Local Rank Deficiency Caused Problems in Analyzing Chemical Data

Multivariate curve resolution (MCR) is a powerful methodology for analyzing chemical data in different application fields such as pharmaceutical analysis, agriculture, food chemistry, environment, and industrial and clinical chemistry. However, MCR results are often complicated by rotational ambiguity, meaning that there is a range of feasible solutions that fulfill the constraints and explain equally well the observed experimental data. Constraints determine the properties of resolved profiles in MCR methods by enforcing different assumptions on data. The applied constraints on chemical data sets should be derived from the physical nature and prior knowledge of the system under study. Therefore, the reliability of the constraints in order to get accurate results is a critical aspect that should be considered by analytical chemists who use MCR methods. Local rank information plays a key role in the curve resolution of multicomponent chemical systems. Applying the local rank constraint can reduce the extent of rotational ambiguity considerably, and in some cases, unique solutions can be achieved. Local rank exploratory methods like Evolving Factor Analysis (EFA) method provide local rank maps in order to obtain the presence pattern of components on the main assumption that the number of components in each window is equal to its rank. It is shown in this work that the local rank is a mathematical concept that may not be in concordance with chemical information. Thus, applying the local rank constraint for restricting the rotational ambiguity in MCR methods can lead to incorrect solutions! This problem is due to "local rank deficiency", which is introduced in this contribution.