www-ai.cs.tu-dortmund.de/en/LEHRE/FACHPROJEKT/SS14/Papers/svmtutorial.pdf
tutorialCorr.dvi
n
R2(n + 1)
( 1 − yip
n + 1
) (35)
Also,
(Hα)i = 1 − yip
n + 1 . (36)
13
Hence
‖w‖2 = n+1∑ i,j=1
αiαjyiyjxi · xj = αTHα
= n+1∑ i=1
αi
( 1 − yip
n + 1
) =
n+1∑ i=1
αi = ( n
R2
)( 1 −
( p
n + 1
)2 )
(37) [...] again be R3 and
Φ(x) = 1√ 2
⎛ ⎝ (x2
1 − x2 2)
2x1x2
(x2 1 + x2
2)
⎞ ⎠ (63)
18
0.2 0.4 0.6 0.8 1 -1
-0.5 0
0.5 1
0 0.2 0.4 0.6 0.8
1
Figure 8. Image, in H, of the square [−1, 1] × [−1, 1] ∈ R2 under the mapping [...] origin. Furthermore CA − CB is convex, since ∀x1 = a1−b1, x2 = a2−b2, λ ∈ [0, 1], a1, a2 ∈ CA, b1,b2 ∈ CB , we have (1−λ)x1+λx2 = ((1 − λ)a1 + λa2) − ((1 − λ)b1 + λb2) ∈ CA − CB . Hence it is sufficient to …
