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Aktuelle wissenschaftliche Fachartikel der
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Quadratic PLS1 regression revisited
Within the framework of nonlinear partial least squares (PLS), the quadratic PLS regression approach, involving both linear and quadratic terms in the criterion, is discussed. A new algorithm for the determination of the components is proposed, and its advantages over the original algorithm are outlined. The approach of analysis is illustrated on the basis of simulated and real data. Copyright © 2012 John Wiley & Sons, Ltd.
Evaluation of variation in dynamic processes via online spectrometers
Theory of sampling offers powerful tools for process optimization. An adequate sampling interval can be determined for spectral measurements when utilizing a multivariate extension of variography by applying score vectors as independent sources of uncertainty. The traditional way is to apply variographic analyses into single process variables independently. In the multivariate extension, those process variables are replaced with score vectors of principal component analysis. The combined uncertainty found this way depends not only on the variance in the spectra, but also, for example, on the number of utilized score vectors and the preprocessing method. This approach is illustrated with a crystallization process continuously followed with an attenuated total reflectance Fourier transform infrared instrument. The results show that the approach is highly applicable but should only be utilized as an indicative tool. Copyright © 2012 John Wiley & Sons, Ltd.
Robust PARAFAC for incomplete data
Different methods exist to explore multiway data. In this article, we focus on the widely used PARAFAC (parallel factor analysis) model, which expresses multiway data in a more compact way without ignoring the underlying complex structure. An alternating least squares procedure is typically used to fit the PARAFAC model. It is, however, well known that least squares techniques are very sensitive to outliers, and hence, the PARAFAC model as a whole is a nonrobust method. Therefore a robust alternative, which can deal with fully observed data possibly contaminated by outlying samples, has already been proposed in literature. In this paper, we present an approach to perform PARAFAC on data that contain both outlying cases and missing elements. A simulation study shows the good performance of our methodology. In particular, we can apply our method on a dataset in which scattering is detected and replaced with missing values. This is illustrated on a real data example. Copyright © 2012 John Wiley & Sons, Ltd.
Journal Highlight: Physics of MRI: A primer
A non-mathematical conceptual approach is presented for understanding magnetic resonance image formation from an intuitive perspective. It is based on an introductory lecture given for the past many years during the "MR Physics and Techniques for Clinicians" course at the Annual Meeting of the ISMRM.
Journal Highlight: The role of targeted chemical proteomics in pharmacology
The role of chemical proteomics in determining the specificity of drugs and their analogues for anticipated known targets, which leads to the discovery of unexpected targets and potential side effects, is discussed with examples. The process leads to the refinement of second- and third-generation drug design for treatment of many diseases.
X-ray solution to obesity: Structural target revealed
Researchers at the University of Sheffield, UK, have used X-ray crystallography to obtain a detailed structure of a key component of the human obesity receptor, the binding domain for the satiety hormone leptin.
Robust preprocessing and model selection for spectral data
To calibrate spectral data, one typically starts with preprocessing the spectra and then applies a multivariate calibration method such as principal component regression or partial least squares regression. In the model selection step, the optimal number of latent variables is determined in order to minimize the prediction error. To protect the analysis against the harmful influence of possible outliers in the data, robust calibration methods have been developed. In this paper, we focus on the preprocessing and the model selection step. We propose several robust preprocessing methods as well as robust measures of the root mean squared error of prediction (RMSEP). To select the optimal preprocessing method, we summarize the results for the different RMSEP values by means of a desirability index, which is a concept from industrial quality control. These robust RMSEP values are also used to select the optimal number of latent variables. We illustrate our newly developed techniques through the analysis of a real data set containing near-infrared measurements of samples of animal feed. Copyright © 2012 John Wiley & Sons, Ltd.
Optimization of two-step batch processes and the method of compensation for random error
This paper considers the problem of the optimal setting of controllable variables in two-step processes with quality constraints. The optimal setting minimizes the cost and satisfies quality constraints defined for the final output. The main emphasis is given to processes where it is possible to make intermediate measurements after the first processing step and to utilize these measurements before the control variables in the second step are set. Optimization based on this method of compensation for random error can yield substantially lower cost than does optimization based on a strategy where all variables are fixed before the process starts. An example of application of the method is taken from the food industry. Copyright © 2012 John Wiley & Sons, Ltd.
