Algorithm 1.

The CBP-JMF algorithm.

Input:

P data matrices X(1), X(2), ..., X(P), parameters β ω

Output:

P basis matrices U(1), U(2), ..., U(P), P relation matrices S(1), S(2), ..., S(P), factor matrices V, weight vector Π = (π(1), π(2), ..., π(P))

1: Begin

2: InitializeU(1), U(2), ..., U(P), S(1), S(2), ..., S(P), V

3: Initialize $\left({\pi }^{(1)},{\pi }^{(2)},...,{\pi }^{(P)}\right)\mathrm{\text{=}}\left(\frac{1}{P},\frac{1}{P},...,\frac{1}{P}\right)$

4: loop

5: for p=1 to P do

6: Fix V, update U(p), S(p)

7: end for

8: Fix U(1), U(2), ..., U(P), update VL

9: Fix U(1), U(2), ..., U(P), update VUL

10: for p=1 to P do

11: Fix U, S, V, compute $c^{(p)}=\Vert {\text{X}}^{(p)}-{\text{U}}^{(p)}{\text{S}}^{(p)}\text{V}{\Vert }_F^2$

12: end for

13: Update Π

14: break loop if convergence

15: End