Spherical dissimilarity indices and normed multidimensional scaling

Our concern here, is the characterization of dissimilarity indexes defined over finite sets, whose spatial representation is spherical. Consequently, we propose a methodology (Normed MultiDimensional Scaling) to determine the spherical euclidean representation of a set of items best accounting for the initial dissimilarity between items. This methodology has the advantage of being graphically readable on individual qualities of projection like the normed PCA, of which is constitutes a generalization. Moreover, it avoids the arbitrary character of spherical encloding which the use of similitude functions currently used in MDS implies.