Improvements to multivariate data analysis and monitoring of batch processes by multilevel methods
Batch process data contain between-run and within-run sources of variation, which complicates data analysis and process monitoring. Multilevel methods, such as multilevel simultaneous component analysis, greatly enhance the interpretation of large sets of batch process data by separating the between-run and within-run variation. Using a multilevel approach in batch process monitoring greatly reduces the occurrence of false alarms that are caused by trivial variations and process changes that were made on purpose. This also reduces the need for model updating, which often is a large effort and causes downtime of the monitoring system. Furthermore, relevant phenomena that are masked by larger but uninteresting sources of variation when standard batch process monitoring methods are applied can often be detected if the multilevel approach is used. Chemical batch process data are used to illustrate the methods. Copyright © 2012 John Wiley & Sons, Ltd.
Cross-validation in PCA models with the element-wise k-fold (ekf) algorithm: theoretical aspects
Cross-validation has become one of the principal methods to adjust the meta-parameters in predictive models. Extensions of the cross-validation idea have been proposed to select the number of components in principal components analysis (PCA). The element-wise k -fold (ekf ) cross-validation is among the most used algorithms for principal components analysis cross-validation. This is the method programmed in the PLS_Toolbox, and it has been stated to outperform other methods under most circumstances in a numerical experiment. The ekf algorithm is based on missing data imputation, and it can be programmed using any method for this purpose. In this paper, the ekf algorithm with the simplest missing data imputation method, trimmed score imputation, is analyzed. A theoretical study is driven to identify in which situations the application of ekf is adequate and, more importantly, in which situations it is not. The results presented show that the ekf method may be unable to assess the extent to which a model represents a test set and may lead to discard principal components with important information. On a second paper of this series, other imputation methods are studied within the ekf algorithm. Copyright © 2012 John Wiley & Sons, Ltd.
Orthogonal signal correction-based prediction of total antioxidant activity using partial least squares regression from chromatograms
The multivariate calibration methods—partial least squares (PLS), orthogonal signal correction and partial least squares (OSC-PLS)—were employed for the prediction of total antioxidant activities of four Prunella L. species. High-performance liquid chromatography (HPLC) and spectrophotometric approaches were used to determine the total antioxidant activity of the Prunella L. samples. Several preprocessing techniques such as smoothing and normalization were employed to extract the chemically relevant information from the data after alignment with correlation optimized warping. The importance of the preprocessing was investigated by calculating the root mean square error for the calibration set for the total antioxidant activity of Prunella L. samples. The models developed on the basis of the preprocessed data were able to predict the total antioxidant activity with a precision comparable to that of the reference 2,2-azino-di-(3-ethylbenzothialozine-sulfonic acid) and 2,2-diphenyl-1-picrylhydrazyl methods. The OSC-PLS model seems preferable because of its predictive and describing abilities and good interpretability of the contribution of compounds to the total antioxidant activity. The contribution of individual phenolic compounds to the total antioxidant activity was identified by HPLC. Copyright © 2012 John Wiley & Sons, Ltd.
Overview of two-norm (L2) and one-norm (L1) Tikhonov regularization variants for full wavelength or sparse spectral multivariate calibration models or maintenance
Building a multivariate calibration model is typically accomplished using partial least squares, principal component regression, or ridge regression, also derived as the standard form of Tikhonov regularization (TR). These approaches can be used in a full variable mode (full wavelengths for spectroscopic data) or with wavelength selection (bands and/or individual for sparse models). Calibration maintenance is an important aspect of multivariate calibration and describes the situation of maintaining acceptable predictions from a model over time. In terms of TR, this amounts to updating an existing model (determined under primary conditions) to handle new secondary conditions such as a new instrument, sample matrix, or environmental conditions. This paper overviews TR in its ability to form a primary calibration model or update a primary model to new secondary conditions while using full wavelengths or simultaneously selecting wavelengths to form respective sparse models. These objectives can be accomplished in two-norm (L2 ) or one-norm (L1 ) or combined formats. Also included is a TR design that minimizes the effect of the standardization set composition, i.e., reduces the effect of an outlier. Ongoing work that removes all reference samples from the TR framework is also described. Copyright © 2012 John Wiley & Sons, Ltd.
