Supporting Information for: Weighted distance functions improve analysis of high-dimensional data: application to molecular dynamics simulations

SAPPHIRE plot for Beta3S (Figure 6 in the main text). We represented the peptide by the sine and cosine values of 99 nonsymmetric dihedral angles. We used a stochastic, approximate algorithm to generate the progress indices for the SAPPHIRE plots in Figure 6. The stochastic algorithm is scalable to large data sets because of the preorganization of the data via tree-based, hierarchical clustering. The upper threshold radius and the tree height for the clustering were set to 1 and 8. The lower threshold radius was set to 0.487, 0.433, and 0.449 for the SAPPHIRE plots based on the UW (eq 1), GW (eq2), and LAW (eq 4) measures, respectively. These settings were chosen to have roughly 100000 clusters at the leaf-level. All the SAPPHIRE plots use snapshot 468441 as the starting snapshot. The number of guesses to find near neighbors was set to 4000. We made use of two recent improvements to the algorithm for generating the approximate progress index (Vitalis, manuscript submitted). First, after the initial clustering of the data, we cluster the data on the three levels of finest resolution again. This improves the homogeneity in the clustering on these levels. The algorithm for generating the approximate progress index requires the computation of near neighbors for the individual snapshots, and the hierarchical clustering is used to focus the search-space. Here, we allow to enlarge this search space if the number of 4000 guesses can otherwise not be satisfied. This is controlled via the CAMPARI keyword “FMCSC_CPROGRDEPTH,” which was set to 3.