Since we want a parameterization in terms of a few scalar values, the main method we will use from the class is the backproject method. It takes principal component coordinates of projected vectors and reconstructs the original ones. We could retrieve the original vectors if we retained all the components, but the difference will be very small if we just use a couple of components; that's one of the reasons for using PCA. Since we want some variability around the original vectors, our parameterized scalars will be able to extrapolate the original data.