Algorithm 1.

NLCTF

Input: ${\left\{y_s\right\}}_{s=1}^{\text{S}}$, α, τ, θ, μ and other parameters;

1:Initialization: $\left\{{\mathcal{X}}^{(0)}\right\}\leftarrow 0$; $\left\{{\mathcal{X}}_l^{(0)},{\mathcal{W}}_l^{(0)}\right\}\leftarrow 0$, initializing $Q_{l_n}^{(0)}$, ${\mathcal{C}}_l^{(0)}$ by high-order SVD of ${\mathcal{X}}_l^{(0)}$; $\left\{{\mathcal{M}}_{l_n}^{(0)},{\mathcal{Z}}_{l_n}^{(0)},{\mathcal{T}}_l^{(0)}\right\}\leftarrow {\mathcal{X}}_l^{(0)}$, ∀n = 1,2,3 and l = 1, …L; k = 0

2: While not convergence do

3: Updating ${\mathcal{X}}^{(k+1)}$ using Eq. (14);

4: Constructing all cubes ${\mathcal{X}}_l^{(k+1)}(l=1,\dots L)$ using normalized ${\mathcal{X}}^{(k+1)}$ by Eq. (8);

6: for l = 1:L

7:  Updating ${\mathcal{C}}_l^{(k+1)}$ using Eq. (22);

8:  Updating $Q_{l_n}^{(k+1)}(n=1,2,3)$ using Eq. (26);

9:  Updating ${\mathcal{M}}_{l_n}^{(k+1)}(n=1,2,3)$ using Eq. (30);

10:  Updating ${\mathcal{Z}}_{l_n}^{(k+1)}(n=1,2,3)$ using Eq. (31);

11:  Updating the denormalized ${\mathcal{T}}_l^{(k+1)}={\mathcal{C}}_l^{(k+1)}{\times }_1{Q}_{l_1}^{(k+1)}{\times }_2{Q}_{l_1}^{(k+1)}{\times }_3{Q}_{l_1}^{(k+1)}$

12:  Updating ${\mathcal{W}}_l^{(k+1)}$ using Eq. (15);

13: End for

14: k = k + 1;

15: End while

Output: $\mathcal{X}$