Construction of stable multivariate calibration models using unsupervised segmented principal component regression

In multivariate spectral calibration by principal component regression (PCR), the principal components (PCs) are calculated from the response data measured at all employed instrument channels; however some channels are redundant and their responses do not possess useful information. Thus, the extracted PCs possess mixed information from both useful and redundant channels. In this work, we propose a segmentation approach based on unsupervised pattern recognition to identify the most informative spectral region and then to construct a stable multivariate calibration model by PCR. In this method, the instrument channels are clustered into different segments via Kohonen self‐organization map. The spectral data of each segment are then subjected to PCA and the derived PCs are used as input variables for an inverse least square (ILS) regression model employing stepwise selection of the informative PCs. The proposed method was evaluated by the analysis of four simulated and six experimental data sets. It was found that our proposed method can model the above data sets with prediction errors lower than conventional partial least squares (PLS) and PCR methods. In addition, the prediction ability of our method was better than the previously reported models for these data sets. Copyright © 2011 John Wiley & Sons, Ltd.     

Sorting variables by using informative vectors as a strategy for feature selection in multivariate regression

A new procedure with high ability to enhance prediction of multivariate calibration models with a small number of interpretable variables is presented. The core of this methodology is to sort the variables from an informative vector, followed by a systematic investigation of PLS regression models with the aim of finding the most relevant set of variables by comparing the cross‐validation parameters of the models obtained. In this work, seven main informative vectors i.e. regression vector, correlation vector, residual vector, variable influence on projection (VIP), net analyte signal (NAS), covariance procedures vector (CovProc), signal‐to‐noise ratios vector (StN) and their combinations were automated and tested with the main purpose of feature selection. Six data sets from different sources were employed to validate this methodology. They originated from: near‐Infrared (NIR) spectroscopy, Raman spectroscopy, gas chromatography (GC), fluorescence spectroscopy, quantitative structure‐activity relationships (QSAR) and computer simulation. The results indicate that all vectors and their combinations were able to enhance prediction capability with respect to the full data sets. However, regression and NAS informative vectors from partial least squares (PLS) regression, both built using more latent variables than when building the model presented in most of tested data sets, were the best informative vectors for variable selection. In all the applications, the selected variables were quite effective and useful for interpretation. Copyright © 2008 John Wiley & Sons, Ltd.     

Independent component analysis of 2-D electrophoresis gels

We present a novel application of independent component analysis (ICA), an exploratory data analysis technique, to two-dimensional electrophoresis (2-DE) gels, which have been used to analyze differentially expressed proteins across groups. Unlike currently used pixel-wise statistical tests, ICA is a data-driven approach that utilizes the information contained in the entire gel data. We also apply ICA on wavelet-transformed 2-DE gels to address the high dimensionality and noise problems typically found in 2-DE gels. Also, we use an analysis-of-variance (ANOVA) approach as a benchmark for comparison. Using simulated data, we show that ICA detects the group differences accurately in both the spatial and wavelet domains. We also apply these techniques to real 2-DE gels. ICA proves to be much faster than ANOVA, and unlike ANOVA it does not depend on the selection of a threshold. Application of principal component analysis reduces the dimensionality and tends to improve the performance by reducing the noise.     

Independent component analysis of nanomechanical responses of cantilever arrays

The ability to detect and identify chemical and biological elements in air or liquid environments is of far reaching importance. Performing this task using technology that minimally impacts the perceived environment is the ultimate goal. The development of functionalized cantilever arrays with nanomechanical sensing is an important step towards this goal. This report couples the feature extraction abilities of independent component analysis (ICA) and the classification techniques of neural networks to analyze the signals produced by microcantilever-array-based nanomechanical sensors. The unique capabilities of this analysis unleash the potential of this sensing technology to accurately identify chemical mixtures and concentrations. Furthermore, it is demonstrated that the knowledge of how the sensor array reacts to individual analytes in isolation is sufficient information to decode mixtures of analytes—a substantial benefit, significantly increasing the analytical utility of these sensing devices.     

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.     