Bi-modal OnPLS
This paper presents an extension to the recently published OnPLS data analysis method. Bi-modal OnPLS allows for arbitrary block relationships in both columns and rows and is able to extract orthogonal variation in both columns and rows without bias towards any particular direction or matrix: the method is fully symmetric with regard to both rows and columns.
Bi-modal OnPLS extracts a minimal number of globally predictive score vectors that exhibit maximal covariance and correlation in the column space and a corresponding set of predictive loading vectors that exhibit maximal correlation in the row space. The method also extracts orthogonal variation (i.e. variation that is not related to all other matrices) in both columns and rows. The method was applied to two synthetic datasets and one real data set regarding sensory information and consumer likings of dairy products. It was shown that Bi-modal OnPLS greatly improves the intercorrelations between both loadings and scores while still finding the correct variation. This facilitates interpretation of the predictive components and makes it possible to study the orthogonal variation in the data. Copyright © 2012 John Wiley & Sons, Ltd.
Liver functional magnetic resonance imaging analysis using a latent variables approach
The liver is a highly vascular organ with a dual blood supply, and it performs a remarkable number of vital functions. Here, we show, through measurement of blood oxygen level-dependent (BOLD) signal, that liver arterial and hepatic portal blood supplies can be modulated through hyperoxia exposure and by consumption of a standardized meal, respectively. As such, we suggest that hyperoxia modulates the hepatic arterial BOLD signal, whereas a controlled meal changes predominantly the hepatic portal BOLD signal. The hemodynamics of the dual liver blood supplies in response to the aforementioned challenges are complex and variable across subjects, making a general linear model-based analysis difficult. Therefore, we present the application of two local (at each voxel) hemodynamic response-independent techniques—principal component analysis and partial least squares—to observe the hypothesized reduction in BOLD contrast during cycles of hyperoxic breathing, when comparing preprandial versus postprandial states in a normally functioning liver. We illustrate the ability of our techniques to differentiate between healthy and diseased livers with an analysis of 17 subjects—11 with normal livers and 6 with liver disease (hepatitis or cirrhosis). Our local analysis can correctly classify all of the subjects. Copyright © 2012 John Wiley & Sons, Ltd.
Active learning for spectroscopic data regression
In this work, we introduce an active learning approach for the estimation of chemical concentrations from spectroscopic data. Its main objective is to opportunely collect training samples in such a way as to minimize the error of the regression process while minimizing the number of training samples used, and thus to reduce the costs related to training sample collection. In particular, we propose two different active learning strategies developed for regression approaches based on partial least squares regression, ridge regression, kernel ridge regression, and support vector regression. The first strategy uses a pool of regressors in order to select the samples with the greatest disagreements among the different regressors of the pool, while the second one is based on adding samples that are distant from the current training samples in the feature space. For support vector regression, a specific strategy based on the selection of the samples distant from the support vectors is proposed. Experimental results on three different real data sets are reported and discussed. Copyright © 2012 John Wiley & Sons, Ltd.
Parameter estimation in differential equation models with constrained states
We introduce a method to estimate parameters and states from a differential equation model while enforcing interpretability constraints such as monotone or non-negative states. We motivate the methodology using a real data chemical engineering example and show that a variety of restrictive constraints from earlier analyses do not address the problem of interpretability. Our proposed method estimates parameters using a smoothing-based relaxation of the model to enforce interpretability of the observed and unobserved system states. Copyright © 2012 John Wiley & Sons, Ltd.
Significance of the structure of data in partial least squares regression predictions involving both natural and human experimental design
When predicting the chemical composition of food samples from near-infrared spectroscopy using partial least squares regression, deep knowledge of the origin of the information is not present. We are aiming at opening a Pandora's box of how the prediction of protein proceeds in a unique set of chemically diverse barley mutant samples. An external validation of the sources of co-variation in nature that are exploited by chemometric models would give a framework for manipulating the deciding information to make expensive calibration more economical. The barley samples were supplemented by two designed data sets: one mirroring the coarse composition of the barley samples by mixing six main chemical components and one set where the biological covariance between the six chemical components had been reduced.
