Predicting the uniqueness of single non-negative profiles estimated by multivariate curve resolution methods.

In many kinds of chemical data, one or more species are unknown and the only efficient way to identify and/or quantify them is by mathematical resolution of the mixture spectra. The major problem with such mathematical decompositions is the possibility of obtaining a range of feasible solutions instead of a unique solution due to insufficient prior information about the system under study. However, even with the minimal non-negativity assumptions, there may be some levels of uniqueness, i.e., full/partial/fractional, in the results of the bilinear decomposition of chemical data which is very important to detect. In this study, a procedure is proposed to predict the uniqueness of the resolved non-negative profiles obtained by MCR-ALS (or analogous methods like NMF, EFA, SIMPLISMA, ITTFA, HELP, etc.). This uniqueness prediction is based on the data-based uniqueness (DBU) theorem and the general rule of uniqueness (GRU) presented in previous studies. The proposed procedure is easy to implement, has no additional computational cost, and is general for different systems with any number of components. Several simulated and experimental datasets containing different numbers of components were used to examine and evaluate the proposed procedure.

Soft known-value constraints for improved quantitation in multivariate curve resolution.

Multivariate curve resolution (MCR) is a powerful tool in chemometrics that has been involved in the solution of many analytical problems. The introduction of partial or incomplete knowledge of reference values as known-value constraints in an MCR model can considerably reduce the extent of rotational ambiguity for all components. Known-value constraints can provide enough information for MCR methods to perform both the identification and quantitative analysis of first-order data sets. In practice, in addition to noise and non-ideal behavior, limitations in the reference methods or procedures cause deviation in measured known values. It is shown that deviation in the measured known values, when used as known-value constraints, may result in considerable quantification errors in MCR results and can challenge identification analysis. This contribution investigates the importance and effect of soft known-value constraints on the accuracy of MCR solutions. The influence of noise levels, the amount of deviation of known values from true values, and the interaction of these two factors were evaluated with simulated data. An illustration using soft known-value constraints is given for a batch reaction experiment.

Discriminating normal regions within cancerous hen ovarian tissue using multivariate hyperspectral image analysis.

RATIONALE: Identification of subregions under different pathological conditions on cancerous tissue is of great significance for understanding cancer progression and metastasis. Infrared matrix-assisted laser desorption electrospray ionization mass spectrometry (IR-MALDESI-MS) can be potentially used for diagnostic purposes since it can monitor spatial distribution and abundance of metabolites and lipids in biological tissues. However, the large size and high dimensionality of hyperspectral data make analysis and interpretation challenging. To overcome these barriers, multivariate methods were applied to IR-MALDESI data for the first time, aiming at efficiently resolving mass spectral images, from which these results were then used to identify normal regions within cancerous tissue. METHODS: Molecular profiles of healthy and cancerous hen ovary tissues were generated by IR-MALDESI-MS. Principal component analysis (PCA) combined with color-coding built a single tissue image which summarizes the high-dimensional data features. Pixels with similar color indicated similar composition. PCA results from healthy tissue were further used to test each pixel in cancerous tissue to determine if it is healthy. Multivariate curve resolution-alternating least squares (MCR-ALS) was used to obtain major spatial features existing in ovary tissues, and group molecules with the same distribution patterns simultaneously. RESULTS: PCA as the predominating dimensionality reduction approach captured over 90% spectral variances by the first three PCs. The PCA images show the cancerous tissue is more chemically heterogeneous than healthy tissue, where at least four regions with different m/z profiles can be differentiated. PCA modeling assigns top regions of cancerous tissue as healthy-like. MCR-ALS extracted three and four major compounds from healthy and cancerous tissue, respectively. Evaluating similarities of resolved spectra uncovered the chemical components that were distinct in some regions on cancerous tissue, serving as a supplementary way to differentiate healthy and cancerous regions. CONCLUSIONS: Two unsupervised chemometric methods including PCA and MCR-ALS were applied for resolving and visualizing IR-MALDESI-MS data acquired from hen ovary tissues, improving the interpretation of mass spectrometry imaging results. Then possible normal regions were differentiated from cancerous tissue sections. No prior knowledge is required using either chemometric method, so our approach is readily suitable for unstained tissue samples, which allows one to reveal the molecular events happening during disease progression.

Known-value constraint in multivariate curve resolution.

Multivariate curve resolution (MCR) methods are powerful chemometric approaches that have been significantly involved to study the complex chemical systems. The accuracy of MCR results is directly related to the applied constraints which determine the properties of the resolved profiles. Constraints have been, and still are, an active field of research in MCR studies. Different constraints have different impacts on the range of feasible solutions, so it is important to study the effect of each constraint, to examine its compliance with physico-chemical principles, and to find sufficient conditions to ensure unique solutions. In this study, we focus on known-value constraint and the requirements for reducing the range of feasible solutions under this constraint. In addition, several theoretical rules are presented to determine the minimum number of required known-values in order to get a unique solution. The theory of known-values was accessed using several simulated and experimental datasets. As shown previously, known-value information can be applied in quantitative analysis of first-order data. The prediction performance of MCR-ALS method under known-value constraint was compared to the results of the well stablished partial least squares (PLS) method in the presence of minimum number of required calibration samples. The comparison shows the advantage of using MCR-ALS method under known-value constraint over the PLS results in such experiments.

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.