Algorithm 1. ADMM for LMVSC-Sparse.

Input: multi-view data the multi-view data samples, denoted by $X=\left\{X^{\left(1\right)},\cdots ,X^{\left(V\right)}\right\}$ , ${\lambda }_1$ , ${\lambda }_2$ , and the numbers of clusters.

Initialize: $\mu ={10}^{-3}$ , $\rho =1.2$ , ${\mu }_{\max }={10}^6$ , $\gamma =100$ , $L^{\left(v\right)}=0$ , $C^{\left(v\right)}=0$ , $\forall v$ , stooping tolerance $ϵ$ .

Repeat:

Step 1: Computing ${\left\{Z^{\left(v\right)}\right\}}_{v=1}^V$ by (19).

Step 2: Computing ${\left\{L^{\left(v\right)}\right\}}_{v=1}^V$ by (25).

Step 3: Computing ${\left\{C^{\left(v\right)}\right\}}_{v=1}^V$ by (30).

Step 4: Computing ${\left\{Y^{\left(v\right)}\right\}}_{v=1}^V$ by $Y^{\left(v\right)}=Y^{\left(v\right)}+\mu \left(Z^{\left(v\right)}-L^{\left(v\right)}{C}^{\left(v\right)}\right)$ .

Step 5: Computing $\mu =\min \left(\rho \mu ,{\mu }_{\max }\right)$ .

Until ${\displaystyle {\sum }_{v=1}^V{\Vert Z^{\left(v\right)}-L^{\left(v\right)}{C}^{\left(v\right)}\Vert }_{\propto }}\le ϵ$ or achieved maxim iteration number.

Output $Z^{\left(v\right)}$ .