\begin{equation*} \quad min_{M,C_1,C_2}\frac{1}{N_T N_L} \sum_{\substack{ 1\le i \le N_T\\ j s.t. f_l(z_i,z_j)=1 m}}V(M,z_i,z_j)+\beta\|M\|_F^2 \end{equation*} \begin{equation*} \qquad \space \qquad \quad s.t. \qquad V(M,z_i,z_j) = \begin{cases} [C_1-d_M(x_i,x_j)]_+ & \text{if } l_i \neq l_j \\ [d_M(x_i,x_j)-C_2]_+ &\text{if } l_i = l_j \end{cases} ,\qquad \end{equation*}

\begin{equation*} \quad , \qquad \end{equation*} \begin{equation*} \qquad \qquad \quad \qquad M_{i,j}\geq 0, \qquad 0 \leq i,j \leq dim(M) \end{equation*}