模式识别与人工智能
模式識彆與人工智能
모식식별여인공지능
Moshi Shibie yu Rengong Zhineng
2014年
1期
60-69
,共10页
线性可分%伪分类超平面%空间映射%分类复杂度
線性可分%偽分類超平麵%空間映射%分類複雜度
선성가분%위분류초평면%공간영사%분류복잡도
Linear Separability%Pseudo-Separating Hyperplane%Space Mapping%Classification Complexity
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。
針對模式分類中線性可分的問題,文中將模式看作是歐氏空間中的點,研究歐氏空間中點與麵的關繫等解析幾何性質,在一般的分類超平麵概唸上定義偽分類超平麵。根據線性可分等價性,在需降維時進行空間映射。研究根據數據尋找偽分類超平麵,給齣幾何意義明顯的線性可分判斷方法,在該方法的基礎上給齣一種分類複雜度的度量方法。實驗結果錶明,該方法較好地體現數據的分類複雜度。
침대모식분류중선성가분적문제,문중장모식간작시구씨공간중적점,연구구씨공간중점여면적관계등해석궤하성질,재일반적분류초평면개념상정의위분류초평면。근거선성가분등개성,재수강유시진행공간영사。연구근거수거심조위분류초평면,급출궤하의의명현적선성가분판단방법,재해방법적기출상급출일충분류복잡도적도량방법。실험결과표명,해방법교호지체현수거적분류복잡도。
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.