Fast Second-Order Orthogonal Tensor Subspace Analysis for Face Recognition

Algorithm 3

Newton's method for trace ratio optimization.

Input: 𝐴,𝐵 and a dimension 𝑙

Output: 𝑉 which solves the trace ratio optimization problem (27)

  (1) Select an initial 𝑛×𝑙 unitary matrix 𝑉;

  (2) Compute

      𝑉𝜌=tr^𝑇𝐴𝑉tr𝑉^𝑇𝐵𝑉;

  (3) Until convergence Do:

   (3.1) Compute the 𝑙 eigenvectors {𝑣_𝑖}^𝑙_𝑖=1 of the matrix 𝐴−𝜌𝐵

     corresponding to the largest 𝑙 eigenvalues.

   (3.2) Set 𝑉=[𝑣₁,𝑣₂,…,𝑣_𝑙];

   (3.3) Compute

        𝑉𝜌=tr^𝑇𝐴𝑉tr𝑉^𝑇𝐵𝑉.

   End Do