The three original data sets give remarkably comparable prediction models, albeit their regression coefficients are quite different. The origin of the prediction ability of the data is elucidated by splitting the natural barley samples into two parts: one based on simulated biology extracted from a set of chemical mixtures, and the residual after the chemistry has been removed from the raw data. As much as 98.1% of the spectral information in the natural barley data is explained through the simulated biology, leaving as little as 1.9% of the spectral information for the unexplained biological variation and noise. However, unexplained biological variation still gives a fair prediction of protein (RMSECV = 1.23 and r 2 = 0.80, compared with RMSECV = 0.46 and r 2 = 0.97 for the natural data), and it gives a clear principal component analysis separation of the three genotype classes. The results were interpreted by conducting spectral inspection on the origin of the unique covariate patterns appearing in self-organised biological systems that should motivate researchers and industry to investigate the compressive effect that the model has on the essential deterministic biological data. Copyright © 2012 John Wiley & Sons, Ltd.
A QSAR study for modeling of thyroid receptors β1 selective ligands by application of adaptive neuro-fuzzy inference system and radial basis function
A quantitative structure–activity relationship study of thyroid hormone receptors β1 is described in this paper. We used adaptive neuro-fuzzy inference system (ANFIS) and radial basis function (RBF) methods coupling to genetic algorithm (GA) to predict binding affinity of some ligands with β1 thyroid receptors. A set of 83 selective ligands with known affinity of thyroid receptors β1 (pIC50 ) were selected, and a large number of molecular descriptors were calculated for each molecule by Dragon . Seven most relevant descriptors were selected by GA-stepwise partial least squares as variable selection tool. The best descriptors (SCBO and EEig08x) and (SCBO, EEig08x, and BEHe1) were applied to train the ANFIS and RBF models, respectively. Then the number and shape of related functions were optimized. The ability and robustness of the GA-ANFIS, GA-RBF, and GA-multiple linear regression (MLR) models in predicting the pIC50 of thyroid receptors β1 are illustrated by internal validation technique of leave one out and also heuristic and randomized techniques as external validation methods. The results have indicated that the proposed models of ANFIS and RBF in this work are superior to MLR method because of generation of simpler models with only two and three descriptors, respectively. Copyright © 2012 John Wiley & Sons, Ltd.
Validation of model of multivariate calibration: an application to the determination of biodiesel blend levels in diesel by near-infrared spectroscopy
The practical implementation of multivariate calibration models has been limited in several areas because of the requirement of appropriate development and validation to prove their performance to standardization agencies. This paper describes the development and validation of a multivariate calibration model on the basis of partial least squares and net analyte signal, which can be directly applied to determine biodiesel concentrations between 2–90% in biodiesel/diesel blends analyzed by near-infrared spectroscopy. The model was validated with regard to accuracy, limit of detection, limit of quantification, sensitivity, and selectivity by calculation of the corresponding figures of merit. This work demonstrated that the proposed method is valid to determine biodiesel in diesel, simple, rapid, sensitive, and economic. Copyright © 2012 John Wiley & Sons, Ltd.
Independent component analysis applied to diffusion-ordered spectroscopy: separating nuclear magnetic resonance spectra of analytes in mixtures
Nuclear magnetic resonance spectrum of a mixture contains the overall peaks of all the analytes. It is impossible to perform structural assignment on the mixture without the knowledge of individual spectra of the components. Spectral separation is thus an important means of teasing out pure components of a mixture before spectral assignment. We propose a strategy called diffusion-ordered independent component analysis (DIFFICA) to achieve this task. This strategy applies independent component analysis algorithms to diffusion-ordered spectroscopy (DOSY) to extract spectra of pure components in a mixture. DIFFICA was tested in a simulation and experimentally in two three-component systems with and without water suppression, in 1D and 2D DOSY data. Pure spectra were achieved in both cases. The selection of diffusion parameters to guarantee pure spectra is guided by the distance correlation between separated spectra. Copyright © 2012 John Wiley & Sons, Ltd.
