论文部分内容阅读
本文发展了一个因子分析软件(FACANA),它包括主因子分析、非正交变换以及目标检测。因子分析在自然科学和社会科学中有着广泛的应用。在分析化学方面,因子分析可以分解混合物的原始数据矩阵,得出抽象行矩阵和列矩阵,行矩阵和列矩阵分别相应于本征光谱矩阵和浓度矩阵。但不幸的是,抽象行矩阵和列矩阵不具有明确的物理和化学意义。FACANA的核心是采用非正交变换将抽象行矩阵和列矩阵转换成具有物理意义的本征光谱矩阵和浓度矩阵。FACANA可以从混合物中分离纯化合物光谱,混合物中组分数可达6个。如果组分数超过6个,可将非正交变换得到的结果作为FACANA的目标检测子程序的初始检测矩阵,目标检测程序可以用迭代逼近优化行矩阵,使之成为可供解释的光谱矩阵。除非正交变换和目标检测以外,本文研究、比较了不同的主因子分析方法并提出一个综合方法,提高了确定因子数目的准确度。因此,FACANA可用于分离混合物中的各组分光谱,特别是在对混合物的组成缺乏了解的情况下,它是得到纯组分光谱的有力手段。
This article developed a factor analysis software (FACANA), which includes the main factor analysis, non-orthogonal transformation and target detection. Factor analysis has a wide range of applications in the natural sciences and social sciences. In analytical chemistry, factor analysis can decompose the original raw data matrix of the mixture, yield abstract row and column matrices, and row and column matrices correspond to the eigen spectral matrix and the concentration matrix, respectively. Unfortunately, abstract row matrices and column matrices do not have a clear physical and chemical meaning. At the heart of FACANA is the use of non-orthogonal transformations to convert abstract row and column matrices into physically meaningful eigen spectral matrices and concentration matrices. FACANA separates pure compound spectra from a mixture of up to 6 components. If the number of components is more than 6, the result of non-orthogonal transformation can be used as the initial detection matrix of FACANA’s target detection subroutine. The target detection program can optimize the row matrix by iterative approximation and make it an interpretable spectral matrix. Except for orthogonal transformation and target detection, this paper studies and compares different principal factor analysis methods and proposes an integrated method to improve the accuracy of determining the number of factors. Therefore, FACANA can be used to separate the spectra of individual components in a mixture, especially in the absence of knowledge of the composition of the mixture, which is a powerful means of obtaining a pure component spectrum.