Optimal Number Of Latent Variables Research Articles

The Potential of NIR Spectroscopy and Chemometrics to Discriminate Roast Degrees and Predict Volatiles in Coffee.

This study aimed to establish a rapid and practical method for monitoring and predicting volatile compounds during coffee roasting using near-infrared (NIR) spectroscopy coupled with chemometrics. Washed Arabica coffee beans from Ethiopia and Congo were roasted to industry-validated light, medium, and dark degrees. Concurrent analysis of the samples was performed using gas chromatography-mass spectrometry (GC-MS) and NIR spectroscopy, generating datasets for partial least squares (PLS) regression analysis. The results showed that NIR spectroscopy successfully differentiated the differently roasted samples, similar to the discrimination achieved by GC-MS. This finding highlights the potential of NIR spectroscopy as a rapid tool for monitoring and standardizing the degree of coffee roasting in the industry. A PLS regression model was developed using Ethiopian samples to explore the feasibility of NIR spectroscopy to indirectly measure the volatiles that are important in classifying the roast degree. For PLSR, the data underwent autoscaling as a preprocessing step, and the optimal number of latent variables (LVs) was determined through cross-validation, utilizing the root mean squared error (RMSE). The model was further validated using Congo samples and successfully predicted (with R2 values > 0.75 and low error) over 20 volatile compounds, including furans, ketones, phenols, and pyridines. Overall, this study demonstrates the potential of NIR spectroscopy as a practical and rapid method to complement current techniques for monitoring and predicting volatile compounds during the coffee roasting process.

Спектрофотометрическое определение некоторых β-лактамных антибиотиков в их бинарных смесях с использованием метода проекций на латентные структуры

The method has been proposed for the spectrophotometric determination of antibiotics of the cephalosporin (cefuroxime, ceftriaxone, cefotaxime, cefazolin) and penicillin (amoxicillin) groups using chemometric data processing (method of partial least squares, PLS). The absorption spectra of 24 binary mixtures of “cephalosporin – cephalosporin” and 16 binary mixtures of “cephalosporin – amoxicillin” with various concentrations in the range of 3–27 and 5–140 μg/ml have been recorded. The optimal number of latent variables for each chemometric method (PLS-1 and PLS-2) has been selected, which ranged from 2 to 7 depending on the type of model and the nature of the antibiotics. The smallest root mean square calibration errors (RMSEC) have been found for the ceftriaxone–cefazolin system, which have been 0.09 and 0.08 for PLS-1 and PLS-2, respectively. The smallest root mean square errors of prediction (RMSEP) for the mixture “cefuroxime – amoxicillin” have been 0.07 for both methods (PLS-1 and PLS-2). It has been established that equations of linear relationships “measured-predicted” are characterized by a regression coefficient and the square of the approximation coefficient close to 1; which indicates the high quality of the models. The relative error of determination in test mixtures has been 0.4–6.2% by the PLS-1 method for “cephalosporin – cephalosporin” mixtures, and 0.07–6.0% by the PLS-2 method. At the same time, there is no significant difference in the error in determining the components of the mixture, in contrast to the “cefuroxime – amoxicillin” system, for which the error is 0.1–1.1% for the first component and 2.6–14.7% for the second component using the PLS-1 method and 0.2–1.2% for the first component and 4.3–13.3% for the second component using the PLS-2 method. Thus, it has been shown that the use of chemometric methods ensures high accuracy of the spectrophotometric determination of the studied antibiotics with overlapping absorption bands in their mixtures.

Toward a better interpretation of the partial least squares regression models for fluoropolymers treated by dielectric barrier discharges at atmospheric pressure

AbstractIn this article, partial least squares regression was applied to a continuous dielectric discharge process aiming to modify the surface of a fluoropolymer. Cross‐validation was used to find the optimal number of latent variables that minimize the error from the model. Then, the key parameters affecting the process were highlighted with the variable importance on the projection (VIP) and the biplot exploratory graph produced from the algorithm. Finally, the model was used to predict additional data not included in the training set. The new predictions were used to assess the ability of the model to predict data outside of the training range. The applicability domain for this model was also discussed. The results showed that less prediction errors occurred when the surface modification remained close to the untreated fluoropolymer surface characteristics.