Advantages of orthogonal inspection in chemometrics
The demand for chemometrics tools and concepts to study complex problems in modern biology and medicine has prompted chemometricians to shift their focus away from a traditional emphasis on model predictive capacity toward optimizing information exchange via model interpretation for biological validation. The interpretation of projection-based latent variable models is not straightforward because of its confounding of different systematic variations in the model components. Over the last 15 years, this has spurred the development of orthogonal-based methods that are capable of separating the correlated variation (to Y) from the noncorrelated (orthogonal to Y) variations in a single model. Here, we aim to provide a conceptual explanation of the advantages of orthogonal variation inspection in the context of Partial Least Squares (PLS) in multivariate classification and calibration. We propose that by inspecting the orthogonal variation, both model interpretation and information quality are improved by enhancement of the resulting level of knowledge. Although the predictive capacity of PLS using orthogonal methods may be identical to that of PLS alone, the combined result can be superior when it comes to the model interpretation. By discussing theory and examples, several new advantages revealed by inspection of orthogonal variation are highlighted. Copyright © 2012 John Wiley & Sons, Ltd.
Genetic algorithms in chemometrics
This review covers the application of Genetic Algorithms (GAs) in Chemometrics. The first applications of GAs in chemistry date back to the 1970s, and in the last decades, they have been more and more frequently used to solve different kinds of problems, for example, when the objective functions do not possess properties such as continuity, differentiability, and so on. These algorithms maintain and manipulate a family, or population, of solutions and implement a “survival of the fittest” strategy in their search for better solutions. GAs are very useful in the optimization and variable selection in modeling and calibration because of the strong effect of the relationship between presence/absence of variables in a calibration model and the prediction ability of the model itself. This review is not a complete summary of the applications of GAs to chemometric problems; its goal is rather to show the researchers the main fields of application of GAs, together with providing a list of references on the subject. Copyright © 2012 John Wiley & Sons, Ltd.
Process analytical technology: a critical view of the chemometricians
The role of chemometrics in process analytical technology (PAT) solutions development is presented in the review on the basis of publications from 1993 to 2011. Main areas of application, stages of implementation, instruments, and chemometric methods used for the PAT implementations are reviewed. Generally speaking, PAT is considered to be an approach applicable not only in pharmaceutical industry but also in any production area such as food industry and biotechnology. PAT is claimed to be a new flexible manufacturing concept that accounts for variability and adapts the process to fit it. Copyright © 2012 John Wiley & Sons, Ltd.
Algorithm combination strategy to obtain the second-order advantage: simultaneous determination of target analytes in plasma using three-dimensional fluorescence spectroscopy
ABSTRACT Although a number of algorithms have established to obtain the well-known second-order advantage that quantifies analytes of interest in the presence of interferents, each has associated problems. In this work, for the first time, the optimization procedure of trilinear decomposition has been divided into three subparts, and a novel strategy is developed for assembling the advantages of the alternating trilinear decomposition (ATLD) algorithm, the self-weighted alternating trilinear decomposition (SWATLD) algorithm, and the parallel factor analysis (PARAFAC) algorithm. The performance of the proposed strategy was evaluated using a simulated data set, a published fluorescence data set together with a new fluorescence data set that simultaneously quantifies procaine and tetracaine in plasma. Results show that the novel method can accurately and effectively estimate the qualitative and quantitative information of analytes of interest. Besides, the resolved profiles are very stable with respect to the number of components as long as the employed number is chosen to be equal or larger than the underlying one. Additionally, the study confirms that better prediction can be obtained by the new strategy when compared with ATLD, SWATLD, and PARAFAC as well as the strategy that employs direct trilinear decomposition method as initial values for PARAFAC. Moreover, the strategy can be directly extended to third-order or higher-order data analysis. Copyright © 2012 John Wiley & Sons, Ltd.
Support vector machine classification of suspect powders using laser-induced breakdown spectroscopy (LIBS) spectral data
Classification of suspect powders, by using laser-induced breakdown spectroscopy (LIBS) spectra, to determine if they could contain Bacillus anthracis spores is difficult because of the variability in their composition and the variability typically associated with LIBS analysis. A method that builds a support vector machine classification model for such spectra relying on the known elemental composition of the Bacillus spores was developed. A wavelet transformation was incorporated in this method to allow for possible thresholding or standardization, then a linear model technique using the known elemental structure of the spores was incorporated for dimension reduction, and a support vector machine approach was employed for the final classification of the substance. The method was applied to real data produced from an LIBS device. Several methods used to test the predictive performance of the classification model revealed promising results. Published 2012. This article is a US Government work and is in the public domain in the USA.
