Input: Data set $X\in R^{D\times n}$ ; The reduced dimension d, parameter p. Output: optimal transformation matrix $W\in R^{D\times d}$ .

1: Initialize $W$ by using LDA [35] ;

2: Repeat step 3-step 5;

3: Update $d_{ij}^t$ by using $d_{ij}={\Vert W^{\text{T}}\left(x_i-x_j\right)\Vert }_2^{p-2}$ ;

4: Update $W^t$ by using the eigenvalue decomposition of Equation (10);

5: $t=t+1$ ;

6: Until Convergence;

7: Return transformation matrix $W$ .