A new regression method based on independent component analysis

Based on independent component analysis (ICA), a new regression method, independent component regression (ICR), was developed to build the model of NIR spectra and the routine components of plant samples. It is found that ICR and principal component regression (PCR) are completely equivalent when they are applied in quantitative prediction. However, independent components (ICs) can give more chemical explanation than principal components (PCs) because independence is a high-order statistic that is a much stronger condition than orthogonality. Three ICs are obtained by ICA from the NIR spectra of plant samples; it is found that they are strongly correlated to the NIR spectra of water, hydrocarbons and organonitrogen compounds, respectively. Therefore, ICA may be a promising tool to retrieve both quantitative and qualitative information from complex chemical data sets.     

Multivariate concentration determination using principal component regression with residual analysis

Data analysis is an essential tenet of analytical chemistry, extending the possible information obtained from the measurement of chemical phenomena. Chemometric methods have grown considerably in recent years, but their wide use is hindered because some still consider them too complicated. The purpose of this review is to describe a multivariate chemometric method, principal component regression, in a simple manner from the point of view of an analytical chemist, to demonstrate the need for proper quality-control (QC) measures in multivariate analysis and to advocate the use of residuals as a proper QC method.     

Independent component analysis and its applications in signal processing for analytical chemistry

Independent component analysis (ICA) is a statistical method the goal of which is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible. In an ICA procedure, the estimated independent components (ICs) are identical to or highly correlated to the spectral profiles of the chemical components in mixtures under certain circumstances, so the latent variables obtained are chemically interpretable and useful for qualitative analysis of mixtures without prior information about the sources or reference materials, and the calculated demixing matrix is useful for simultaneous determination of polycomponents in mixtures. We review commonly used ICA algorithms and recent ICA applications in signal processing for qualitative and quantitative analysis. Furthermore, we also review the preprocessing method for ICA applications and the robustness of different ICA algorithms, and we give the empirical criterion for selection of ICA algorithms in signal processing for analytical chemistry.     

Simultaneous spectrophotometric determination of ethinylestradiol and levonorgestrel by partial least squares and principal component regression multivariate calibration

Two spectrophotometric methods for the determination of Ethinylestradiol (ETE) and Levonorgestrel (LEV) by using the multivariate calibration technique of partial least square (PLS) and principal component regression (PCR) are presented. In this study the PLS and PCR are successfully applied to quantify both hormones using the information contained in the absorption spectra of appropriate solutions. In order to do this, a calibration set of standard samples composed of different mixtures of both compounds has been designed. The results found by application of the PLS and PCR methods to the simultaneous determination of mixtures, containing 4–11 μg ml⁻¹ of ETE and 2–23 μg ml⁻¹ of LEV, are reported. Five different oral contraceptives were analyzed and the results were very similar to that obtained by a reference liquid Chromatographic method.     

Application of principal component analysis and discriminant analysis using latent structure regression to the identification of highly volatile organic compounds in gas mixtures based on piezoelectric quartz microweighing parameters

The applicability of the new parameters of piezoelectric quartz microweighing and principal component and discriminant analysis with the use of latent structure regression to the treatment of the output data of an array of piezoelectric sensors in the identification of individual highly volatile compounds in model three-component gas mixtures is discussed. The parameters proposed and the methods of chemometrics were used in the treatment of the multidimensional data of an electronic nose for detecting individual aromaforming compounds and evaluating changes in the aroma of food systems with functional additives.     

Simultaneous multicomponent analysis of overlapping spectrophotometric signals using a wavelet-based latent variable regression

A wavelet-based latent variable regression (WLVR) method was developed to perform simultaneous quantitative analysis of overlapping spectrophotometric signals. The quality of the noise removal was improved by combining wavelet thresholding with principal component analysis (PCA). A method for selecting the optimum threshold was also developed. Eight error functions were calculated for deducing the number of factor. The latent variables were made by projecting the wavelet-processed signals onto orthogonal basis eigenvectors. Two-programs WMRA and WLVR, were designed to perform wavelet thresholding and simultaneous multicomponent determination. Experimental results showed the WLVR method to be successful even where there was severe overlap of spectra.     