Evaluation of the predictive power of biplot axes to automate the construction and layout of biplots based on the accuracy of direct readings from common outputs of multivariate analyses: 1. application to principal component analysis
Predictive biplots, as developed by J.C. Gower and coworkers, can be a very useful tool to aid the interpretation of the outcomes of multivariate analyses. This paper covers a statistical methodology that enables the automation of the construction of predictive biplots, as well as an R function, AutoBiplots.PCA( ) , which applies the methodology to principal components analysis. A case study based on the sensory analysis of coffees is used to illustrate the methodology as well as the outputs of the R function.
The method relies on the definition of a variable's mean standard predictive error, mspe , as the degree of accuracy in the process of predicting the original values from the biplots, which is compared with a predefined tolerance value (Taxis ) to decide if the correspondent biplot axis is drawn in the biplot. Standard predictive errors, spe , are calculated for each unit in relation to each biplot axis in each two-dimensional plot and are compared with a predefined tolerance value (Tunits ) to decide which units shall be faced as outliers. The R function automates the process, enabling the user to decide on the degree of precision of the actual analysis.
Besides providing a solution for the automatic production of predictive biplots, the methodology offers new insights for the interpretation of multivariate analyses outputs on the basis of a sound principle, the degree of precision of the analysis. This provides an automatic way for the selection of variables that explain latent dimensions and also helps in deciding on the number of important latent dimensions for model developments. Copyright © 2012 John Wiley & Sons, Ltd.
Chemometric approach to chromatic spatial variance. Case study: patchiness of the Skyros wall lizard
In this paper, we demonstrate how to take advantage of the large number of spatial samples provided by commercial multispectral RGB imagers. We investigate the possibility to use various multidimensional histograms and probability distributions for decomposition and predictive models. We show how these methods can be used in an example using images of different Skyros wall lizards and demonstrate improved performance in prediction of color morph compared with traditional parameterization techniques of spatial variance. Copyright © 2012 John Wiley & Sons, Ltd.
Correction of fluorescence bias on Affymetrix genotyping microarrays
Fluorescence signals obtained from microarrays for single nucleotide polymorphism genotyping show systematic strong variations in the levels for single nucleotide polymorphisms and arrays as well as genotypes. Linear models that take all three effects into account fit very well. Once the model parameters have been estimated for a set of reference arrays, they can be used to calibrate new arrays in a simple way, thereby improving genotyping and analysis of copy number variations and allelic imbalance. Copyright © 2012 John Wiley & Sons, Ltd.
Estimation of volume fraction and flow regime identification in inclined pipes based on gamma measurements and multivariate calibration
A combination of gamma measurements and multivariate calibration was applied to estimate multiphase flow mixture density and to identify flow regime. The experiments were conducted using recombined hydrocarbon fluids sampled from an onshore receiving terminal including hydrate thermodynamic inhibitors (monoethylene glycol and methanol (MeOH)). These hydrate inhibitors were added to deionised water at 60% concentration by volume. The experiments were conducted at a temperature of 0 °C and a 75-bar pressure, comparable with deep water production on the Norwegian continental shelf. Two angles of inclination (1° and 5°) and two water cuts (15% and 85%) were investigated. A single-energy gamma densitometer was installed on the test facility for measuring the mixture density, whereas the dual-energy gamma densitometer was traversed linearly from the bottom to the top of the pipe for multivariate calibration and prediction. Seventy partial least square prediction models were calibrated based on single-phase experimental data. These models were used in estimating the mixture density and identifying the flow regime in all the experiments. The estimated mixture densities were accurate as compared with those from the single-energy gamma densitometer with the root mean square error of prediction of 13.6 and 9.7 kg/m3 for 1° angle of inclination and 17 and 26.6 kg/m3 for 5° pipe inclination. The models were also able to identify the flow regimes investigated for both 1° and 5° angles of inclination. Copyright © 2012 John Wiley & Sons, Ltd.
