prml lecture07a svm模式识别与机器学习

PatternRecognition&Machine

•• –SupportVectorMachine-PatternRecognition&Machine

C.G. 2y(x)=wTφ(x)+N个向量x1N目标输出t1,..., 二值数据tn∈{−tny(xn)>-PatternRecognition&Machine

C.G. w w•-PatternRecognition&Machine

C.G. -PatternRecognition&Machine

C.G. 1

w-PatternRecognition&Machine

C.G. 1

wgs.g-Pattern

s.-PatternRecognition&Machine

C.G. -PatternRecognition&Machine

C.G. (QuadraticProgramming-PatternRecognition&Machine

C.G.

an= tny(xn)=-PatternRecognition&Machine

C.G.

ConstraintQualificationqqmaxDmaxminLw,b, pminPw,b1wT -PatternRecognition&Machine

C.G. y(x)=wTφ(x)+-PatternRecognition&Machine

C.G. tny(xn)=-PatternRecognition&Machine

C.G.

E(z)

z z-PatternRecognition&Machine

C.G. -PatternRecognition&Machine

C.G. 变量ξn

y=-

ξn=

ξn=|tn−

Theclassification-PatternRecognition&Machine

C.G. s.

n n1,...,其中C>0是正则化参数(regularization-PatternRecognition&Machine

C.G. Laranian函数变为KKT-PatternRecognition&Machine

wheren=1,..., C.G. 对wb{ξn}求导，令导数为0模式识别与机器学习-PboxconstraintsneLearni C.G. 对于支持向量(supportvectors)，其中0an<C对应于ξn=0，tny(xn1，即满足-PatternRecognition&Machine

C.G. an<an=

ξn=ξn≤ξn>

-PatternRecognition&Machine

C.G. SMO(SequentialMinimalSMO(SequentialMinimaltt,protectedconjugategradientsprotectedconjugategradients(Burges,positionmethods(Osunaetal.,-PatternRecognition&Machine

C.G. -PatternRecognition&Machine

C.G. Hinge-PatternRecognition&Machine

C.G. -PatternRecognition&Machine

C.G. AnthonyandBiggs,1992;KearnsandVazirani,1994;Vapnik,1995;Vapnik,1998Probably yCorrect,orThegoalofthePACframeworkistounderstandhowlargeadatasetneedstobeinordertogivegoodgeneralization-PatternRecognition&Machine

C.G. –令D表示包含所有输入向量{x1,x2,…,xN的最小球的直wTxb0 D2hminm,2 22 t2Sxb: ct1,2,...,t2 St满足VCh1h2L vs.Nothingismorepracticalthanagood