浙江大学研究生 《 人工智能 》 课件
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(Congfu Xu) PhD, Associate Professor
Email: xucongfu@zju.edu.cnInstitute of Artificial Intelligence, College of Computer Science, Zhejiang University, Hangzhou 310027, P.R. China
September 11, 2003Oct. 16, 2006 SVM(Chapter8 SLT & SVM )
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8.1.1 SLT & SVM
8.1
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8.1.2 SLT & SVM
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. from JOHN 3:16-17 NIV
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8.1.3 SLT&SVM
SLT&SVM
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8.1.4 SLT&SVM
SVM
SVM
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SLT & SVMSRM
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8.2 SLT
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, (),
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8.3 F. Rosenblatt1958,1962
Novikoff(1962)
Tikhonov(1963), Ivanov(1962), Phillips(1962)
VanikChervonenkis(1968)VCVC
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SLT()VapnikChervonenkis(1974)SRM
VapnikChervonenkis(1989),
90,,(Statistical Learning Theory,SLT)
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8.4
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8.4.1
G
LM
S
X
y
y
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(G)xRn ,F(x)
(S)xy F(y|x)
(LM)f(x, a)aAA
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8.4.2 f(x,)(),n , ,
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(ill-posed problem)
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,, ,,, (ERM)w
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,
w,,w,
,
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,,
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,,,
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8.5 SLT
SLT:
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VC()SLTVC(Vapnik-Chervonenkis Dimension)
VC01h2hhVC
VC
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VC,VC, ,VC,VCNVCn+1Sin(ax)VC
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VC Open problem: ,VC
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SLT,SLT,, : hVC,n
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1:( ,VC
,VC,,
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2, ,VC,,
SLT
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,
,,VC;,,(Structural Risk Minimization)SRM
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1
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2SRM,
,,
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8.6
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8.6.1 1963Vapnik,,,(SV)
1971KimeldorfSV,
1990Grace,BoserVapnikSVM
1995Vapnik
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8.6.2 SVM(0),SVM,,(margin)H1,H2
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1
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1
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2
Minimize
Subject to
Lagrange
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3Lagrange
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x1 =(0, 0), y1 = +1x2 =(1, 0), y2 = +1x3 =(2, 0), y3 = -1x4 =(0, 2), y4 = -1Matlab1, 2, 3, 4wb
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8.6.3 Vapnik
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(xixj),,,,
SLT,Hibert-Schmidt,Mercer,
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Mercer
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,
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8.6.4 SVM,
S
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8.6.5 SVMlight - satyr.net2.private:/usr/local/binsvm_learn, svm_classifybsvm - satyr.net2.private:/usr/local/binsvm-train, svm-classify, svm-scalelibsvm - satyr.net2.private:/usr/local/binsvm-train, svm-predict, svm-scale, svm-toymySVMMATLAB svm toolbox
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8.7
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8.7.1 SVM
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SVMNNSVMNNSVM NN NNNN
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by R. Feynman from The Feynman Lectures on Physics, Addison-Wesley
SVMNN
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8.7.2
SVM,
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8.7.3 ,,,,SVM
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11SMO(Sequential Minimal Optimization)
2
3SVM
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2SVM,
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3SVMSVMOne-class SVMSVMOne-against-the-restOne-against-oneMulti-class Objective FunctionsSVMDecision Directed Acyclic Graph, DDAGSVM Decision TreeSVM
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SVMSVM
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SVM
SVMBBSnews
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A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery,1998,2(2)Vapnik V N. The Nature of Statistical Learning Theory, NY: Springer-Verlag, 1995..,2000
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Introduction to Support Vector Machine.Vapnik V N. . ... . , 20001.. SVMHRRP. , 2005.
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THANKS FOR YOUR PRESENCE!A righteous man may have many troubles, but the LORD delivers him from them all; he protects all his bones, not one of them will be broken. from Psalms 34:19-20 NIV
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