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

Algorithm 1

Expectation-Maximization algorithm.

Input:  Matrix  x

Output:  Matrix  eigenvectors  (𝑈),  eigenvalues  (𝜆)

(1)    Estimate  the  mean  vector:  𝜇=(1/𝑁)∑^𝑁_𝑖=1𝑥_𝑖

(2)    Center  the  input  data  around  the  mean: 𝑋=𝑋−𝜇_1×𝑁

(3)    Set  elements  of  𝑈∈ℝ^𝑀×𝑘  to  random  values.

(4)    repeat

(5)     E-step:  𝐴=𝑈^𝑇𝑈⁻¹𝑈^𝑇𝑋

(6)     M-step:  𝑈=𝑋𝐴^𝑇(𝐴𝐴^𝑇)⁻¹

(7)    until  the  change  of  𝜎²=(1/(𝑁−𝑘))(VAR(𝑋)−VAR(𝐴))≤threshold

(8)    Orthogonalize  𝑈

(9)    Project  input  data  on  𝑈∶𝐴=𝑈^𝑇𝑋

(10) Perform  PCA  on  𝐴.  Obtain  𝑈^′  and  𝜆^′

(11) Rotate  𝑈  for  𝑈∶𝑈^′=𝑈𝑈^′

(12) Determine  the  eigenvalues  𝜆=𝜆^′