3.txt

This complete matlab for neural network

发信人: GzLi (笑梨), 信区: DataMining
标  题: svm and bayes rule in Classification
发信站: 南京大学小百合站 (Thu Jul  4 12:40:28 2002), 站内信件

篇名： Support Vector Machines and the Bayes Rule in Classification 
刊名： Data Mining and Knowledge Discovery 
ISSN： 1384-5810 
卷期： 6 卷 3 期 出版日期： 200207  
页码： 从 259 页到 275 页共 17 页 
作者： Lin Yi   Department of Statistics, University of Wisconsin, Madison
, 1210 West Dayton Street, Madison, WI 53706-1685, USA. [e-mail]
 
文摘： 
The Bayes rule is the optimal classification rule if the underlying distribution
 of the data is known. In practice we do not know the underlying distribution
, and need to “learn” classification rules from the data. One way to derive
 classification rules in practice is to implement the Bayes rule approximately
 by estimating an appropriate classification function. Traditional statistical
 methods use estimated log odds ratio as the classification function. Support
 vector machines (SVMs) are one type of large margin classifier, and the 
relationship between SVMs and the Bayes rule was not clear. In this paper
, it is shown that the asymptotic target of SVMs are some interesting classif
ication
 functions that are directly related to the Bayes rule. The rate of convergence
 of the solutions of SVMs to their corresponding target functions is explicitly
 established in the case of SVMs with quadratic or higher order loss functions
 and spline kernels. Simulations are given to illustrate the relation between
 SVMs and the Bayes rule in other cases. This helps understand the success
 of SVMs in many classification studies, and makes it easier to compare SVMs
 and traditional statistical methods.
 

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