Department of Chemistry, Sharif University of Technology, P.O. Box 11155-9516, Tehran, Iran.
Faculty of Chemistry, Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-159, Zanjan, Iran.
Anal Chim Acta. 2022 Sep 22;1227:340330. doi: 10.1016/j.aca.2022.340330. Epub 2022 Aug 30.
In the present contribution, a new approach based on mutual information (MI) is proposed for exploring the independence of feasible solutions in two component systems. Investigating how independent are different feasible solutions can be a way to bridge the gap between independent component analysis (ICA) and multivariate curve resolution (MCR) approaches and, to the best of our knowledge, has not been investigated before. For this purpose, different chromatographic and hyperspectral imaging (HSI) datasets were simulated, considering different noise levels and different degrees of overlap for two-component systems. Feasible solutions were then calculated by both grid search (GS) and Lawton-Sylvester (LS) plots. MI map which is the plot of MI vs. rotation matrix elements was used to estimate the degree of independence between different solutions. Inspection of the results showed that the different solutions in the feasible bands correspond to different MI values and that those values are lower for spectral profiles (more independent) than for concentration profiles (more dependent) as expected from the duality concept and the opposite is true. In addition, component profiles are found near more dependent solutions for concentration profiles and near less dependent solutions for spectral profiles which is due to the fact that "independence" constraint was applied to the spectral profiles in ICA algorithms. The performance of three well-known ICA algorithms (mean-field independent component analysis (MF-ICA), mutual information-based least dependent component analysis (MILCA) and joint approximate diagonalization of eigenmatrices (JADE)) as well as MCR-alternating least squares (MCR-ALS) were investigated. MI maps showed that the solutions of MF-ICA and MCR-ALS are in the feasible bands but the MILCA and JADE solutions which are just based on the independence maximization are outside the MI maps.
在本研究中，提出了一种基于互信息（MI）的新方法，用于探索两个分量系统中可行解的独立性。研究不同可行解的独立性可以作为连接独立成分分析（ICA）和多变量曲线解析（MCR）方法的桥梁，据我们所知，这在以前的研究中尚未得到探讨。为此，模拟了不同的色谱和高光谱成像（HSI）数据集，考虑了两个分量系统的不同噪声水平和不同重叠程度。然后，通过网格搜索（GS）和 Lawton-Sylvester（LS）图计算可行解。MI 图是 MI 与旋转矩阵元素的关系图，用于估计不同解之间的独立性程度。检查结果表明，可行波段中的不同解对应于不同的 MI 值，并且正如对偶概念和相反情况所预期的那样，对于光谱分布（更独立）而言，这些值低于浓度分布（更依赖）。此外，对于浓度分布，在更依赖的解附近找到组分分布，对于光谱分布，在较不依赖的解附近找到组分分布，这是由于在 ICA 算法中对光谱分布应用了“独立性”约束。还研究了三种著名的 ICA 算法（均值场独立成分分析（MF-ICA）、基于互信息的最小依赖成分分析（MILCA）和特征矩阵的联合近似对角化（JADE））以及 MCR 交替最小二乘法（MCR-ALS）的性能。MI 图表明，MF-ICA 和 MCR-ALS 的解在可行波段内，但仅基于独立性最大化的 MILCA 和 JADE 解在 MI 图之外。
