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PCA factor loadings' directionality?

Hi Charles,

I've finished the HUDK4051 collaborative filter assignment but have some outstanding question about PCA we had to run in the end.

Is it appropriate that we apply absolute value (abs()) onto the eigenvectors to count the proportional contribution to PCs in all cases (what we did last semester)?

My previous training (hope not trapped in education stats again) taught me after we rotate the axes, the direction matters to interpret the PCs. So when looking at the loadings, I assume we should check each column and pick the positive values which make positive contribution (correlation), and hope that there is no overlap of such values in different PCs. If we apply abs(), we won't achieve this?

Also, I am assuming the purpose of running PCA on this is to see if "pred" unit will converge with other units, but what's the point to do doth interest & difficulty? Ideally, is it because we want to see "pred" unit will converge with other units NOT just for interest, but also for difficulty, too? Or simply put, what will be the worst case if student is just picking the easiest unit to their interest?

Thank you so much ~

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