www-ai.cs.tu-dortmund.de/de/LEHRE/SEMINARE/SS09/AKTARBEITENDESDM/LITERATUR/tsochantaridis05aSVMstruct.pdf
tsochantaridis05a.dvi
algebra
〈
Ψ(x,y),Ψ(x′,y′) 〉
= D·K ∑ r=1
D·K ∑ s=1
ψr(x,y)ψs(x′,y′) = D
∑ d=1
K
∑ k=1
D
∑ d′=1
K
∑ k′=1
φd(x)λk(y)φd′(x′)λk′(y′)
= D
∑ d=1
D
∑ d′=1
φd(x)φd′(x′) K
∑ k=1
K
∑ k′=1
λk(y)λk′(y′) = 〈
Φ(x),Φ(x′) 〉
· [...] t function
F(x,y;w) = T
∑ t=1
∑ σ∈Σ 〈w̄σ,Φ(xt)〉δ(yt ,σ)+η
T−1
∑ t=1
∑ σ∈Σ
∑̄ σ∈Σ
ŵσ,σ̄δ(yt ,σ)δ(yt+1, σ̄)
=
〈
w̄, T
∑ t=1
Φ(xt)⊗Λc(yt)
〉
+η
〈
ŵ, T−1
∑ t=1
Λc(yt)⊗Λc(yt+1)
〉
. (13)
Herew = (w̄′, ŵ′)′ [...] Algorithm 1 Algorithm for solving SVM0 and the loss re-scaling formulations SVM∗1 and SVM∗2 .
1: Input: (x1,y1), . . . ,(xn,yn), C, ε 2: Si ← /0 for all i = 1, . . . ,n 3: repeat 4: for i = 1, . . . ,n …