基于伪分类超平面的线性可分几何判定方法及应用  

A Geometrical Judgment Method for Linear Separability Based on Pseudo-Separating Hyperplane and Its Application

作　　者：张银川[1] 韩立新[1] 曾晓勤[1] 

机构地区：[1]河海大学计算机与信息学院智能科学与技术研究所南京211100

出　　处：《模式识别与人工智能》2014年第1期60-69,共10页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金资助项目(No.60971088)

摘　　要：针对模式分类中线性可分的问题,文中将模式看作是欧氏空间中的点,研究欧氏空间中点与面的关系等解析几何性质,在一般的分类超平面概念上定义伪分类超平面.根据线性可分等价性,在需降维时进行空间映射.研究根据数据寻找伪分类超平面,给出几何意义明显的线性可分判断方法,在该方法的基础上给出一种分类复杂度的度量方法.实验结果表明,该方法较好地体现数据的分类复杂度.Aiming at the problem of linear separability in pattern classification, the patterns are taken as pt,,~t~ in Euclidean space, the geometric properties including the relationship between points and planes in Euchdean space are studied, and the pseudo-separating hyperplane is defined based on the general separating hyperplane. By analyzing linear separability equivalence, the mapping from a higher dimensional space to a lower dimensional space is developed when spatial dimension reduction is required. The method for finding pseudo-separating hyperplane is studied and a judgment method for linear separability is presented with obvious geometric meaning. A classification complexity measure is proposed based on this method. The experimental results show that the proposed method reflects the complexity of data classification well.

关 键 词：线性可分 伪分类超平面 空间映射 分类复杂度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]