I was reading the descriptions for Variable decorrelation (4.1.2) and Principal component decomposition (4.1.3) in the TMVA User’s Guide. Between the two sections a distinction is made between signal (U=S) and background (U=B) transformations in Principal component decomposition.
What made sense to me is that when not specifying transformations on signal or background, the transformation would be calculated using a sample containing both signal and background together. Then the initial variables would be transformed and the analysis would proceed with the transformed variables. If Principal component decomposition (Principal Component Analysis, PCA) is indeed applied to separate samples of signal and background, that would mean there is one PCA basis for the signal sample and another PCA basis for the background sample. How then are the transformed variables coming from the signal basis related to the variables from the background basis in a linear discriminant analysis (LDA)? It is my understanding with LDA that signal and background are distinguished using the same set of variables.