A general question aiming at the application of a PCA: I want to detect abnormal data points and therefore I want to use a PCA for it at first. The next step is to try several distance functions or quantils of distributions or something similar to check if it is working. My problem is: How do I know this when I operate on the dimensionally reduced data set? Or in other words: How do I transform it back to see if the certain marked data points match the ones from the original non-transformed data?
I expect something to do like here:
How do I know that this outlier in the transformed/reduced data is sensefull? I think I have to cross-check it somehow in the original data?