摘要
分析了李群流形空间的几何结构、核函数和KFDA(kernel Fisher linear discriminant analysis)的原理,推导了矩阵李群内积空间的度量形式,进一步推导出5个李群核函数,并以此设计实现了KLieDA(kernel Lie group linear discriminant analysis)算法。李群核函数是适应性更广的核函数形式,由于欧氏空间的几何结构是李群的子集,李群函数不仅适用于矩阵李群的样本集,同时也适用于常规的向量形式的样本集。实验表明,基于李群函数和李群均值理论的KLieDA算法是一种快速高效的李群样本分类器。实验部分除了KLieDA的分类,还对基于李群核的SVM(support vector machine)算法进行手写体分类,结果表明,手写体图像的区域协方差李群特征具有较好的线性分布特性。
This paper analyzes the geometry structure of Lie group manifold, kernel function and principles of KFDA （kernel Fisher linear discriminant analysis）, derives the measure of matrix Lie group dot-product space, then derives five Lie group kernel functions and designs KLieDA （kernel Lie group linear discriminant analysis） algorithm. Lie group kernel functions are more adaptive kernel functions. Due to the geometry of Euclidean space is a subset of Lie group, Lie group functions apply to not only the sample sets of matrix Lie group but also the sample sets of conventional vector form. The experiments show that KLieDA algorithm, based on theories of Lie group functions and Lie groups mean, is a fast and efficient Lie group sample classifier. Additionally, in the experiment section, the paper does a handwritten classification through SVM （support vector machine） based on Lie group kernel functions, and the results show that the region image covariance Lie group feature of the handwritten has a good linear distribution.
出处
《计算机科学与探索》
CSCD
2012年第11期1026-1038,共13页
Journal of Frontiers of Computer Science and Technology
基金
国家自然科学基金(61033013
60970045)
东吴学者计划(14317360)
苏大国家预研基金(SDY2011A25)~~
关键词
李群
李群核
李群均值
李群协方差特征
分类器
Lie group
Lie group kemel
Lie group mean
Lie group covariance feature
classifier
