www-ai.cs.tu-dortmund.de/en/LEHRE/FACHPROJEKT/SS14/Papers/svmtutorial.pdf
tutorialCorr.dvi
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 [...] r1!r2! · · · (p − r1 − r2 · · ·)!
∫ xr1
1 xr2 2 · · · yr1
1 yr2 2 · · · g(x)g(y)dxdy (69)
to the left hand side of Eq. (67), which factorizes:
= p!
r1!r2! · · · (p − r1 − r2 · · ·)! ( ∫
xr1 1 xr2
2 · · [...] vectors in R2, and you choose K(xi,xj) = (xi · xj)2. Then it’s easy to find a space H, and mapping Φ from R2 to H, such that (x · y)2 = Φ(x) ·Φ(y): we choose H = R3 and
Φ(x) =
⎛ ⎝ x2
1√ 2 x1x2
x2 2
⎞ ⎠ (62) …
