The overlap profiles were clustered using the Ward agglomerative method and the binary distance metric (see hclust documentation in the R statistical computing framework [65]).
For the congruence analyses with tissue type information, we represented each cell line as a binary indicator vector based on its tissue origin, resulting in binary distance matrix (0 for the same tissue origin, 1 otherwise).
Hierarchal clustering among genomes using presence/absence of MCL gene clusters was performed using the complete linkage method and binary distances as implemented in the R package pvclust (Suzuki and Shimodaira 2006).
We used a bell-shaped function of distance to highway to overcome the inherent arbitrariness in defining a binary distance index and to explore the profiles of risk gradients.
Bivariate correlations obtained using genetic (≥98%, <98% homology), Euclidean (≤5, >5 km), temporal (≤1, >1 month) binary distances and ownership (same, different) are also presented in Table 3. Significant correlations involving genetic distances were marginally influenced by adjustment for anyone of the other binary distances using the Partial Mantel Test (Table 4).
Considering the special situation of the structured ontology, we defined two types of binary distance metrics, as shown in Equations (1) and (2).
In order to find the DO terms with very similar associated genes, we perform clustering based on gene-to-DO mapping matrix M. Two types of clustering based on two different binary distance metrics, as shown in Equations (1) and (2), are performed.
We calculated the distance in the promoter motifs between any two promoters by using the dist function in R [ 56] with the asymmetric binary distance measure.
In some cases the distances in the binary complexes are shorter than in the ternary complex.
With binary distances, two to three times more combinations of strains having ≥98% homology were observed in pairs of sites located at ≤5 km from each other compared to others with distances >5 km, and this association was supported by the Mantel using binary distances (Tables 2 3 and 4).
