Figure 9. Concept-pair promiscuity decreases as score increases.

Spearman’s rank correlation rho for OA is −0.4934008, and for oA is −0.3893343. Promiscuity of a domain-pair (a, b) is [N(a)+N(b)]/2 where N(d) is the number of times domain d occurs in a set of proteins. For a concept-pair (c_i, c_j), promiscuity is the average promiscuity of all domain-pairs in A^L(c_i) × A^L(c_j), and the score is the log-odds ratio of interacting protein-pairs to non-interacting protein-pairs in O^L(c_i) × O^L(c_j). For OA concept-pairs that produce a score in [−12, −10), the median promiscuity is 133.5 and the mean promiscuity is 129.2; when the score is 0.0, the median promiscuity falls to 13.25 and the mean promiscuity is 23.47. There were no oA scores smaller than −12.0. In non-attribute-reduced concept lattices (OA and oA), a domain-pair can be generated by more than one concept-pair (c_i, c_j) through the cross-product of their attribute-label sets, i.e. A^L(c_i) × A^L(c_j). This paves the way for a more promiscuous domain-pair to have the same score as a less promiscuous domain-pair. The piggy-backing mechanism takes effect when a domain-pair improves its score because either one or both of its domain partners happen to occupy the same attribute-label set as one or more rarer domains.