PCA and SVD
Using the SVD on matrix X (column as features)
We have X = U\sigmaV* where V contains the PCs and U\sigma would be the transformed data
PCA with linear regression
The application of PCA with linear regression is called Principal component regression (PCR), in which we use PCs as new predictors. With gene expression data, those PCs would be called eigengenes which could represent major expression patterns of genes with similar expression patterns across samples.(PCR has its own problem that PCs with low variation could have a significant effect on the response)
My question is: Why don't we use U\sigma, the transformed data as predictors? In what situations, could we use transformed data as predictors? What do those predictors mean?