Unraveling putative antiulcer phytoconstituents against Helicobacter pylori urease and human H+/K+-ATPase from Jacaranda mimosifolia using UPLC-MS/MS coupled to chemometrics and molecular docking

Globally peptic ulcer disease is a severe public health issue caused by an imbalance between the defensive and aggressive mechanisms. In the current study, the phytochemical components of various organs (leaf, fruit, seed, and bark) of Jacaranda mimosifolia D. Don collected from Egypt at different seasons and geographical locations were investigated. UPLC-MS/MS allows a tentative identification of 53 compounds where flavonoids, quinoids, and triterpenoids represented the major identified classes. Multivariate statistical analysis (principle component analysis (PCA), hierarchical cluster analysis (HCA)-heat map and orthogonal projection to latent structures-discriminate analysis (OPLS-DA), and accompanied coefficient plots) was applied to investigate in-between and within-class discrimination of the different organs of Jacaranda mimosifolia D. Don. The obtained extracts were tested for their inhibitory activities against Helicobacter pylori Urease and human H+/K+-ATPase enzymes. Fruit extract showed the highest inhibitory activity against H. pylori urease. Meanwhile, leaf extract was found to be more potent, against human H+/K+-ATPase. The results of the biological activities were further modeled using Partial Least Squares Regression (PLSR) analysis together with the quantitative data. The optimal number of latent variables was determined with the aid of Variables important for the projection (VIP) plot to remove the uninformative variables. The developed model was validated using root mean square error of calibration (RMSEC), cross-validation (RMSECV) and prediction (RMSEP). PLS model coefficient plots showed that flavonoids as isoquercitrin and rutin were the most contributing metabolites/biomarkers to the detected anti-urease and H+/K+-ATPase activities, respectively. Molecular docking analysis was utilized to gain more insights into the interaction modalities for the top fifteen metabolites obtained from the PLS model with the active sites of urease and H+/K+-ATPase enzymes. In agreement with the model coefficients, isoquercitrin and rutin were ranked as the top hits for the studied enzymes. To validate the results, in vitro inhibitory assays were performed on isoquercitrin and rutin. Potent inhibitory activities were determined against urease and H+/K+-ATPase with IC50 ± SD of 9.10 ± 0.75 µM and 0.61 ± 0.06 µM for isoquercitrin and rutin, respectively.

Integration of NIR spectroscopy and chemometrics for authentication and quantitation of adulteration in sweet marjoram (Origanum majorana L.)

Origanum majorana L. (marjoram) has considerable promise as a folk remedy for digestive ailments in addition to its ethnomedicinal use in gynecological disorders. Due to the high demand for the botanical raw material, it is prone to intentional and inadvertent adulteration by morphologically similar herbs. In the current study, the adulteration of marjoram with its common adulterants; oregano, thyme, olive, basil and sage has been thoroughly investigated. To distinguish between marjoram and its prevalent adulterants, an integrated near infrared (NIR) spectroscopic method coupled with chemometric data analysis was developed. For exploratory pattern recognition, unsupervised multivariate models such as principal component analysis (PCA) and hierarchical cluster analysis (HCA) were implemented, followed by supervised models. Authentication of marjoram was successfully assessed using soft independent modelling of class analogy (SIMCA) with 100% sensitivity. Orthogonal projection to latent structures-discriminant analysis (OPLS-DA) modeling was employed to discriminate pure marjoram from its deliberately adulterated mixtures. Further, amounts of the adulterants were quantified in the botanical mixtures using partial least squares regression (PLS-R). The calibration and validation goodness of fit were determined to be greater than 0.9 and almost one, with a low root mean square error of prediction (RMSEP) and high ratio of performance to deviation (RPD) and range error ratio (RER) which highlight the model significant potential. Moreover, the optimal number of latent variables was found to be 5 as computed by permutation test. In the current study, the validity and reliability of the models employed to assess marjoram authenticity and purity was evidenced by both internal and external validation methods with a little to no data pre-processing.