Exploratory data analysis with noisy measurements
Multivariate chemical and biological data are increasingly characterized by measurement error variances that are highly heterogeneous. Such heteroscedasticity may be inherent in the measurements themselves or a consequence of data pretreatment. The presence of measurements with large error variances among more precise observations leads to problems in data analysis. For exploratory data analysis and in particular the low-dimensional visualization of data structures, these complications can result from sources that include preprocessing, subspace estimation, and the projection of objects with erroneous measurements, as well as contamination of the projection space with unreliable samples that preclude the effective visualization of data structures that may be present. In this work, a general strategy is proposed for the exploratory data analysis of multivariate data exhibiting a high degree of non-uniformity in measurement error variance, where estimates of the variance are available. This strategy involves three principles: (1) mitigation of the effects of noisy measurements through a preprocessing step that uses maximum likelihood principal components analysis; (2) propagation of measurement uncertainty through all steps of the procedure; and (3) incorporation of the uncertainty information into the projection of data onto the visualization subspace. To carry out this last step, a new technique, referred to as the partial transparency projection, is introduced in which the quality of measurements is interactively imbedded into the appearance of the object in the space. The advantages of this strategy are demonstrated with simulated measurements and using experimental microarray gene expression data from a yeast time course study. Copyright © 2012 John Wiley & Sons, Ltd.
Subspace methods for dynamic model estimation in PAT applications
One primary goal in the application of process analytical technology tools is improved process monitoring and control. A second is to obtain a better understanding of how a normal process behaves (i.e. the normal dynamics). In order to perform feed-forward control, time series models of the process data are required. Such models could be developed on the basis of known physical/chemical knowledge of the system (i.e. first principal or mechanistic modeling). However, very often, this is not possible because of the lack of sufficient information. This leads to the need of system identification (SI). One class of models within SI is the state space models, linear models that relate the input of the system at time k to the output at time k via estimation of the so-called system states. State space models may be fitted using what is known as the subspace methods. Subspace methods are based on the projection of data on subspaces identified by, for example, the singular value decomposition of time-shifted data during a training phase. This paper introduces state space models, illustrates how subspace methods are closely related to known chemometric tools, and how they can be applied in, for example, model-based feed-forward process monitoring and control. The concepts are illustrated using a data set from an intrinsically nonlinear milk coagulation process that can be approximated well by a linear dynamic model using a small set of virtual (or principal) states. We present an alternative process-monitoring strategy where the dynamic components and boundary conditions of a developing milk coagulation batch are estimated in real-time and compared to normal operating conditions. Copyright © 2012 John Wiley & Sons, Ltd.
Application of genetic algorithm-support vector regression (GA-SVR) for quantitative analysis of herbal medicines
In this paper, a genetic algorithm-support vector regression (GA-SVR) coupled approach was proposed for investigating the relationship between fingerprints and properties of herbal medicines. GA was used to select variables so as to improve the predictive ability of the models. Two other widely used approaches, Random Forests (RF) and partial least squares regression (PLSR) combined with GA (namely GA-RF and GA-PLSR, respectively), were also employed and compared with the GA-SVR method. The models were evaluated in terms of the correlation coefficient between the measured and predicted values (R p), root mean square error of prediction, and root mean square error of leave-one-out cross-validation. The performance has been tested on a simulated system, a chromatographic data set, and a near-infrared spectroscopic data set. The obtained results indicate that the GA-SVR model provides a more accurate answer, with higher R p and lower root mean square error. The proposed method is suitable for the quantitative analysis and quality control of herbal medicines. Copyright © 2012 John Wiley & Sons, Ltd.
THEME-SEER: a multidimensional exploratory technique to analyze a structural model using an extended covariance criterion
In this work, we present a new approach to path modeling based on an extended multiple covariance criterion: system extended multiple covariance (SEMC). SEMC is suitable to measure the quality of any structural equations system. We show why SEMC may be preferred to criteria based on usual covariance of components and also to criteria based on residual sums of squares. We give a pursuit algorithm ensuring that SEMC increases and converges. When one wishes to extract more than one component per variable group, a problem arises of component hierarchy. To solve it, we define a local nesting principle of component models that makes the role of each component statistically clear. We then embed the pursuit algorithm in a more general algorithm that extracts sequences of locally nested models. We finally provide a component backward selection strategy. The technique is applied to cigarette data to model the generation of chemical compounds in smoke through tobacco combustion. Copyright © 2012 John Wiley & Sons, Ltd.
