Henry E R
Laboratory of Chemical Physics, National Institute of Health, Bethesda, Maryland 20892-0520, USA.
Biophys J. 1997 Feb;72(2 Pt 1):652-73. doi: 10.1016/s0006-3495(97)78703-4.
We describe a general approach to the model-based analysis of sets of spectroscopic data that is built upon the techniques of matrix analysis. A model hypothesis may often be expressed by writing a matrix of measured spectra as the product of a matrix of spectra of individual molecular species and a matrix of corresponding species populations as a function of experimental conditions. The modeling procedure then requires the simultaneous determination of a set of species spectra and a set of model parameters (from which the populations are derived), such that this product yields an optimal description of the measured spectra. This procedure may be implemented as an optimization problem in the space of the (possibly nonlinear) model parameters alone, coupled with the efficient solution of a corollary linear optimization problem using matrix decomposition methods to obtain a set of species spectra corresponding to any set of model parameters. Known species spectra, as well as other information and assumptions about spectral shapes, may be incorporated into this general framework, using parametrized analytical functional forms and basis-set techniques. The method by which assumed relationships between global features (e.g., peak positions) of different species spectra may be enforced in the modeling without otherwise specifying the shapes of the spectra will be shown. We also consider the effect of measurement errors on this approach and suggest extensions of the matrix-based least-squares procedures applicable to situations in which measurement errors may not be assumed to be normally distributed. A generalized analysis procedure is introduced for cases in which the species spectra vary with experimental conditions.
我们描述了一种基于矩阵分析技术的对光谱数据集进行基于模型分析的通用方法。通常可以通过将测量光谱矩阵写成单个分子物种光谱矩阵与作为实验条件函数的相应物种丰度矩阵的乘积来表达模型假设。然后，建模过程需要同时确定一组物种光谱和一组模型参数（由此得出丰度），以使该乘积能对测量光谱给出最佳描述。此过程可以仅在（可能是非线性的）模型参数空间中作为一个优化问题来实现，并结合使用矩阵分解方法有效求解一个推论线性优化问题，以获得与任何一组模型参数相对应的一组物种光谱。已知的物种光谱以及关于光谱形状的其他信息和假设，可以使用参数化分析函数形式和基集技术纳入这个通用框架。将展示在建模过程中如何在不另行指定光谱形状的情况下强制不同物种光谱的全局特征（例如，峰位置）之间的假设关系的方法。我们还考虑了测量误差对该方法的影响，并提出了适用于测量误差可能不被假定为正态分布情况的基于矩阵的最小二乘法的扩展。针对物种光谱随实验条件变化的情况引入了一种广义分析程序。
