一种基于证据理论和核函数的k-NN分类新方法.doc

一种基于证据理论与核函数的k-NN分类新方法 摘要：实际分类中,训练样本所属类别往往具有模糊性和不确定性,导致分类时难以决策,影响分类的性能．将证据理论与核函数理论用于k-NN分类中,通过引入两样本间的核距离,突出了不同类别样本间的特征差异;利用自适应方法对参数进行学习,采用规划方法得到待识别样本所属类别的相容概率并与其它的Pignistic概率转换方式比较;最后利用相容概率做出决策,有效解决训练样本所属类别存在的模糊性和不确定性问题,提高了k-NN分类的准确度.通过与传统k-NN分类、基于D-S理论的k-NN分类、基于核的k-NN分类算法比较,体现了该分类方法的有效性． 关键词：证据理论; 核函数;规划; 相容概率; k-NN分类 k-Nearest Neighbor New Algorithm based on Dempster-Shafer Theory and Kernel Function LI Can-Ze WU Gen-Xiu YAN Wei-Feng ZHOU Li (College of Mathematics and Information Science, Jiangxi Normal University, Jiangxi Nanchang 330022) Abstract: In practical classification,the category of training samples is always fuzzy and uncertain which leads to difficult decision and affects the capability of classification. It applied the evidence theory and kernel function to k-nearest neighbor algorithm,introduced kernel distance of two samples which highlighted the feature differences ;and learned parameter by adaptive method; exploited programming method to gain compatible probability of the category of samples and compared with other pignistic probability transforms, then made decision by compatible probability; it solves the problem of fuzzy and uncertain of training samples ,and improves the accuracy of classification.Finally, compares the results with traditional k-nearest neighbor method, k-nearest neighbor method based on D-S theory, k-nearest neighbor method based on kernel distance,and proves the validity of our method． Key words: Dempster-Shafer theory; kernel function; programming; compatible probability; pignistic probability; k-nearest neighbor classification  0 引言 k-NN算法作为一种分类算法,因其具有简单、直观、容易实现等优点,已广泛应用于模式识别和数据挖掘等各个领域．而在现实操作中,训练样本所属类别往往具有模糊性和不确定性,影响k-NN分类性能.文[1]利用证据理论、文[2]利用TBM模型对样本进行k-NN分类能处理某些训练样本类别的不确定性.由于k-NN通常使用欧氏距离来度量样本间的距离,导致k-NN分类方法对不同类别的样本分类效果差别较大：对于高斯分布与椭圆分布,k-NN分类效果较好,而对于其他分布则分类效果不佳[3][4]．特别对于高维空间上的数据,其计算复杂度很高,并且当样本特征属性之间存在相关关系时用欧氏距离来刻画样本间的距离会导致分类准确度不高等问题． 为解决该问题,很多算法通过“降维”的方式将高维空间中的样本按照某个条件映射到低维空间[5],然而这容易损失一些有用的特征,导致性能的下降．核函数的方法具有很强的非线性