Algorithm 1: The early customer-clustering technique

Input:User–item rating matrix, clustering number k Output:The smoothed dense user–item matrix Start:  Select user set $u=\left\{u_1, u_2,u_3 \dots ,u_m\right\}$;  Select item set i $=\left\{i_1, i_2,i_3 \dots ,i_n\right\}$;  Select the top k rating users as the clustering $\mathrm{c}u=\left\{c{u}_1, c{u}_2,c{u}_3 \dots ,c{u}_m\right\}$;  The clustering center is null as c $=\left\{c_1, c_2,c_3 \dots ,c_k\right\}$;  do    for each user $u_i\in u$     for each cluster center c$u_i\in cu$        calculate the similarity ($u_i$, c$u_i$);     end for      sim($u_i$, c$u_m) = \max \left\{\mathit{sim}(u_i, \mathrm{c}{u}_1),\mathit{sim}(u_i, \mathrm{c}{u}_2) \dots ,\mathit{sim}(u_i, \mathrm{c}{u}_k)\right\}$;     $c_m=c_m{\displaystyle \cup }{u}_i$     end for     for each cluster $c_i\in c$       for each user $u_j\in u$       c$u_i=average\left(c_i,u_j\right)$;      end for     end for    while (c is not change) End