msiDBN: A Method of Identifying Critical Proteins in Dynamic PPI Networks

Algorithm 1

Multisource integrated deep belief nets (msiDBNs).

Input: 2nd order of adjacency matrices of dynamic networks

  𝐴⁽¹⁾,…,𝐴^(𝑇) and learning rate 𝜀;

Output: Weight matrices 𝐴^(1)′,…,𝐴^(𝑇)′, bias for each network

   𝑑_𝑡 and bias for top common layer 𝑐;

 (1) Initialize Weight matrices 𝐴^(1)′,…,𝐴^(𝑇)′, 𝑑_𝑡 and 𝑐

 (2) repeat

 (3)  repeat

 (4)    pick up the samples 𝑣^(𝑡) of proteins 𝑠 at all time points;

 (5)     for all hidden units 𝑖  do

 (6)    compute 𝑃ℎ^(1𝑖)=1𝑣⁽¹⁾,…,𝑣^(𝑇) using (14);

 (7)    sample ℎ^(1𝑖) from 𝑃ℎ^(𝑡)=1𝑣⁽¹⁾,…,𝑣^(𝑇);

 (8)     end for

 (9)     for all  𝑡 in [1∶𝑇]  do

 (10)    compute 𝑃𝑣^(𝑡)′ℎ⁽¹⁾ using (13);

 (11)     sample 𝑣^(𝑡)′ from 𝑃𝑣^(𝑡)′ℎ⁽¹⁾;

 (12)    end for

 (13)    for all hidden units 𝑖  do

 (14)    compute 𝑃ℎ^(2𝑖)=1𝑣^(1)′,…,𝑣^(𝑇)′ using (14);

 (15)    end for

 (16)   until for all samples in 𝐴

 (17)  𝐴^(𝑡)′←𝐴^(𝑡)′+𝜀ℎ⁽¹⁾𝑣^(𝑡)′−𝑃(ℎ⁽²⁾=1∣𝑣^(𝑡))𝑣^(𝑡)′;

 (18)  𝑐←𝑐+𝜀ℎ⁽¹⁾−𝑃ℎ⁽²⁾=1𝑣^(1)′,…,𝑣^(𝑇)′;

 (19)  𝑑^(𝑡)←𝑑^(𝑡)+𝜀𝑣^(𝑡)−𝑣^(𝑇)′;

 (20) until all parameters are converged