I am supposed to write a literature review on a particular paper for my University and I am lost after reading the main paper I am supposed to read. The link to the paper is here. The paper is from CERN and deals with using machine learning techniques to speed up the ATLAS calorimeter simulation.
In this, to simulate particle shower at CERN, they use a double PCA technique. First the events are decorrelated using PCA, the first principle component is taken and each event is grouped into 10 binns of the first PC. I don't understand this part. Can someone please tell me what one is doing when you bin the data points using a principle component? I tried searching but I cannot seem to find any reference to this concept anywhere. Even a pointer to a paper/write-up explaining this binning(why and how) would be really great.
The energy deposits per layer are correlated with each other. If, for example a large amount of energy is lost in the first layers, less will be deposited in the layers behind. In order to decorrelate those energy deposits, a principal component analysis (PCA) is used. A PCA is a transformation of a set of variables into a set of orthogonal and uncorrelated, so-called principal components. The first component has the largest variance. In order to achieve a better decorrelation, the events are divided into bins of the first (and/or second) component. The bins have approximately the same number of events, and typically a number of bins between 5 and 10 is chosen. A second PCA transformation is applied to the energy deposits per layer for the events in each of those bins, and hence the components of that second transformation are now largely decorrelated.
This is the paragraph explaining the procedure. The section which is bold is where I am confused.