Table 1.

Discriminatively Learning Θ

Input: Θ(0) estimated by A-SGBN
Output: Θ* learned by (7)
1. Let Θ(t–1) = Θ(0)
2. Compute ${\Phi }_{\Theta }^{(t-1)}$ and ${\mathbf{K}}_{\Theta }^{(t-1)}$ by (3)
3. Compute $\mathrm{t}r{\left({\mathbf{S}}_T\right)}^{(t-1)}=\mathrm{tr}\left({\mathbf{K}}_{\Theta }^{(t-1)}\right)-1^{⊺}{\mathbf{K}}_{\Theta }^{(t-1)}1∕n$
4. Solve J0(Θ(t–1)) and α* by (9)
5. J(Θ(t–1)) = J0(Θ(t–1)) × tr(ST)(t–1)
6. Compute ▿Θ(t–1)J by (10)
7. For a given α*, minimize (7) using J(Θ(t–1)) and  ▿(Θ(t–1)J; Obtain the optimal Θ(t)
8. Let Θ(t–1) = Θ(t)
9. Repeat Step 2-8 until convergence, let Θ* = Θ(t)