Boosting model performance and interpretation by entangling preprocessing selection and variable selection

The aim of data preprocessing is to remove data artifacts—such as a baseline, scatter effects or noise—and to enhance the contextually relevant information. Many preprocessing methods exist to deliver one or more of these benefits, but which method or combination of methods should be used for the specific data being analyzed is difficult to select. Recently, we have shown that a preprocessing selection approach based on Design of Experiments (DoE) enables correct selection of highly appropriate preprocessing strategies within reasonable time frames.     

Alignment of high resolution magic angle spinning magnetic resonance spectra using warping methods

The peaks of magnetic resonance (MR) spectra can be shifted due to variations in physiological and experimental conditions, and correcting for misaligned peaks is an important part of data processing prior to multivariate analysis. In this paper, five warping algorithms (icoshift, COW, fastpa, VPdtw and PTW) are compared for their feasibility in aligning spectral peaks in three sets of high resolution magic angle spinning (HR-MAS) MR spectra with different degrees of misalignments, and their merits are discussed. In addition, extraction of information that might be present in the shifts is examined, both for simulated data and the real MR spectra. The generic evaluation methodology employs a number of frequently used quality criteria for evaluation of the alignments, together with PLS-DA to assess the influence of alignment on the classification outcome.Peak alignment greatly improved the internal similarity of the data sets. Especially icoshift and COW seem suitable for aligning HR-MAS MR spectra, possibly because they perform alignment segment-wise. The choice of reference spectrum can influence the alignment result, and it is advisable to test several references. Information from the peak shifts was extracted, and in one case cancer samples were successfully discriminated from normal tissue based on shift information only. Based on these findings, general recommendations for alignment of HR-MAS MRS data are presented. Where possible, observations are generalized to other data types (e.g. chromatographic data).     

Opening the kernel of kernel partial least squares and support vector machines

Kernel partial least squares (KPLS) and support vector regression (SVR) have become popular techniques for regression of complex non-linear data sets. The modeling is performed by mapping the data in a higher dimensional feature space through the kernel transformation. The disadvantage of such a transformation is, however, that information about the contribution of the original variables in the regression is lost. In this paper we introduce a method which can retrieve and visualize the contribution of the variables to the regression model and the way the variables contribute to the regression of complex data sets. The method is based on the visualization of trajectories using so-called pseudo samples representing the original variables in the data. We test and illustrate the proposed method to several synthetic and real benchmark data sets. The results show that for linear and non-linear regression models the important variables were identified with corresponding linear or non-linear trajectories. The results were verified by comparing with ordinary PLS regression and by selecting those variables which were indicated as important and rebuilding a model with only those variables.     

Automatic correction for phase shifts, frequency shifts, and lineshape distortions across a series of single resonance lines in large spectral data sets

A new model-free method is presented that automatically corrects for phase shifts, frequency shifts, and additional lineshape distortions of one single resonance peak across a series of in vivo NMR spectra. All separate phase and frequency variations are quickly and directly derived from the common lineshape in the data set using principal component analysis and linear regression. First, the new approach is evaluated on simulated data in order to quantitatively assess the phase and frequency shifts which can be removed by the proposed correction procedure. Subsequently, the value of the method is demonstrated on in vivo (31)P NMR spectra from skeletal muscle of the hind leg of the mouse focusing on the phosphocreatine resonance which is distorted by the experimental procedure. Phase shifts, frequency shifts, and lineshape distortions with respect to the common lineshape in the spectral data set could successfully be removed.     

Visualisation and interpretation of Support Vector Regression models

This paper introduces a technique to visualise the information content of the kernel matrix and a way to interpret the ingredients of the Support Vector Regression (SVR) model. Recently, the use of Support Vector Machines (SVM) for solving classification (SVC) and regression (SVR) problems has increased substantially in the field of chemistry and chemometrics. This is mainly due to its high generalisation performance and its ability to model non-linear relationships in a unique and global manner. Modeling of non-linear relationships will be enabled by applying a kernel function. The kernel function transforms the input data, usually non-linearly related to the associated output property, into a high dimensional feature space where the non-linear relationship can be represented in a linear form. Usually, SVMs are applied as a black box technique. Hence, the model cannot be interpreted like, e.g., Partial Least Squares (PLS). For example, the PLS scores and loadings make it possible to visualise and understand the driving force behind the optimal PLS machinery. In this study, we have investigated the possibilities to visualise and interpret the SVM model. Here, we exclusively have focused on Support Vector Regression to demonstrate these visualisation and interpretation techniques. Our observations show that we are now able to turn a SVR black box model into a transparent and interpretable regression modeling technique.     

Validation of remote, on-line, near-infrared measurements for the classification of demolition waste

The classification performance, based on measurements obtained by a dedicated remote near-infrared sensor, is validated. Goal is the separation of demolition waste in three fractions: wood, plastic, and stone. In phase one, reference objects are collected and measured in order to develop the classification algorithm and to obtain reference classification results. In phases two and three, the validation performance and robustness are tested under laboratory and industrial conditions. In phase two, preliminary measurements are performed in the laboratory, indicating that some sensor hardware modifications are necessary. In phase three, measurements are performed on a pilot plant according to the following validation design. On the conveyor belt, objects are measured in the middle and at both borders, wet objects are measured in the middle, and a small set of objects is measured during 4 consecutive days. It is checked whether the classification performance obeys the predefined demands. The applied chemometrical techniques are well capable of separating dry demolition waste if the objects are positioned in the middle of the conveyor belt. It is recommended to overcome the sensor miniaturization-scale limitations by applying larger optical parts. The hardware sensor is not robust to wet objects, although this problem was accounted for during the development of the classification procedure. Including wet objects in the training set might overcome this restriction.     

Diagnostic analysis of experimental artefacts in DOSY NMR data by covariance matrix of the residuals

Multivariate curve resolution (MCR) has been applied to separate pure spectra and pure decay profiles of DOSY NMR data. Given good initial guesses of the pure decay profiles, and combined with the nonlinear least square regression (NLR), MCR can result in good separation of the pure components. Nevertheless, due to the presence of artefacts in experimental data, validation of a MCR model is still necessary. In this paper, the covariance matrix of the residuals (CMR), obtained by postmultiplying the residual matrix with its transpose, is proposed to evaluate the quality of the results of an experimental data set. Plots of the rows of this matrix give a general impression of the covariance in the frequency domain of the residual matrix. Different patterns in the plot indicate possible causes of experimental imperfections. This new criterion can be used as diagnosis in order to improve experimental settings as well as suggest appropriate preprocessing of DOSY NMR data.     

Powder pattern indexing using the weighted crosscorrelation and genetic algorithms

X-ray diffraction is a powerful technique for investigating the structure of crystals and crystalline powders. Unfortunately, for powders, the first step in the structure elucidation process, retrieving the unit cell parameters (indexing), is still very critical. In the present article, an improved approach to powder pattern indexing is presented. The proposed method matches peak positions from experimental X-ray powder patterns with peak positions from trial cells using a recently published method for pattern comparison (weighted crosscorrelation). Trial cells are optimized with Genetic Algorithms. Patterns are not pretreated to remove any existing zero point shift, as this is determined during optimization. Another improvement is the peak assignment procedure. This assignment is needed for determining the similarity between lines from trial cells and experiment. It no longer allows calculated peaks to be assigned twice to different experimental peaks, which is beneficial for the indexing process. The procedure proves to be robust with respect to false peaks and accidental or systematic absensences of reflections, and is successfully applied to powder patterns originating from orthorhombic, monoclinic, and triclinic compounds measured with synchrotron as well as with conventional laboratory X-ray diffractometers.