I'm recently reading a tutorial on Principal component analysis( A tutorial on principal components analysis/Lindsay I Smith). At the end it discusses about "getting the old data back". I'm wondering if there's any point of doing this? I've actually tried this with the dataset named "USArrests" under princomp function in R. By transforming back to the old dataset I get exactly the same number of variables as we have for the original dataset, and what's worse, the transformed variables are 100% correlated. In this sense PCA cannot reduce the number of original variables and therefore eliminate the correlations between them.
Thanks for your advice!
principal components analysis
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PCA is useful for certain data set, not every one. One example PCA works well is for face image noise reduction. You can get well reconstructed image with much lower dimensions than original one.