Slide 23
Slide 23 text
Applications SVM
Primal feasibility:
yi(⟨w, xi⟩ + b) ≥ 1, ∀i ∈ [1, m] (15)
Dual feasibility:
αi ≥ 0, ∀i ∈ [1, m] (16)
Complementary slackness:
αi[yi(⟨w, xi⟩+b)−1] = 0 ⇒ αi = 0∨yi(⟨w, xi⟩+b) = 1, ∀i ∈ [1, m] (17)
L(w, b, α) =
1
2
m
∑
i=1
αiyixi
2
−
m
∑
i=1
m
∑
j=1
αiαjyiyj⟨xi, xj⟩
=− 1
2
∑
m
i=1
∑
m
j=1
αiαjyiyj⟨xi,xj⟩
−
m
∑
i=1
αiyib
=0
+
m
∑
i=1
αi
(18)
then
L(w, b, α) =
m
∑
i=1
αi −
1
2
m
∑
i=1
m
∑
j=1
αiαjyiyj⟨xi, xj⟩ (19)
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