Personalized PageRank analysis for FELLA.
The PageRank method uses the personalized PageRank algorithm to propagate importance from input compounds through the KEGG network.
Mathematical formulation: M = transition matrix (column-stochastic) d = damping factor (default 0.85) p = personalization vector (uniform over input compounds) PR = (1-d) (I - dM)^{-1} * p
The damping factor d controls the trade-off between:
- Following the network structure (d close to 1)
- Restarting from input compounds (d close to 0)
P-score computation follows the same approach as diffusion: z_i = (pr_i - mu_i) / sigma_i p_i = Phi(z_i)