Fig. 6

Comparison of classical and nonclassical metric MDS methods. a, b Action of the MDS step at various scales of the 3D structure, analyzed quantitatively by computing for each pair of sites (i,j) the relative difference |D _ij −R _ij | / D _ij between the shortest-path distances D _ij and the reconstructed distances R _ij . This relative difference is represented component-wise as a scatter plot with respect to the distances D _ij for two values α=0.2 and α=1 of the edge-length exponent α, for both nonclassical metric MDS (mMDS, top) and classical MDS (cMDS, bottom). The color scale is related to the density of points in the scatter plot (increasing density from blue to red). c, d 3D structures obtained for α=0.2 and α=1 with classical MDS (blue) and nonclassical MDS (red). A comparison between panels (c and d) would require a suitable 3D alignment, see Fig. 7 below. Same data as in Fig. 4 a