Should I use normalized data for correlation calculation or not?

Question

I write down a script to calculate correlation to remove highly correlated variable before feature selection and ML model building.

library('caret')

df1 = read.csv("stack.csv")

print (df1)

     GA     PN     PC   MBP    GR    AP
1 0.033  6.652  6.681 0.194 0.874 3.177
2 0.034  9.039  6.224 0.194 1.137 3.400
3 0.035 10.936 10.304 1.015 0.911 4.900
4 0.022 10.110  9.603 1.374 0.848 4.566
5 0.035  2.963 17.156 0.599 0.823 9.406
6 0.033 10.872 10.244 1.015 0.574 4.871
7 0.035 21.694 22.389 1.015 0.859 9.259
8 0.035 10.936 10.304 1.015 0.911 4.500


df2 = cor(df1)
hc = findCorrelation(df2, cutoff=0.3) # putt any value as a "cutoff" 
hc = sort(hc)
reduced_Data = df1[,-c(hc)]
print (reduced_Data)

     GA     PN    GR    AP
1 0.033  6.652 0.874 3.177
2 0.034  9.039 1.137 3.400
3 0.035 10.936 0.911 4.900
4 0.022 10.110 0.848 4.566
5 0.035  2.963 0.823 9.406
6 0.033 10.872 0.574 4.871
7 0.035 21.694 0.859 9.259
8 0.035 10.936 0.911 4.500

My question is that to remove the correlated feature should I used normalized data.

preObj <- preProcess(nd[,2:(x-1) ], method=c("center", "scale"))
normalized_Data <- predict(preObj, nd[,2:(x-1)])

or I can use the raw data to calculate the correlation.

Thank you.

Answer 1

Since the formula for calculating the correlation coefficient standardizes the variables, changes in scale or units of measurement will not affect its value. For this reason, normalizing will NOT affect the correlation.