www-ai.cs.tu-dortmund.de/en/LEHRE/FACHPROJEKT/SS14/Papers/kernelmethods.pdf
Kernel methods in machine learning
with b= 1 2(‖c−‖
2 −‖c+‖ 2). Substituting the expressions for c± yields
y = sgn
(
1
n+
∑
{i:yi=+1}
〈Φ(x),Φ(xi)〉 ︸ ︷︷ ︸
k(x,xi)
− 1
n−
∑
{i:yi=−1}
〈Φ(x),Φ(xi)〉 ︸ ︷︷ ︸
k(x,xi)
+ b
)
,(5)
where b= 1 2( 1
n2 − [...] algorithm, described in Figure 1, where Y = {±1}. The idea is to compute the means of the two classes in the feature space, c+ = 1
n+
∑
{i:yi=+1} Φ(xi), and c− = 1 n−
∑
{i:yi=−1} Φ(xi),
where n+ and n− are [...] have
〈f, f〉= n∑
i,j=1
αiαjk(xi, xj)≥ 0.(13)
Next, note that given functions f1, . . . , fp, and coefficients γ1, . . . , γp ∈R, we have
p ∑
i,j=1
γiγj〈fi, fj〉=
〈 p ∑
i=1
γifi, p ∑
j=1
γjfj
〉
≥ 0.(14)
Here …
