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How to make a forecast using ATP

I was able to calculate the eigenvectors / values ​​of my sample data (N samples of dimension M), and I would like to reduce the dimension to say 3. If I'm right, I need to select the first 3 eigenvectors (with the largest eigenvalues).

From these 3 PCs and from observing (in the initial base) a new sample (now looking only at 3 dimensions).

How can I predict what other values ​​of M-3 will be?

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Yes, using the x most significant components in the model, you reduce the dimension from M to x

If you want to predict - that is, you have Y (or several Y), you end up in the PLS, not the PCA

Trusting Wikipedia comes to the rescue as usual (sorry, it doesn't seem to add a link when writing on an iPad)

http://en.wikipedia.org/wiki/Partial_least_squares_regression

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