We now apply the Linear Discriminant Analysis (see section 2.2.5. for the mathematical details) to this high-dimensional dataset and ensure that they are projected in a low-dimensional space (here a 1D line) in such a way that the clusters (representative of the datasets in a given bin) are maximally separated. Each cluster represent a given state: the reference state or any one of the two perturbed states, corresponding to a given bin. A given cluster in a given bin corresponding to a given state (reference or perturbed) consists of datapoints associated with the average value of nxy in that bin corresponding to the chosen state. Thus, we get clusters corresponding to bin k (k = 1, 2,…,7) for either the reference or the perturbed state.