Table 1 Overall framework of the HEPT method

Algorithm 1: HEPT method

Input: A PPI network G, protein domain, GO annotation, orthologs datasets, subcellular localization datasets; stopping threshold ε

Output: Top N proteins sorted by VA in descending order

Step 1. Construct the tensor T according to Equation (1), (2), (3), (4)

Step 2. Calculate jump probability vector D with Equation (12), (13), (14), (15)

Step 3. Construct two transition probability tensors T^(a) , T^(h), and T^(e) with Equation (6)-(8)

Step 4. Initialize VA₀ = 1/n, VH₀ = 1/n, VE₀ = 1/m

Step 5. Let t = 1

Step 6. Calculate VA_t = (1 − α) × D + α × T^(a) × VH_t − 1VE_t − 1

Step 7. Calculate VH_t = T^(h) × VA_t × VE_t − 1

Step 8. Calculate VE_t = T^(e) × VA_t × VH_t

Step 9. If ‖VA_t − VA_t − 1‖ + ‖VH_t − VH_t − 1‖ + ‖VE_t − VE_t − 1‖ ≥ ε_{, then let VA = VAt, VH = VHt, VE = VEt. Otherwise, let t = t + 1, and then go to Step 6.}

Step 10. Sort proteins by the value of VA in the descending order

Step 11. Output top N of sorted proteins