Algorithm 1 low-rank regularized self-representation (LRRSR)

Input: data matrix $X\in {ℝ}^{n\times m}$ , parameters $\lambda$ and $\beta$ , maximum iteration MaxIter.

Initial: $J_0=Z_0=W_0=E_0=0$ , ${\mu }_0={10}^{-4}$ , ${\mu }_{\max }={10}^{30}$ , $\rho =1.1$ , $Y_1^0=Y_2^0=Y_3^0=0$ , $\epsilon ={10}^{-6}$ , $k=0$ .

1: while ${\Vert X-XZ-E\Vert }_{\infty }>\epsilon$ , ${\Vert Z-J\Vert }_{\infty }>\epsilon$ , ${\Vert Z-W\Vert }_{\infty }>\epsilon$ , $k<MaxIter$ do

2: Update $J_{k+1}$ by solving formula (5);

3: Update $W_{k+1}$ by solving formula (6);

4: Update $Z_{k+1}$ by solving formula (10);

5: Update $E_{k+1}$ by solving formula (11);

6: Update $Y_1^{k+1}$ , $Y_2^{k+1}$ , $Y_3^{k+1}$ , ${\mu }_{k+1}$ by solving formula (12);

7: $k=k+1$ ;

8: return $Z_{\ast }=Z_k$ , $E_{\ast }=E_k$ .

Output: self-representing coefficient matrix $Z_{\ast }$ , residual matrix $E_{\ast }$ .