FODA 127

supportFUacbinesf.vn?Kernels

,and non-linear

classification

Perceptron-lgorithm-lnp.tn/,gER&a---w=yixituansxi,gi)c-4g ¥t WEIRDsay

.tw#osign(cw,xi7)--sisnCgi)reP.?--angx.i.ais09iLX.,w> < o-

then update w - w + yi×i=?$§☒return w/ 1) WII

i+

+

+ 1- +4-t.is#oehmwrA• if student earns a B

+ it student earns not - B

Generaliz-edw.YI-sod.cl#p.xc-1Rdd

linear inner product Lp ,

✗> = ¥ ,

P;X ;

dot product

kernelfp.DEKlp . ×) = exp (-11×-1-11%-2) Gaussian

) RBFG. ✗{ = Klp, ×) = exp ( -4×-1>11 G) Laplace

4.x>p= klp ,×) - ftp.x > + c)

^

polynomial

Polynomial Classifier ☒ CIR yet -1 , -113

%÷÷!÷÷÷€:-'Xi

Xi→ qi-cxi.fi)

Kernetpereptronchange classifier i mistake counter

w = EY ☒i 9i✗i

✗ =(✗, ,h,. . .tn) C- IR

"

c- =L

predictor function✗ i = # updates v1

glp) = (w , p> =(¥^figi✗i , P> xi.simostly ✗i- o

= É✗iyiG✗i,p>

i-1-EIxiy.tl/i,p)⇐ I

a- ( o ,

Choose di - l'c-C.in]

"

repeatif some ✗i.Sittig

§=l

then ✗ i=di -11

Return gc . > = ETAHf- I

✗data pointPolynomi.IE/pansioup--(✗

,Z)

of = to t da ✗ + Xz ✗Zt ✗zz + ✗*-22 + ✗g- ✗ Z

✗ EIR'

degree r ⇒ dim (g) - old')

(X,W>r= 4 , × , ✗ ? z ,z ? ✗z)

,✗)