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06-05-2012 04:28 PM

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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Solution

06-05-2012
04:43 PM

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Posted in reply to doudou66

06-05-2012 04:43 PM

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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Solution

06-05-2012
04:43 PM

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Posted in reply to doudou66

06-05-2012 04:43 PM

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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Posted in reply to PGStats

06-05-2012 04:52 PM

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?

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Posted in reply to doudou66

06-05-2012 05:02 PM

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

PG

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Posted in reply to PGStats

06-05-2012 05:03 PM

Thank you very much.