模式特征的几何代数多向量表示方法  

Geometric algebra multi-vector representation method of pattern features

作　　者：徐永红[1] 洪文学[1] 高直[1] 

机构地区：[1]燕山大学电气工程学院,河北秦皇岛066004

出　　处：《燕山大学学报》2010年第2期119-122,137,共5页Journal of Yanshan University

基　　金：国家自然科学基金资助项目(60873121)

摘　　要：模式表示是模式识别的一个基本问题。传统统计模式识别理论中模式特征一般表示为一个数值向量,并被视作维欧式空间中的一个点。这种表示方法只利用了一阶特征,容易丢失模式特征间的关联信息和高阶结构。本文首先阐述了几何代数的公理化定义和一些基本概念,然后将传统的模式特征向量表示推广为几何代数空间的多向量表示,接着讨论了该表示的两种特例,最后阐述了基于该多向量表示进行特征提取和分类的一般思想和需要进一步研究的问题。Pattern representation is a basic problem of pattern recognition. In traditional statistical pattern recognition theory, pattern features are usually represented as a numeric vector and can be considered as a point in an n dimensional Euclidean space. This representation model uses only one order features, is prone to lose the interrelation of multiple features and higher order structure. Firstly the axiom definition of geometric algebra and some basic concepts is introduced, then the traditional pattern vector repres- entation is generalized to the multi-vector representation in geometric algebra space. Two special cases of this representation are discussed. The basic framework of pattern recognition based on the multi-vector representation is presented. In conclusion, the prospect of geometric algebra applying to visual pattern recognition and work to do in the future are outlined.

关 键 词：模式识别 模式表示 几何代数 多向量 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]