Max-correlation embedding computation

In this paper, we present a method to compute an embedding matrix which maximises the dependence of the embedding space upon the graph-vertex coordinates and the incidence mapping of the graph. This treatment leads to a convex cost function which, by construction, attains its maximum at the leading singular value of a matrix whose columns are given by the incidence mapping and the embedded vertex coordinates. This, in turn, maximises the correlation between the spaces in which the embedding and the graph vertex coordinates are defined. It also maximises the dependence between the embedding and the incidence mapping of the graph. We illustrate the utility of the method for purposes of approximating the colour sensitivity functions of a set of over 20 commercially available digital cameras using a library of spectral reflectance measurements.