Autonomous construction of parameterizable 3D leaf models from scanned sweet pepper leaves with deep generative networks

Abstract Visible traits can be criteria for selecting a suitable crop. Three-dimensional (3D)-scanned plant models can be used to extract visible traits; however, collecting scanned data and physically manipulating point-cloud structures of the scanned models are difficult. Recently, deep generative models have shown high performance in learning and creating target data. Deep generative models can improve the versatility of scanned models. The objectives of this study were to generate sweet pepper (Capsicum annuum) leaf models and to extract their traits by using deep generative models. The leaves were scanned, preprocessed and used to train the deep generative models. The variational autoencoder, generative adversarial network (GAN) and latent space GAN were used to generate the desired leaves. The optimal number of latent variables in the model was selected via the Jensen–Shannon divergence (JSD). The generated leaves were evaluated by using the JSD, coverage and minimum matching distance to determine the best model for leaf generation. Among the deep generative models, a modified GAN showed the highest performance. Sweet pepper leaves with various shapes were generated from eight latent variables following a normal distribution, and the morphological traits of the leaves were controlled through linear interpolation and simple arithmetic operations in latent space. Simple arithmetic operations and gradual changes in the latent space modified the leaf traits. Deep generative models can parameterize and generate morphological traits in digitized 3D plant models and add realism and diversity to plant phenotyping studies.

Rapid quantification of adulterated Panax notoginseng powder by ultraviolet-visible diffuse reflectance spectroscopy combined with chemometrics

• The feasibility of quantification of Panax notoginseng (PN) with its three adulterants by ultraviolet-visible diffuse reflectance spectroscopy is investigated. • PLS serves as the modeling tool and Haaland-Thomas F -test is used for determine the number of latent variables. • To achieve optimal models, several spectral preprocessing and variable selection methods were investigated. As a valuable traditional Chinese medicine (TCM), Panax notoginseng (PN) is often adulterated with similar and much cheaper adulterants, such as rhizoma curcumae (RC), Curcuma longa (CL) and rhizoma alpiniae officinarum (RAO). The feasibility of ultraviolet-visible (UV-Vis) diffuse reflectance spectroscopy combined with chemometrics is investigated for rapid quantitative analysis of adulterated PN powder. Partial least squares (PLS) is used for calibration modeling. To avoid over-fitting of PLS, the Haaland-Thomas F-test is introduced to determine the optimal number of latent variables (LVs). For further improving the predictive performance of PLS model, six preprocessing and three variable selection methods are investigated. Results show that correlation coefficients ( R p ) of the optimal models for PN and its three adulterants in prediction set are all above 0.98. Thus, UV-Vis diffuse reflectance spectroscopy combined with chemometrics provides an economic alternative for rapid and non-destructive quantification of adulterated PN samples.

Anomaly detection using Autoencoders and Deep Convolution Generative Adversarial Networks

The current trend in transport (road, railway, unmanned aerial vehicle) introduces autonomous transport means. As the autonomy of vehicles increases, situations arise for which the models have not been trained, which increases the safety risk. Therefore, we propose systems that would detect such “anomaly” situations. We designed two anomaly detectors - an Adversarial Autoencoder (AAE) and a Deep Convolutional Generative Adversarial Networks (DCGAN). These models are build up on models from resources Autoencoders (2020) and Deep (2020). Networks are trained using picture datasets MNIST, Fashion-MNIST and CIFAR10.With DCGAN network, cumulative and reverse cumulative distribution functions are used to find an optimal decision threshold. In the case of autoencoder networks – an optimal number of latent variables is found using reconstruction error ratio function. Then, in both cases (AAE and DCGAN network), cumulative and reverse cumulative distribution functions are used to find an optimal decision threshold. Finally, influence of image picture complexity on the anomaly detection is discussed. We got best results with anomaly detectors trained on the less complex datasets comparing to test datasets. For both detectors trained on the simplest database MNIST, under a given anomaly expectation probability equal to 0.5, we reached the anomaly detection error 0.08% (AAE) and 1.89% (DCGAN).

