三线性直接分解法分析高维灰色体系

对于由多个两维测量数据组成的三维阵，本文提出一种新三线性直接分解方法。采用高维ＰＣＡ分解，从三维阵中直接提取抽象光谱和抽象浓度，再结合ＱＺ算法，唯一地确定混合物中各组分光谱的浓度。该方法可以排除其它未知组分的干扰，适用于高维灰色体系定性定量分析和多点校准。用模拟数据讨论了光谱分离度对该方法的影响，应用于混合维生素Ｂ１、Ｂ２和Ｂ６的荧光分析，求得的光谱和浓度与实验值吻合很好。

Analysis of High-dimensional Grey System by the Trilinear Direct Decomposition Algorithm

A novel trilinear direct decomposition algorithm is proposed for the decomposi-tion of a three-dimensional matrix consisting of several samples of measured two-dimensional data. The abstract spectral and concentration matrices are obtained by high-dimensional principal component analysis. Then the unique solutions of spectra and concentrations of the components are determined by the QZ algorithm. The new method is robust in noise environment and suitable for qualitative and quantitative analysis of high-dimensional grey system and multi-point calibration. The simulated data were used for exploring the effect of spectral resolution to the precision of prediction. In fluorescence analysis of mixtures of vitamin B1, vitamin B2 and vitamin B6, the results show that the obtained spectra and concentrations are in agreement with the experimental values.