Dimension Reduction Using Samples’ Inner Structure Based Graph for Face Recognition

Algorithm 1

Construction of SISG.

INPUT: Sample set 𝐴={𝐴₁,…,𝐴_𝑖,…,𝐴_𝑁}, where 𝐴_𝑖 is a sample matrix.

OUTPUT: The weighted adjacency matrix 𝑊^SISG of SISG

Algorithm:

for 𝑖=1 to 𝑁 (𝑁 is the number of the training samples)

 for 𝑗=1 to 𝑁

  for 𝑙=1 to 𝑚 (𝑚 is the column number of sample matrix)

   if exp{−𝐶(𝐴^𝑙_𝑖,𝐴^𝑙_𝑗)/𝑡}>(1/𝑛)∑^𝑁_𝑘=1exp{−𝐶(𝐴^𝑙_𝑖,𝐴^𝑙_𝑘)/𝑡}

    𝐺^𝑙_𝑖𝑗=1;

   else

    𝐺^𝑙_𝑖𝑗=0;

   end if

  end for

 end for

 for 𝑗=1 to 𝑁

  𝑆_𝑖𝑗=∑^𝑚_𝑙=1𝐺^𝑙_𝑖𝑗;

  if 𝑆_𝑖𝑗>𝑆_𝑖^⋅₁/𝑆_𝑖^⋅₀

   𝑊^SISG_𝑖𝑗=𝑆_𝑖𝑗⋅𝑥−exp^𝑖−𝑥_𝑗²𝑡;

      (𝑋_𝑖 is the vectorization representation of 𝐴_𝑖)

  else

   𝑊^SISG_𝑖𝑗=0;

  end if

 end for

end for