High dimensional model representation constructed by support vector regression. I. Independent variables with known probability distributions

High dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing high dimensional input-output system behavior. In practice, the HDMR component functions are each approximated by an appropriate basis function expansion. This procedure often requires many input-output samples which can restrict the treatment of high dimensional systems. In order to address this problem we introduce svr-based HDMR to efficiently and effectively construct the HDMR expansion by support vector regression (SVR) for a function \(f(\mathbf{x})\). In this paper the results for independent variables sampled over known probability distributions are reported. The theoretical foundation of the new approach relies on the kernel used in SVR itself being an HDMR expansion (referred to as the HDMR kernel ), i.e., an ANOVA kernel whose component kernels are mutually orthogonal and all non-constant component kernels have zero expectation. Several HDMR kernels are constructed as illustrations. While preserving the characteristic properties of HDMR, the svr-based HDMR method enables efficient construction of high dimensional models with satisfactory prediction accuracy from a modest number of samples, which also permits accurate computation of the sensitivity indices. A genetic algorithm is employed to optimally determine all the parameters of the component HDMR kernels and in SVR. The svr-based HDMR introduces a new route to advance HDMR algorithms. Two examples are used to illustrate the capability of the method.     

Partial least-squares regression on design variables as an alternative to analysis of variance

The partial least-squares (PLS) algorithm has become popular for explorative multivariate data analysis and for multivariate calibration. The same PLS algorithm can also be used for confirmatory data analysis. The discussion is limited to analysis of a single response variable. A close correspondence of PLS1 regression to classical analysis of variance (ANOVA) is demonstrated. The design of an experiment is described in terms of discrete design variables for main effects and simple interactions (dummy variables). These are used as regressors X = (x₁, x₂,…,) for modelling the response variable of the experiment, y. As in conventional use of PLS1 regression, the algorithm gives a concentrated model or diagram of the most important, y-relevant variability types in the X-data. In the present case, this gives the combination of design variables that models the variations in y. A simple plot of the resulting factor loadings immediately reveals the important design variables. Statistical tests and confidence regions in the PLS solution give additional safeguards against interpretation of spurious effects. The method is applied to two data sets. One concerns assessment of personal preference for blackcurrent juice, studied in a 2⁵ factorial experiment; these data are also studied with missing values and as fractional factorials. The other ceoncers spectrophotometric absorbance-based colour assessments of pigment in strawberry jam in a 3-factor design with 2, 2 and 3 levels in the respective factors.     

Near-infrared spectroscopy quantitative determination of Pefloxacin mesylate concentration in pharmaceuticals by using partial least squares and principal component regression multivariate calibration

Pefloxacin mesylate, a broad-spectrum antibacterial fluoroquinolone, has been widely used in clinical practice. Therefore, it is very important to detect the concentration of Pefloxacin mesylate. In this research, the near-infrared spectroscopy (NIRS) has been applied to quantitatively analyze on 108 injection samples, which was divided into a calibration set containing 89 samples and a prediction set containing 19 samples randomly. In order to get a satisfying result, partial least square (PLS) regression and principal components regression (PCR) have been utilized to establish quantitative models. Also, the process of establishing the models, parameters of the models, and prediction results were discussed in detail. In the PLS regression, the values of the coefficient of determination (R²) and root mean square error of cross-validation (RMSECV) of PLS regression are 0.9263 and 0.00119, respectively. For comparison, though applying PCR method to get the values of R² and RMSECV we obtained are 0.9685 and 0.00108, respectively. And the values of the standard error of prediction set (SEP) of PLS and PCR models are 0.001480 and 0.001140. The result of the prediction set suggests that these two quantitative analysis models have excellent generalization ability and prediction precision. However, for this PFLX injection samples, the PCR quantitative analysis model achieved more accurate results than the PLS model. The experimental results showed that NIRS together with PCR method provide rapid and accurate quantitative analysis of PFLX injection samples. Moreover, this study supplied technical support for the further analysis of other injection samples in pharmaceuticals.     

