一种L2软间隔支持向量机的Matlab实现

An Implementation of A L2 Norm Soft Margin Support Vector Machine on Matlab

通过将v-支持向量机的目标函数的L1正则化项变为L2正则化项,构造了一种L2软间隔支持向量机。通过引入拉格朗日乘数,构造拉格朗日函数,导出了L2软间隔支持向量机的对偶二次规划(Quadratic Programming,QP)形式。使用KKT(Karush-Kuhn-Tucker)条件,导出了L2软间隔支持向量机的软间隔ρ及偏置项b的表达式,并通过Matlab数学软件进行编程实现L2软间隔支持向量机的求解。

A L2 norm soft margin support vector machine is constructed by changing the L1 regularization term of the v-support vector machine objective function into L2 regularization term.By introducing Lagrangian multipliers and constructing Lagrangian function,the dual quadratic programming（QP） of the L2 norm soft margin support vector machine is derived.By using Karush-Kuhn-Tucker（KKT） conditions,the expressions of the soft margin ρ and the bias term b of the L2 norm soft margin support vector machine are deduced.Furthermore,the optimal solutions of the L2 norm soft margin support vector machine is implemented by Matlab math software.