# PCA

If I use all of the Principal components, I would expect the Matrix Product:

On the two column x 110row set I am trying, it is not remotely near it.

Are they being normalised wrt the zero-mean data set standard deviations?

or what?

Can anyone help?

• Hi

The case scores are indeed calculated from the standardised raw data (standardised to mean = 0 and for analyses using the correlation matrix to SD = 1). These are then multiplied by the Eigenvectors (the Component Score Coefficients matrix. in the statistiXL output).

Alan
• thanks Alan, that helped a lot, but I am still not quite with it.

I am assuming an SVD: A = U.S.V' with S the matrix of singular values and V the eigenvector matrix.

When I normalise the data as you say, and post-multiply it by the Eigenvector matrix, calculating A.V, I do indeed get the scores matrix, exactly as calculated by StatistiXL. Also the same eigenvalues and eigenvectors.

And the eigenvector matrix V is indeed orthonormal, so I can get from the scores back to the Normalised data by calculating A = Scores.V'.

But where do the loadings come in? I was under the impression that I should have:

willfoscue
• Hi

The factor loadings are calculated as the eigen vectors multiplied by the square root of teh eigenvalues.

Hope this helps.

Phil