For context, please see https://arxiv.org/pdf/1808.00084.pdf (page 6)
I am trying to replicate the results of the above link, which uses dimensionality reduction to observe a phase transition in an off-lattice freezing of hard disks. I have obtained the complete feature set but I am confused by the wording of the paper. Specifically, where it says "As the p_i (component scores) are defined at the feature vector level, ensemble-averaged analogs P_i ≡ < p_i >S are defined so that the average is implicitly limited to data at a single state point S."
Does anybody understand what this means in the context of the paper?