Resolution of spectrally rank-deficient multivariate curve resolution: alternating least squares components in comprehensive two-dimensional liquid chromatographic analysis
The advancements in comprehensive two-dimensional liquid chromatographic systems have led to more efficient and effective analyses of complex biological samples. Correspondingly, there has been an increase in the data complexity. Several chemometric techniques have been proposed to extract the maximum amount of information and to overcome the numerous challenges associated with data analysis. However, quantification remains troublesome, especially when dealing with spectrally rank-deficient peaks. To this end, a new constraint for multivariate curve resolution-alternating least squares (MCR-ALS) is proposed for the separation of chromatographic peaks appearing within the same MCR-ALS component and dividing them among additionally created components with highly similar spectral characteristics. Application of the constraint to every sample individually leads to two important advantages: the need for the selection of an overall dividing point for all samples is avoided, and the serious issue of retention time shifting is handled by the algorithm. Manual quantification of the compounds of interest is facilitated because the peaks in the second-dimension chromatograms can be attributed to a single compound, but it leads to comparable percent relative standard deviations (% RSD) prior to and after application of the constraint. Nonetheless, the presence of a single compound in each component allows for automated quantification by simple summation of the second-dimension chromatograms. Copyright © 2012 John Wiley & Sons, Ltd.
Use of partial least squares discriminant analysis on visible-near infrared multispectral image data to examine germination ability and germ length in spinach seeds
Because of the difficulties in obtaining homogenous germination of spinach seeds for baby leaf production, the possibility of using partial least squares discriminant analysis (PLS-DA) on features extracted from multispectral images of spinach seeds was investigated. The objective has been to discriminate between different seed sizes, as well as to predict germination ability and germ length. Images of 300 seeds including small, medium, and large seeds were taken, and the seeds were examined for germination ability and germ length. PLS-DA loadings plots were used to reduce the multidimensional image features to a few important features. The PLS-DA prediction resulted in an independent test set not only providing discrimination of seed size but also demonstrating how germination ability and germ length vary according to seed size. The result indicated that larger seeds had both a significantly higher germination potential and germ length compared with smaller seeds. The variable importance for projection method showed that the near infrared (NIR) wavelength region is important for germination predictability. However, the PLS-DA model did not improve when only the NIR region was used. Copyright © 2012 John Wiley & Sons, Ltd.
On the effectiveness of cross-fitting in multi-block PLS (CF-MBPLS)
Abstract Multi-block PLS is an extension of partial least squares or projection to latent structures (PLS), where the descriptor matrix is divided into meaningful blocks based on either process units or type of data. A typical application is using process variables as one block and spectral data on another block. It has been utilized in obtaining more information of processes and the effect of different types of variables. In comparison with priority or hierarchical PLS, in multi-block PLS, there is no need to prioritize blocks in advance because they are iteratively calculated at the same time. With multi-block PLS, however, it is easy to overfit data resulting in a poor predictive ability. A recent development called cross-fitting has been reported to alleviate the problem of overfitting in PLS. This approach was adjusted to multi-block PLS and is tested on two different data sets, where overfitting and sensitivity to outliers are issues. Copyright © 2012 John Wiley & Sons, Ltd.
Coclustering—a useful tool for chemometrics
Nowadays, chemometric applications in biology can readily deal with tens of thousands of variables, for instance, in omics and environmental analysis. Other areas of chemometrics also deal with distilling relevant information in highly information-rich data sets. Traditional tools such as the principal component analysis or hierarchical clustering are often not optimal for providing succinct and accurate information from high rank data sets. A relatively little known approach that has shown significant potential in other areas of research is coclustering , where a data matrix is simultaneously clustered in its rows and columns (objects and variables usually).
Coclustering is the tool of choice when only a subset of variables is related to a specific grouping among objects. Hence, coclustering allows a select number of objects to share a particular behavior on a select number of variables.
In this paper, we describe the basics of coclustering and use three different example data sets to show the advantages and shortcomings of coclustering. Copyright © 2012 John Wiley & Sons, Ltd.
