Programming the statistical procedures from SAS

Principle Components Analysis clarification needed

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Principle Components Analysis clarification needed

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 ?


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‎06-05-2012 04:43 PM
Respected Advisor
Posts: 4,606

Re: Principle Components Analysis clarification needed

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

PG

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‎06-05-2012 04:43 PM
Respected Advisor
Posts: 4,606

Re: Principle Components Analysis clarification needed

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

PG
Contributor
Posts: 24

Re: Principle Components Analysis clarification needed

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?

Respected Advisor
Posts: 4,606

Re: Principle Components Analysis clarification needed

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

PG
Contributor
Posts: 24

Re: Principle Components Analysis clarification needed

Thank you very much.

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