Calculate PCA score from coefficient and original data

Hi all,

I want to do cross validation of a non-linear regression on principal components as input. Therefore, I do PCA on my training set, and use the regression coefficient to transform the standardized test set into their principal components. However in the following I found pc score!=zscore(data)*coef. Appreciate if anyone can explain to me. Thanks alot.

[coef2, score2, latent2, explained2, mu2] = pca(data_raw_ccc(:,2:end));
zdata=zscore(data_raw_ccc(:,2:end));
score3=zdata*coef2;
diff=score3-score2; % NOT EQUAL 0, WHY?

Answer 1

[the cyclist]

By default, pca centers the data around the mean, but does not scale it to unit variance.

The original data can be reconstructed by

score2*coef2

[Hadi Hadi]

Hi cyclist,

Do you mean then the score = centered data*coef? I checked the following but they are still not the same. Any idea? Thanks.

data=data_raw_ccc(:,2:end);
[coef2, score2, latent2, explained2, mu2] = pca(data);

% zdata=zscore(data);
mean_data=mean(data);
center_data=data-repmat(mean_data,[size(data,1) 1]);

score3=center_data*coef2;
diff=score3-score2; % NOT EQUAL 0, WHY?

[the cyclist]

Did you notice that the elements of diff are of order 10^-15?

diff is equal to zero, to within floating point error.

[Hadi Hadi]

You are right, the diff are indeed of very small value I did not notice, which I think means the transformation from original data to the scores is correct. Many thanks for pointing it out :)

[Shawn Miller]

I think you are saying score2*coef2' or score2*inv(coef2)?@the cyclist

[the cyclist]

Four years after-the-fact, I have seen this reply. Yes, you are correct. It should be

score2*coef2'

:-)