基于化学子空间对线性变换稳定的秩估计方法

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.

Estimation of Rank by Chemical Subspace Invariant to Linear Transformation Method

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.