Algorithm 2 Alternating least squares (ALS) algorithm for maximizing the weighted tensor least squares criterion (4)

$$\begin{array}{cc}\hfill & \text{Initialize:}{\mathit{B}}_d^{(0)}\in {\mathbb{R}}^{p_d\times R}\text{for}d=1,\dots ,D\hfill \\ \hfill & \text{Repeat}\hfill \\ \hfill & \mathbf{for}d=1,\dots ,D\mathbf{do}\hfill \\ \hfill & {\mathit{B}}_d^{(t+1)}\text{is obtained by minimizing}\hfill \\ \hfill & \frac{1}{2}\sum _i{w}_i(y_i-\langle {\mathit{B}}_d,{\mathit{X}}_{i(d)}({\mathit{B}}_D^{(t)}\odot \cdots \hfill \\ \hfill & \odot {\mathit{B}}_{d+1}^{(t)}\odot {\mathit{B}}_{d-1}^{(t+1)}\odot \cdots \odot {\mathit{B}}_1^{(t+1)})\rangle {)}^2\hfill \\ \hfill & \mathbf{end}\mathbf{for}\hfill \\ \hfill & \text{Until:}L({\theta }^{(t)})-L({\theta }^{(t+1)})<ϵ\hfill \end{array}$$