基于化学子空间对线性变换稳定的秩估计方法  

Estimation of Rank by Chemical Subspace Invariant to Linear Transformation Method

作　　者：谭涌溪[1] 蒋健晖[1] 谢洪平[1] 梁逸曾[1] 俞汝勤[1] 

机构地区：[1]湖南大学化学化工学院,长沙410082

出　　处：《高等学校化学学报》2001年第8期1319-1322,共4页Chemical Journal of Chinese Universities

基　　金：国家自然科学基金 (批准号 :2 9735 15 0 )

摘　　要：提出了一个新的化学计量学方法 ,即线性变换下稳定的化学子空间法 ,用于二维数据的化学秩估计 .该方法的基本思想是具有化学意义的子空间对在一个方向上的二维数据的线性变换是最稳定的 .据此 ,两个新的定量指标投影残差法和子空间夹角法被提出用于衡量两个子空间之间的差异性 .对两个近红外数据的分析结果表明 ,这一方法为二维数据的化学秩估计提供了一个很有价值的工具 .Based on the invariability of the sought for chemical subspace to the linear transformation, a novel approach, called chemical subspace invariant to linear transformation method, is developed for estimation of chemical rank of two way data matrices. The idea of this approach is that the chemically meaningful subspace is the most stable one with respect to the linear transformation of the two way data along one order. Two quantitative indexes, projection residual as well as included angle of subspace, are also proposed to measure the difference of two subspaces. The results of two NIR data show that this method provides a very promising tool for chemical rank estimation of two way data matrices.

关 键 词：子空间差异 二维数据分析 线性变换 秩估计 化学计量学 化学子空间 近红外光谱数据 

分 类 号：O65－37[理学—分析化学]