Improved variable reduction in partial least squares modelling based on predictive-property-ranked variables and adaptation of partial least squares complexity

The calibration performance of partial least squares for one response variable (PLS1) can be improved by elimination of uninformative variables. Many methods are based on so-called predictive variable properties, which are functions of various PLS-model parameters, and which may change during the variable reduction process. In these methods variable reduction is made on the variables ranked in descending order for a given variable property. The methods start with full spectrum modelling. Iteratively, until a specified number of remaining variables is reached, the variable with the smallest property value is eliminated; a new PLS model is calculated, followed by a renewed ranking of the variables. The Stepwise Variable Reduction methods using Predictive-Property-Ranked Variables are denoted as SVR-PPRV. In the existing SVR-PPRV methods the PLS model complexity is kept constant during the variable reduction process. In this study, three new SVR-PPRV methods are proposed, in which a possibility for decreasing the PLS model complexity during the variable reduction process is build in. Therefore we denote our methods as PPRVR-CAM methods (Predictive-Property-Ranked Variable Reduction with Complexity Adapted Models). The selective and predictive abilities of the new methods are investigated and tested, using the absolute PLS regression coefficients as predictive property. They were compared with two modifications of existing SVR-PPRV methods (with constant PLS model complexity) and with two reference methods: uninformative variable elimination followed by either a genetic algorithm for PLS (UVE-GA-PLS) or an interval PLS (UVE-iPLS). The performance of the methods is investigated in conjunction with two data sets from near-infrared sources (NIR) and one simulated set. The selective and predictive performances of the variable reduction methods are compared statistically using the Wilcoxon signed rank test. The three newly developed PPRVR-CAM methods were able to retain significantly smaller numbers of informative variables than the existing SVR-PPRV, UVE-GA-PLS and UVE-iPLS methods without loss of prediction ability. Contrary to UVE-GA-PLS and UVE-iPLS, there is no variability in the number of retained variables in each PPRV(R) method. Renewed variable ranking, after deletion of a variable, followed by remodelling, combined with the possibility to decrease the PLS model complexity, is beneficial. A preferred PPRVR-CAM method is proposed.     

Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

A two-dimensional steady-sate analysis of semi-infinite brittlecrack growth at a constant subcritical rate in an unboundedfully-coupled thermoelastic solid under mixed-mode thermomechanicalloading is made. The loading consists of normal and shear tractionsand heat fluxes applied as point sources (line loads in theout-of-plane direction). A related problem is solved exactly in an integral transformspace, and robust asymptotic forms used to reduce the originalproblem to a set of integral equations. The equations are partiallycoupled and exhibit operators of both Cauchy and Abel types,yet can be solved analytically. The temperature change field at a distance from the moving crackedge is then constructed, and its dominant term is found tobe controlled by the imposed heat fluxes. The role of this termis, indeed, enhanced if the heat fluxes serve to render thecrack as a net heat source/sink for the solid, as opposed tobeing a transmitter of heat across its plane. More generally,the influence of the thermoelastic coupling on this field, aswell as other functions, is found to increase with crack speed.     

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.     

NMR and pattern recognition methods in metabolomics: From data acquisition to biomarker discovery: A review

Metabolomics is the discipline where endogenous and exogenous metabolites are assessed, identified and quantified in different biological samples. Metabolites are crucial components of biological system and highly informative about its functional state, due to their closeness to functional endpoints and to the organism's phenotypes. Nuclear Magnetic Resonance (NMR) spectroscopy, next to Mass Spectrometry (MS), is one of the main metabolomics analytical platforms. The technological developments in the field of NMR spectroscopy have enabled the identification and quantitative measurement of the many metabolites in a single sample of biofluids in a non-targeted and non-destructive manner. Combination of NMR spectra of biofluids and pattern recognition methods has driven forward the application of metabolomics in the field of biomarker discovery. The importance of metabolomics in diagnostics, e.g. in identifying biomarkers or defining pathological status, has been growing exponentially as evidenced by the number of published papers. In this review, we describe the developments in data acquisition and multivariate analysis of NMR-based metabolomics data, with particular emphasis on the metabolomics of Cerebrospinal Fluid (CSF) and biomarker discovery in Multiple Sclerosis (MScl).     

Use of the bootstrap and permutation methods for a more robust variable importance in the projection metric for partial least squares regression

Bio-pharmaceutical manufacturing is a multifaceted and complex process wherein the manufacture of a single batch hundreds of processing variables and raw materials are monitored. In these processes, identifying the candidate variables responsible for any changes in process performance can prove to be extremely challenging. Within this context, partial least squares (PLS) has proven to be an important tool in helping determine the root cause for changes in biological performance, such as cellular growth or viral propagation. In spite of the positive impact PLS has had in helping understand bio-pharmaceutical process data, the high variability in measured response (Y) and predictor variables (X), and weak relationship between X and Y, has at times made root cause determination for process changes difficult. Our goal is to demonstrate how the use of bootstrapping, in conjunction with permutation tests, can provide avenues for improving the selection of variables responsible for manufacturing process changes via the variable importance in the projection (PLS-VIP) statistic. Although applied uniquely to the PLS-VIP in this article, the generality of the aforementioned methods can be used to improve other variable selection methods, in addition to increasing confidence around other estimates obtained from a PLS model.     

Multivariate analysis of a data matrix containing A-DNA and B-DNA dinucleoside monophosphate steps: Multidimensional Ramachandran plots for nucleic acids

A method to construct the equivalent of multidimensional Ramachandran plots for nucleic acids on the basis of singular value decomposition (SVD) is presented. For this purpose, a data matrix containing 244 DNA dinucleoside monophosphate steps, represented by nine torsion angles, was decomposed into a score and loading matrix. It is shown that biplots, containing both score points and loading vectors, provide a simple tool to interpret the principles of DNA class separation. Scores separate the data matrix into one A-DNA class, two different B-DNA classes, and one so-called crankshaft class. Loading vectors correlate torsion angles. The projections of scores on loading vectors indicate which torsion angles play a dominant role in DNA class separation. The results of the biplots are supported by (simple) physical interpretations. From a three-dimensional score space the nine original torsion angles can be reconstructed. Hence, the potential to create the multidimensional equivalent of a Ramachandran plot is available; that is, forbidden and accessible regions in the reduced space reflect these same regions in the nine-dimensional original space. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 695–715, 1998     

The potential of field spectroscopy for the assessment of sediment properties in river floodplains

Investigations have shown that visible-near-infrared (VNIR) spectroscopy can accurately determine soil properties under laboratory conditions. In situ assessment of soil properties is of great benefit for several applications, as spectra can be acquired fast and almost continuously. The present study used partial least squares (PLS) regression to establish a relationship between soil reflectance spectra measured under field conditions and the organic matter and clay content of the soil. Spectra were acquired with a fieldspectrometer in a recently reconstructed floodplain along the river Rhine in The Netherlands. Several spectral pre-processing methods were employed to improve the performance and robustness of the models. Results indicate that, under varying surface conditions, field spectroscopy in combination with multivariate calibration does result in a qualitative relation for organic matter (R²=0.45) and clay content (R²=0.43) while under laboratory conditions more accurate results are obtained (R²=0.69 and 0.92, respectively). Soil moisture and vegetation cover had a negative influence on the prediction capabilities for both soil properties. Although the performance of the spectra measured in situ is not as accurate as physical analysis, the accuracy obtained is useful for rapid soil characterisation and remote sensing applications.