I read book "Data mining methods and models" by Daniel T.Larose chapter 1 for finding correlation in multidimensional dataset by PCA. The chapter explain theory well. I had implemented PCA algorithm in java and also extracted variables as you mentioned in book.
I have one concerned , I want to prioritize/ show the extracted correlated variables from different principal components in deceasing order.
For an example, if first principal component with 1.67 eigen value give me two variables after omitting component weight less than 0.5:
X1 with partial correlation 0.623 X2 with partial correlation 0.567 .
Second principal component with 1.12 eigen value give me three correlated variables after omitting component weight less than 0.5
X1 with 0.98 partial correlation X3 with 0.68 partial correlation X4 with 0.96 partial correlation.
So and so forth might be until first four principal components or principal components that cover 60 % variability. So if i want to show extracted correlation variables from different principal components in descending orders. How i can do that.
Within one principal component is much easy . Variable with highest component weight within same principal component has high correlation than other variable. What about extracted variable from first principal component partial component weight comparison with other extracted variable partial component weight from second principal component. In other words, how i can compare X1 from first principal component and X4 from second principal component.
I read whole chapter, i did not find my answer. Could someone has idea about it ? Kindly suggest me , how in theory i could assign absolute correlation strength to each extracted variable in each principal component.