Algorithm 1:

Input: communication score tensor $𝒴\in {\mathbb{R}}^{I\times J\times K\times L}$, sample-level design matrix $X\in {\mathbb{R}}^{I\times Q}$, rank $\mathit{r}$.

1. Normalize sample-level design matrix via $\mathrm{Q}\mathrm{R}$ factorization $\mathit{X}=\mathit{Q}\mathit{R}$.

2. Project $𝒴$ to the multilinear sample-level variable space to obtain the unconstrained coefficient tensor: $\widetilde{ℬ}=𝒴\times {}_1{\mathit{Q}}^T$.

3. Obtain rank-unconstrained coefficient tensor by performing a rank-$\mathit{r}$ higher-order orthogonal iteration (HOOI)27 on $\widetilde{ℬ}:{\widehat{ℬ}}^{(0)}\leftarrow HOOI(\widetilde{ℬ},\mathit{r})$.

4. Obtain estimated coefficient tensor by re-normalizing ${\widehat{ℬ}}^{\left(0\right)}$ back to the original feature scales: $\widehat{ℬ}={\widehat{ℬ}}^{\left(0\right)}\times {}_1{\mathit{R}}^{-1}$.

5. Estimate $𝒢,{\mathit{M}}_Q,{\mathit{M}}_J,{\mathit{M}}_K,{\mathit{M}}_L$ by performing a rank-$\mathit{r}$ HOOI on $\widehat{ℬ}:\widehat{ℬ}\approx \widehat{𝒢}\times \{\widehat{{\mathit{M}}_Q},\widehat{{\mathit{M}}_J},\widehat{{\mathit{M}}_K},\widehat{{\mathit{M}}_L}\}$,

Output: $\widehat{ℬ},\widehat{𝒢},\widehat{M_Q},\widehat{M_J},\widehat{M_K},\widehat{M_L}$.