PEM-PCA: A Parallel Expectation-Maximization PCA Face Recognition Architecture

Algorithm 2

Parallel matrix manipulation with matrix computation.

Input:   Matrix  left,   Matrix  right

Output:   Matrix  result

(1)    //  Matrix  Subtraction

(2)    parallel  for   i  from  0  to  rows

(3)    for  j  from  0  to  cols

(4)       Subtraction:  𝑟𝑒𝑠𝑢𝑙𝑡[𝑖,𝑗]=𝑙𝑒𝑓𝑡[𝑖,𝑗]−𝑟𝑖𝑔ℎ𝑡[𝑖,𝑗]

(5)    endfor

(6)    endfor

(7)

(8)    //    Matrix  Multiplication

(9)    for  i  from  0  to  leftRows

(10)  parallel  for  j  from  0  to  rightColumns

(11)    for  k  from  0  to  leftColumns

(12)       Calculate  sum:  𝑠𝑢𝑚  +=  𝑙𝑒𝑓𝑡[𝑖,𝑘]×𝑟𝑖𝑔ℎ𝑡[𝑘,𝑗];

(13)    endfor

(14)  𝑟𝑒𝑠𝑢𝑙𝑡[𝑖,𝑗]=𝑠𝑢𝑚;

(15)  endfor

(16) endfor

(17)

(18)   //    Matrix  Transpose

(19) parallel  for  i  from  0  to  rows

(20)  for  j  from  0  to  cols

(21)    Transpose  by  convert  row  to  column:  𝑟𝑒𝑠𝑢𝑙𝑡[𝑗,𝑖]=𝑖𝑛𝑝𝑢𝑡[𝑖,𝑗];

(22)  endfor

(23) endfor

(24) return  result;