Two-Stage Approach for Protein Superfamily Classification

Algorithm 5

ROLSA( ).

Let 𝐍 = number of training samples

𝑛_ℎ = number of randomly chosen hidden centres.

𝐘 = desired output matrix of size 𝑁×𝑝 where 𝑝 is the number of nodes in the output layer.

𝑌 = neural network output matrix of size 𝑁×𝑝.

𝜙 = hidden layer output matrix of size 𝑁×𝑛_ℎ

𝐄 = error matrix of size 𝑁×𝑝.

𝑊_ℎ𝑝 = connecting weight between the hidden and output layer of size 𝑛_ℎ×𝑝.

 Step  1. Perform QR decomposition of 𝜙 matrix.

 Step  2. Evaluate 𝑄^𝑇𝑌𝑌𝑌= where 𝑌 is of size 𝑛_ℎ×𝑝 and 𝑦 is of size 𝑁−𝑛_ℎ×𝑝.

 Step  3. Evaluate the loss function (𝑉)=𝑌(𝑁)²_𝐹/(𝑁)

 Step  4. Evaluate the Akaike's final prediction error ()=𝑛𝐹𝑃𝐸𝑉1+𝛽_ℎ/𝑁1−𝛽𝑛_ℎ𝑉/𝑁

 Step  5. Remove each network center 𝑘 and compute the loss functions.

  𝑟𝑒𝑚𝑜𝑣𝑒−ℎ𝑖𝑑𝑑𝑒𝑛()

  {

  for  every hidden node 𝑖=1 to 𝑛_ℎ  do

   𝑅(∶,𝑖)=[]

   [𝑄^′𝑅^′]=𝑞𝑟(𝑅)

   𝑂𝑃=𝑄^′𝑌

   𝑌_𝑗=𝑜𝑝(1∶𝑛_ℎ−1,∶)

   𝑦_𝑗=𝑜𝑝(𝑛_ℎ,∶)

   𝑅𝑒𝑠𝐾=𝑦_𝑗²_𝐹+𝑉/(𝑁)

   𝑅𝑒𝑠𝐶𝐾(1,𝑖)=𝑅𝑒𝑠𝐾

  end for

  [𝑚𝑖𝑛𝑣𝑎𝑙,𝑚𝑖𝑛𝑖𝑛𝑑]=min(𝑅𝑒𝑠𝐶𝐾)

  𝐹𝑃𝐸𝐾=𝐹𝑃𝐸∗𝑚𝑖𝑛𝑣𝑎𝑙

 }

  if  (𝐹𝑃𝐸𝑘<𝐹𝑃𝐸𝑉)  then

   𝑅(∶,𝑚𝑖𝑛𝑖𝑛𝑑)=[]

   𝑌(𝑚𝑖𝑛𝑖𝑛𝑑,∶)=[]

   𝑉=𝑚𝑖𝑛𝑣𝑎𝑙

   𝐹𝑃𝐸𝐾=𝐹𝑃𝐸𝑉

   𝑛_ℎ=𝑛_ℎ−1

   𝑐𝑎𝑙𝑙𝑟𝑒𝑚𝑜𝑣𝑒−ℎ𝑖𝑑𝑑𝑒𝑛()

 else

  Compute the final optimal weight matrix from the equation 𝑅_𝑗∗𝑊_𝑗=𝑌_𝑗

 end if