Mutual information map as a new way for exploring the independence of chemically meaningful solutions in two-component analytical data.

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.