.07419313  0.08217271 -0.12488575  0.150950134  0.05180459
4 -0.15862241  0.003044418  0.01609690  0.01720151  0.02313224  0.142176889 -0.04013102
5 -0.15848785  0.002944493  0.01606874  0.01725410  0.02304496  0.142527110 -0.04007788
6 -0.13790588  0.197294502  0.07851300 -0.08131269 -0.02091459  0.246810914 -0.01869192
>

来源：https://stackoverflow.com/questions/61146988/interpreting-pca-results

标签

pca