**510**wrote:

I used Principal Component Analysis technique (PCA) under R to reduce the number of explanatory (independent) variables in my model (i.e PCA was used for variable reduction only). After running PCA, I got the components (10 components). What I want to do know is return these components back to the original variables(i.e I want to know what are the variables inside each of these components). My original data matrix contains 35,000 rows and 500 columns.

**4.7k**• written 4.0 years ago by M K •

**510**

What you want are probably the loadings. If you don't have access to them, you can try to calculate them manually. Correct me if I am wrong anyone, but the loadings are essentially the correlation of standardized original observations to the PCs.

15kDo you still have the matrix of loadings, or just the 10 PCs?

12kI have both of them.

510Then you can certainly get very very close to your original data - and you can even interpolate data you don't have, if you wish. Of course, it depends on how much of the variance 10 PCs will explain, but it's likely to be most of it. (...right? should be in the report)

Unfortunately PCA can differ from implementation to implementation depending on how the centering is done, and some other minor details, so you really will have to take a proper look at the code used to generate the loadings and PCs if you didn't use the generic R prcomp().

A good place to start is: http://stats.stackexchange.com/questions/229092/how-to-reverse-pca-and-reconstruct-original-variables-from-several-principal-com

and an R specific demo here: http://stats.stackexchange.com/questions/57467/how-to-perform-dimensionality-reduction-with-pca-in-r/57478#57478

12k