sPCA tuning results y-axis interpretation

Analysis
1

Hi,

I have a question regarding the output of sPCA tuning, so when plotting the “tune.spca” the y-axis says “correlation of components” and it says “average correlation between the predicted and actual components” in the tutorial. It is a bit ambiguous to me how exactly is this correlation calculated and what are “predicted” components?

2

All the tune functions work like this (including tune.spca()):

  • Data randomly segmented into folds
  • For each fold:
    • Use this one as testing and all remaining as training.
    • Build sPCA model using training data. Use this to predict variate values of all testing samples. These are the “predicted components”.
    • Build sPCA model using all data (training and testing). Extract variate values for samples contained in testing data. These are the “actual components”
    • Record the correlation between the predicted components and the actual components
  • Repeat this for all repeats and keepX values

So the “average correlation between the predicted and actual components” is the mean value of the correlation between samples’ variates predicted by a model and the true sample variates (true referring to model which uses all samples). Hope this clears things up!

3

Thanks for your reply.
So, by “variate values”, do you mean loadings?
Also, if I understand it correctly, PCA is a dimensionality reduction technique in which we go from a dataset to a covariance matrix and perform eigendecomposition on that. So, how can this procedure be used to “predict” variates for another dataset (test set)?