Table 2.

Block coordinate decent for group sparse CCA.

Input: iteration step j, uj, vj, ∥uj∥2 = 1, ∥vj∥2 = 1, λ1 , τ1.

Output: u j +1

Solve uj using block coordinate decent until it convergence:

1. For each group k = 0 to L

2. Softk(Kv) = S((Kv)k, τ1), where S(·) is the soft-thresholding function.

3. $\text{If}{\Vert Sof{t}_k\left(\mathit{Kv}\right)\Vert }_2\le {\lambda }_1\text{then}{\mathit{u}}_k^{j+1}=0$.

4. Else

5. $S{g}_k\left(\mathit{Kv}\right)=\frac{1}{2}[Sof{t}_k\left(\mathit{Kv}\right)-{\lambda }_1{\omega }_l\frac{Sof{t}_k\left(\mathit{Kv}\right)}{{\Vert Sof{t}_k\left(\mathit{Kv}\right)\Vert }_2}]$.

6. $\text{Update}{\mathit{u}}_k^{j+1}\frac{S{g}_k\left(\mathit{Kv}\right)}{\Delta }$.

7. End if

8. End for

9. $\text{Update}\Delta =\Vert [S{g}^1\left(\mathit{Kv}\right),S{g}^2\left(\mathit{Kv}\right),\dots ,S{g}^k\left(\mathit{Kv}\right)]\Vert \text{to make}{\Vert {\mathit{u}}^{j+1}\Vert }_2^2=1$.

10. Repeat (1-9), until ∥uj+1 – uj∥2 ≤ ε, else uj = uj+1.