Principle Components Analysis clarification needed

[doudou66]

Hello, All

Suppose my data have two variables A and B. Total_Variance_Original_Data = Var(A) + Var(B) + 2Cov(A,B)

Now I do Principle Components Analysis and get two new variables, say PC_1 and PC_2, with eigenvalues λ_1, and λ_2; Total_Variance_PCA_Explained = λ_1 +  λ_2

My question is: are theses two variances equal to each other, Total_Variance_Original_Data = Total_Variance_PCA_Explained ?

[PGStats · Accepted solution]

Yes, if you do the analysis on the covariance matrix, that is, with the COV option (it is not the default option in PRINCOMP). You should analyse the covariance matrix only when your variables are roughly on the same scale.

PG

[doudou66]

Thank you very much for helping me.

If variables are not on the same scale (say, variable A is ~1000, and variable B is ~1), should I do normalization on each original variable (i.e. (original_variable - mean)/standard_deviation ) before doing PCA? or is there any other method?

[PGStats]

Exactly! PRINCOMP without the COV option does that normalization for you. - PG

[doudou66]

Thank you very much.