支持向量机的乘子极大熵方法  

the Multiplier Maximum Entropy Algorithm of Support Vector Machines

作　　者：于乐源[1] 张勇[2] 

机构地区：[1]济宁学院数学系,山东曲阜273155 [2]中国矿业大学信息与电气工程学院,江苏徐州221116

出　　处：《济宁学院学报》2014年第6期51-55,共5页Journal of Jining University

基　　金：山东省高等学校科技计划项目(J12L152);济宁学院青年基金项目(2013QNKJ14);济宁学院青年基金项目(2012QNKJ10)

摘　　要：对于支持向量机的小样本识别问题,给出了一个近似算法—乘子极大熵算法.首先把支持向量机模型的Wolfe对偶问题转化为极大极小模型,然后利用乘子极大熵算法来求这个极大极小问题的解.支持向量机的乘子极大熵算法是一个集极大熵法和乘子法两者优点于一身的算法,它可以把非光滑的问题变成光滑的,能在一定程度上减少迭代次数,提高计算速度,并且可以避免海森阵病态的问题.对于文中的两个例子,该算法都得到了比较好的实验结果,表明了该算法的有效性.乘子极大熵算法比较适用于小样本的识别问题,特别是医学上的癌前诊断问题的判别.Concerning small sample recognition problems about support vector machines, a proximal algorithm called the multiplier entropy algorithm of support vector machines is constructed. At the beginning the Wolfe dual problem of support vector machines is converted into the Minimax problem which is solved by the way of multiplier entropy algorithm. The multiplier entropy algorithm of support vector machines has the virtues of both multiplier algorithm and entropy algorithm. Entropy algorithm can turn non-smooth problems into smooth ones, and multiplier algorithm can reduce the iteration in some degree and the morbid state of Hessian can also be avoided in this way. For small sample problems, especially the pre-cancer diagnosis, the algorithm can be performed efficiently.

关 键 词：支持向量机 Wolf-对偶 极大极小模型 乘子极大熵 最优性条件 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]