嘧啶硫代水杨酸衍生物的多元回归分析及神经网络法研究

通过量子化学方法计算了 1 4个新型嘧啶硫代水杨酸衍生物的量化参数 ,运用分子力学进行完全构象优化进而计算了分子几何形状等参数。对这些化合物抑制乙酰乳酸合成酶 (ALS)活性进行了QSAR分析 ,结果表明 ,空间因素及静电效应是影响构效关系的主要因素 ,神经网络法得到较优预测结果。     

Monitoring of an industrial process by multivariate control charts based on principal component analysis

The control and monitoring of an industrial process is performed in this paper by the multivariate control charts. The process analysed consists of the bottling of the entire production of 1999 of the sparkling wine "Asti Spumante". This process is characterised by a great number of variables that can be treated with multivariate techniques. The monitoring of the process performed with classical Shewhart charts is very dangerous because they do not take into account the presence of functional relationships between the variables. The industrial process was firstly analysed by multivariate control charts based on Principal Component Analysis. This approach allowed the identification of problems in the process and of their causes. Successively, the SMART Charts (Simultaneous Scores Monitoring And Residual Tracking) were built in order to study the process in its whole. In spite of the successful identification of the presence of problems in the monitored process, the Smart chart did not allow an easy identification of the special causes of variation which casued the problems themselves.     

Comparison of HPLC and multivariate regression methods for hydrocortisone and lidocaine analysis of pharmaceutical preparations

A reverse-phase high-performance liquid chromatographic (HPLC) method to determine hydrocortisone acetate, hydrocortisone hemisuccinate and lidocaine is described in this paper. The separation was made in a LichrCART C(18) column using a methanol-NaH(2)PO(4)/Na(2)HPO(4) (0.1 mol L(-1)) (pH=4.5) buffer solution as a mobile phase in isocratic mode (60:40 (v/v)). The mobile phase flow rate and the sample volume injected were 1 mL min(-1) and 20 micro L, respectively. The detection was made with a diode-array detector measuring at the maximum for each compound. Quantification limits ranging from 0.18 to 0.84 micro g L(-1) were obtained when the peak area was measured. The method was applied in pharmaceutical formulations that were compared with those obtained by through multivariate regression spectrophotometry and micellar capillary electrophoresis (MEKC). HPLC results are in accordance with the results obtained by MEKC. The spectrophotometric method was suitable only for synthetic samples.     

Advances in the development and component recognition of latent fingerprints

Fingerprints have been used as an indispensable tool for personal identification in forensic investigations since the late 19 th century. At present, fingerprinting technology has moved away from its forensic roots and is incorporating a broader scientific range, e.g., material science, spectroscopy and spectral analysis, and even in vitro diagnosis. After a brief introduction to latent fingerprints, this mini-review presents the pioneering progresses of fingerprinting technologies including(i) material and electrochemical techniques, and(ii) spectral and spectroscopy imaging techniques and immunological techniques capable of both the visualization of a fingerprint and the detection of chemicals present in it. Finally, perspectives on this rapidly developing field are discussed.     

Evaluation of peptide electropherograms by multivariate mathematical-statistical methods. I. Principal component analysis.

Depository effects in slowly metabolised proteins, typically glycation or the estimation of products arising from the reaction of unsaturated long-chain-fatty acid metabolites (possessing aldehydic groups) are very difficult to assess owing to their extremely low concentration in the protein matrix. In order to reveal such alterations we applied deep enzymatic fragmentation resulting in a set of small peptides, which, if modified, are likely to change their electrophoretic properties and can be visualised on the resulting profile. Peptide maps of collagen (a mixture of collagen types I and III digested by bacterial collagenase) were applied as the model protein structure for detecting the nonenzymatic posttranslational changes originating during various physiological conditions like high fructose diet and hypertriglyceridemic state. Capillary electrophoresis in acidic media (sodium phosphate buffer, pH 2.5) was used as the separation method capable of (partial) separation of over 60 peptide peaks. Two to 13 changes were revealed in the profiles obtained reflecting the physiological conditions of the animals tested. Combination of peptide profiling with subsequent t-test evaluation of individual peak areas and principal component analysis based on cumulative peak areas of individual sections of the electropherograms allowed to determine in which section (part) of the electropherogram the physiological state indicating changes occurred. Simultaneously it was possible to reveal the qualitative differences between the four physiological regimes investigated (i.e., which regime affects the collagen molecules most and which affects them least). The approach can be used as guidance for targeted preseparation of the very complex peptide mixture.