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文库首页人工智能机器学习人工智能导论：A2.2-Support Vector Machines-I

人工智能导论：A2.2-Support Vector Machines-I

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人工智能导论：A2.2-Support Vector Machines-I

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Support Vector Machines

Outline



What is a Support Vector Machine?



Solving SVMs



Kernel Tricks

What is a Support Vector Machine



SVM is related to statistical learning theory [3]



SVM was first introduced in 1992 [1]



SVM becomes popular because of its success in

handwritten digit recognition



1.1% test error rate for SVM. This is the same as the error rates of

a carefully constructed neural network, LeNet 4.



See Section 5.11 in [2] or the discussion in [3] for details



SVM is now regarded as an important example of “kernel

methods”, one of the key area in machine learning

[1] B.E. Boser et al. A Training Algorithm for Optimal Margin Classiers. Proceedings of the Fifth Annual

Workshop on Computational Learning Theory 5 144-152, Pittsburgh, 1992.

[2] L. Bottou et al. Comparison of classier methods: a case study in handwritten digit recognition.

Proceedings of the 12th IAPR International Conference on Pattern Recognition, vol. 2, pp. 77-82, 1994.

[3] V. Vapnik. The Nature of Statistical Learning Theory. 2

edition, Springer, 1999.

Classification Problem



Given a training set S={(x

, y

),(x

, y

),…,(x

, y

)}, and

∈X=R

, i=1,2,…,N



To learn a function g(x), and make the decision

function f(x)=sgn(g(x)) can classify new input x



So this is a supervised batch learning method



Linear classifier

What is a good Decision Boundary?



Consider a two-class, linearly

separable classification problem



Many decision boundaries!



The Perceptron algorithm can be

used to find such a boundary



Different algorithms have been

proposed



Are all decision boundaries

equally good?

Class +1

Class -1

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