. Author manuscript; available in PMC: 2017 Nov 30.

Published in final edited form as: IEEE Trans Pattern Anal Mach Intell. 2015 Dec 23;38(11):2269–2283. doi: 10.1109/TPAMI.2015.2511754

Algorithm 1.

KL-SGBN: Discriminative Learning

Input: data X₁,X₂ ∈ ℝⁿ^×^m, label y ∈ ℝⁿ^×1

Denote Θ = [Θ₁,Θ₂]

Initialize Θ⁽⁰⁾, o⁽⁰⁾,ϒ⁽⁰⁾ by Algorithm 3 for each class.

Let Θ⁽^t⁻¹⁾ = Θ⁽⁰⁾, o⁽^t⁻¹⁾ = o⁽⁰⁾, ϒ⁽^t⁻¹⁾ = ϒ⁽⁰⁾

repeat

1
Compute $Φ_{Θ}^{(t - 1)}$ and $K_{Θ}^{(t - 1)}$ by Eqn. (3.2)
2
Compute $tr {(S_{T})}^{(t - 1)} = tr (K_{Θ}^{(t - 1)}) - 1^{⊤} K_{Θ}^{(t - 1)} 1 / n$
3
Solve J₀(Θ⁽^t⁻¹⁾) and α^★ by Eqn. (3.9)
4
J(Θ⁽^t⁻¹⁾) = J₀(Θ⁽^t⁻¹⁾) × tr(S_T )⁽^t⁻¹⁾
6
Minimize Eqn. (3.7) with α^★ and obtain Θ⁽^t⁾:
- 6.1
  Let o = o⁽^t⁻¹⁾,ϒ = ϒ⁽^t⁻¹⁾, solve Θ⁽^t⁾ by Eqn. (3.7);
- 6.2
  Let Θ = Θ⁽^t⁾, solve o⁽^t⁾,ϒ⁽^t⁾ by Eqn. (4.2).
7
Let Θ⁽^t⁻¹⁾ = Θ⁽^t⁾, o⁽^t⁻¹⁾ = o⁽^t⁾, ϒ⁽^t⁻¹⁾ = ϒ⁽^t⁾

until convergence/max number of iterations

Output: Θ^★ = Θ⁽^t⁾