Algorithm 1. LRCMC algorithm

Input: Original data $X^1,\dots ,X^m$ with m views, the number of clusters c, the number of neighbors k, the regularization parameter $\beta$. Output: The learned consensus matrix Z. Initialize the affinity matrices $S^1,\dots ,S^m$ for each view by solving the following problem: $\underset{s_j^v}{\min }{\displaystyle \sum _{i=1}^n{\Vert x_i-x_j\Vert }_2^2}{s}_{ij}^v+\alpha {\Vert s_j^v\Vert }_2^2$; Initialize the embedded matrices $F^1,\dots ,F^m$ for each view by using Equation (1); Initialize the weights $w_1,\dots ,w_m$ for each view by $w_v=1/m$; Initialize Z by connecting $S^1,\dots ,S^m$ with $w_1,\dots ,w_m$; Initialize the fused embedded matrix U by using Equation (23); Repeat Fix $F^1,\dots ,F^m$, $w_1,\dots ,w_m$, Z and U, update $S^1,\dots ,S^m$ by using Equation (19); Fix $S^1,\dots ,S^m$, $w_1,\dots ,w_m$, Z and U, update $F^1,\dots ,F^m$ by using Equation (1); Fix $S^1,\dots ,S^m$, $F^1,\dots ,F^m$, Z and U, update $w_1,\dots ,w_m$ by using Equation (6); Fix $S^1,\dots ,S^m$, $F^1,\dots ,F^m$, $w_1,\dots ,w_m$ and U, update Z by using Equation (22); Fix $S^1,\dots ,S^m$, $F^1,\dots ,F^m$, $w_1,\dots ,w_m$ and Z. update U by using Equation (23); Until Satisfy Theorem 1 or the maximum iteration reached. The learned consensus matrix Z with exact c connected components, which are the final clusters.