Heuristic Evolving Latent Projections Research Articles

Factor analytical resolution of simultaneous, dynamic thermal process in thermochromatography of oil shale

In thermochromatography (ThGC), where a series of chromatograms of the headspace vapour of a sample are recorded during temperature programmed heating of the sample and output data are presented as a 2D-plot of retention time versus pyrolysis temperature, chemometric methods are natural to use for data processing. The aim of this work is to assess the performance of evolving factor analysis (EFA) and heuristic evolving latent projection (HELP) methods using native-sample thermochromatography data. An example of analysis by ThGC of oil shale samples is given and clear separation of thermal vaporisation (extraction) and thermal degradation processes are shown and the chemical products estimated. With no a priori assumptions about the chromatograms/thermal peaks, chromatographically very similar processes (these include thermal vaporisation (desorption) and multi-stage degradation) were detected during the thermal programming of sample and resolved.

Resolution of multicomponent profiles with partial selectivity. A comparison of direct methods

Three procedures for resolution of multicomponent systems were tested for their ability to deal with partial selectivity. The methods were evolving factor analysis (EFA), heuristic evolving latent projections (HELP) and the method of orthogonal projections. An extensive data simulation, in which five factors were varied according to a full 2 5 factorial design, was carried out to test the methods. The simulations showed HELP to be the most powerful method for resolution. The importance of the design variables was qualitatively studied by means of PLS models. Several parameters, among them the net analytical signal, were found to be unable to alone say anything conclusively about HELP's chances for successfully resolving the systems.

Multi-array resolution parameter for multidetection chromatography. Performance of alternating regression, iterative target transformation factor analysis and heuristic evolving latent projections

The resolution of multicomponent chromatographic structures is quantified using a parameter ( R 2- D ), ratioing the amount of selective information with the overall information. The performance of the three curve resolution techniques, alternating regression (AR), iterative target transformation factor analysis (ITTFA) and heuristic evolving latent projections (HELP), is evaluated on simulated two- and three-analyte systems. The multi-array resolution parameter ( R 2- D ) showed to be a valuable tool for a three-analyte system in predicting concentration errors and quality of resolved spectra for the three methods. As for the curve resolution techniques, the multi-array resolution parameter itself showed to be vulnerable to heteroscedastic noise. Overall the HELP method performed best while AR performed poorest, both regarding prediction of concentrations and resolving spectra.

Assessment of peak origin and purity in one-dimensional chromatography by experimental design and heuristic evolving latent projections

A new procedure for assessing peak origin and purity in chromatographic calibration is presented. Chemical analytes were mixed according to an experimental design in order to achieve independent concentration patterns. One-dimensional chromatograms were analysed as digital profiles with the heuristic evolving latent projections (HELP) method after minimization of the retention time shifts between target peaks by a simplex technique. The origin of peaks was assessed by calculating the correlation between concentration patterns, obtained as the first loadings in HELP from principal component analysis (PCA) on selective chromatographic regions, and the patterns in the designed mixtures. Co-eluting impurities and overlapping peaks could be detected, resolved and quantified. Only a few non-overlapping data points were needed to assess the origin of peaks. Latent-variable correlation chromatograms are introduced as a powerful tool for the assignment of chromatographic areas with similar concentration patterns.

Resolution of embedded chromatographic peaks by sequential rank analysis of the first-order differentiated elution profile in the time domain

Assuming local symmetry around chromatographic peak maxima of the individual analytes, a new procedure is developed for identification of such maxima in multiwavelength chromatograms with embedded peaks. At these maxima the spectroscopic profiles of the pure analytes are directly available from the first-order differentiated elution profile in the time domain. When the chromatographic profiles of the pure analytes are not symmetric, for instance due to tailing of peaks, the identification of the maxima still appears to be possible by means of latent-projective graphs. The quality of the results can be checked by comparison with partial resolution results from other procedures, such as heuristic evolving latent projections (HELP) or orthogonal projections. The approach is investigated on some simulated systems.

Resolution of strongly overlapping two‐way multicomponent data by means of heuristic evolving latent projections

AbstractHigh‐performance liquid chromatography with diode array detection (HPLC––DAD) is used to characterize mixtures from chlorophyll a degradation experiments. Overlapping chromatographic peaks are resolved by means of the heuristic evolving latent projections (HELP) method. The HELP method is a self‐modelling curve resolution method. No assumptions are made about spectral and/or chromatographic peak shape. In the first step the method establishes the real noise level in the data by use of the so‐called zero‐component regions. This information is used to reveal selective chromatographic information and the number of chemical species at every retention time in unresolved chromatographic peaks. Utilising the selective chromatographic regions in combination with the zero‐concentration windows, unique resolution into concentration profiles and spectra of the pure chemical species is accomplished. HPLC–DAD data from six chlorophyll a degradation experiments were analysed. Consistent results were obtained even with very similar spectra for six or seven overlapping chemical components.

Deconvolution in one-dimensional chromatography by heuristic evolving latent projections of whole profiles retention time shifted by simplex optimization of cross-correlation between target peaks

A new approach to the detection and resolution of co-eluting components is developed for one-dimensional chromatographic analysis. In essence, the method consists of two steps. First, chromatograms from different runs are made comparable by using a simplex technique for adjusting the retention-time shifts so as to optimize the cross-correlation between selected target peaks in the chromatograms. Second, the heuristic evolving latent projections (HELP) method is used to detect and resolve co-eluting peaks in the resulting two-way data array. The new method represents a hybrid between conventional one-way and two-way resolution methods by which a collection of one-way chromatograms on samples with the same chemical components can be treated with chemometrics procedures developed for instruments with multi-wavelength detection. This permits the determination of the number of chemical components under a peak and subsequent resolution and quantification of the chemical components. Hence the hybrid method bridges the gap between traditional and coupled chromatography. The method provides the concentration pattern of each of the chemical components in different samples. In this respect, the approach makes traditional one-way chromatography an important supplement to coupled chromatography for solving problems of, e.g. peak homogeneity, in a series of samples with similar chemical components.

Heuristic evolving latent projections: resolving two-way multicomponent data. 1. Selectivity, latent-projective graph, datascope, local rank, and unique resolution

Heuristic evolving latent projections (HELP) are proposed as a new method to resolve two-way bilinear multicomponent data into spectra and chromatograms of the pure constituents. The method is founded on four elements: (I) the use of the so-called zero-component regions in order to establish the detection limit for the chemical species, (II) the use if latent-projective graphs (datascope) to reveal selective (one-component) chormatographic and/or spectral regions, (III) local rank analysis in order to check the selectivity of the regions found by visual detection, and (IV) the use of the selective information for unique resolution into spectra and chromatograms of the pure chemical constituents