基于特征矢量集的核Logistic回归  

Kernel Logistic Regression Based on Feature Vector Set

作　　者：李滔[1] 王俊普[1] 吴秀清[2] 

机构地区：[1]中国科技大学自动化系,安徽合肥230027 [2]中国科技大学电子工程与信息科学系,安徽合肥230027

出　　处：《小型微型计算机系统》2006年第6期980-985,共6页Journal of Chinese Computer Systems

基　　金：国家"八六三"基金项目(2002AA783055)资助.

摘　　要：将经典Logistic回归推广到高维RKHS空间,提出了一种基于特征矢量选择的核Logistic回归算法--FVS-KLR.该算法利用特征矢量选择(FVS)从训练样本集中选择一个特征矢量集,原样本在RKHS空间中的映射可用该集合中元素映射的线性组合近似.以特征矢量集为基得到核Logistic回归的目标泛函,并采用Newton-Raphson方法寻优,将优化的计算量由O(N3)降到O(NL2),LN.同时文章推导了多类情况下的核Logistic回归算法.通过与SVM的对比实验表明,该算法对后验概率的估计优于SVM方法,同时在分类错误率不高于SVM的基础上能显著降低分类器的计算量.In this paper, the classical Logistic Regression is generalized to the RKHS space, and a new Kernel Logistic Regression method FVS-KLR is proposed. Using the Feature Vector Selection algorithm, a feature vector set is selected, which forms a set of bases to approximate the mapping of training samples in the RKHS space. Based on the feature vector set, the objective function of the Kernel Logistic Regression is deduced and the Newton-Raphson method is used for the optimization. The computation complexity decreases from O（N^3） to （NL^2） with L〈〈N. The algorithm in the multi-class situation is also deduced. The experimental results show this method is superior to SVM in the estimation of posterior and can decrease the computation of classifiers while preserving the same performance.

关 键 词：核Logistic回归 特征矢量选择 SVM 分类 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]