基于伪分类超平面的线性可分几何判定方法及应用

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 points in Euclidean space, the geometric properties including the relationship between points and planes in Euclidean 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.