Algorithm 1.

Multi-scale affinities with missing data

Initialize ${\mathcal{E}}_r$ and ${\mathcal{E}}_c$

Set dr(i, j) = 0 and dc(i, j) = 0

Set nr = m, nc = n, k = k0 and l = l0

while nr > 1 do

while nc > 1 do

$\left\{U^{(l,k)},{\tilde{X}}^{(l,k)},n_r,n_c\right\}$ ← CO-CLUSTER-MISSING $\left({\mathcal{P}}_{\Theta }(X),{\gamma }_r=2^l,{\gamma }_c=2^k\right)$

$d\left({\tilde{X}}_{i·}^{(l,k)},{\tilde{X}}_{j·}^{(l,k)}\right)\leftarrow {\left({\gamma }_r{\gamma }_c\right)}^{\alpha }{\Vert {\tilde{X}}_{i·}^{(l,k)}-{\tilde{X}}_{j·}^{(l,k)}\Vert }_2$

$d\left({\tilde{X}}_{·i}^{(l,k)},{\tilde{X}}_{·j}^{(l,k)}\right)\leftarrow {\left({\gamma }_r{\gamma }_c\right)}^{\alpha }{\Vert {\tilde{X}}_{·i}^{(l,k)}-{\tilde{X}}_{·j}^{(l,k)}\Vert }_2$

Update row distances: $d_r(i,j)+=d\left({\tilde{X}}_{i·}^{(l,k)},{\tilde{X}}_{j·}^{(l,k)}\right)$

Update column distances: $d_c(i,j)+=d\left({\tilde{X}}_{·i}^{(l,k)},{\tilde{X}}_{.j}^{(l,k)}\right)$

k ← k + 1

end while

l ← l + 1

end while

Return dr(i, j) and dc(i, j)