Figure 4

Illustration of the graph pyramid search subroutine. Here we elaborate the algorithm 1 using 5 different queries. For simplicity assume T _AC = 0, t _AC = {t₁, t₂, t₃} and only 3 protein classes i.e. $\left|{ℂ}_M\right|=3$. Each query q _i , is analyzed first at the highest level (t₃) where we look for all classes $c\in {ℂ}_M$, having ΔAC(c, t₃) > T _AC and collect them in ${ℂ}_{AC}\subseteq {ℂ}_M$. For q₁ we can not find any such classes c at t₃, so we descend the GP to t₂ level and discover ${ℂ}_{AC}=\left\{c_2,c_3\right\}$ with threshold t^∗ = t₂. This secondary threshold (T _AC ) is necessary, otherwise there will be many spurious classes (false positives (FP)) having nonzero ΔAC(·).