Permeability prediction from mercury injection capillary pressure curves by partial least squares regression method in tight sandstone reservoirs

Permeability is an essential petrophysical parameter for reservoir modeling, reservoir classification, and productivity prediction in tight sandstone reservoirs. In this study, multiple parameters are extracted from the mercury injection capillary pressure (MICP) curves and the degree of multicollinearity between these parameters is analyzed. The partial least squares regression (PLSR) method is used for establishing the permeability prediction model and the optimal number of latent variables of the model is determined by the leave-one-out cross-validation (LOOCV) method. A comparison of the existing empirical models, the permeability prediction model by ordinary least square (OLS) method, and the permeability prediction model by PLSR method based on the MICP curves indicates that the permeability prediction model by PLSR method is superior to the other models for tight sandstone reservoirs.

Determination of the optimal number of components in independent components analysis

Independent components analysis (ICA) may be considered as one of the most established blind source separation techniques for the treatment of complex data sets in analytical chemistry. Like other similar methods, the determination of the optimal number of latent variables, in this case, independent components (ICs), is a crucial step before any modeling. Therefore, validation methods are required in order to decide about the optimal number of ICs to be used in the computation of the final model. In this paper, three new validation methods are formally presented. The first one, called Random_ICA, is a generalization of the ICA_by_blocks method. Its specificity resides in the random way of splitting the initial data matrix into two blocks, and then repeating this procedure several times, giving a broader perspective for the selection of the optimal number of ICs. The second method, called KMO_ICA_Residuals is based on the computation of the Kaiser-Meyer-Olkin (KMO) index of the transposed residual matrices obtained after progressive extraction of ICs. The third method, called ICA_corr_y, helps to select the optimal number of ICs by computing the correlations between calculated proportions and known physico-chemical information about samples, generally concentrations, or between a source signal known to be present in the mixture and the signals extracted by ICA. These three methods were tested using varied simulated and experimental data sets and compared, when necessary, to ICA_by_blocks. Results were relevant and in line with expected ones, proving the reliability of the three proposed methods.

Quantitative analysis of biofluids based on hybrid spectra space

Direct determination of chemical constituents in complex biofluids without the need for any reagent or pre-processing of samples has become a promising technique for clinical analysis. Attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy has been widely studied as a powerful method of reagent-free biofluids analysis. In this work, to further utilize information and improve prediction performance, new hybrid spectra space was constructed based on different derivative spectra space. Then, hybrid spectra space ensemble interval partial least squares modeling (HSEiPLS) was proposed for quantification analysis of biofluids. In the experiment of determining glucose concentrations in 58 whole blood samples, the F-test is used to determine the optimal number of latent variables for models and the F-test significance level is set to 0.25. HSEiPLS model provided lower root mean square error of prediction (RMSEP) values 0.352mM/L compared with other methods. In the experiment of determining cholesterol concentrations in 50 whole blood samples, HSEiPLS model provided RMSEP values 0.205mM/L under the same condition of the significance level. Experimental results demonstrate that the proposed HSEiPLS based on hybrid spectra space provides superior predictive power for biofluids.

Prediction of raspberries puree quality traits by Fourier transform infrared spectroscopy

FTIR applications combined with chemometric methods can provide alternative techniques to conventional methods to determine quality traits of fruits or vegetables. In the present study, these techniques were used to predict the main traits involved in sensory quality of raspberry fruits (such as soluble solids content, total acid, pH, fructose, glucose and sucrose) and the main bioactive compounds implied in antioxidant capacities (vitamin C, phenolics and anthocyanins). Partial Least Squares regressions (PLS) were used to develop the prediction models. A leave-one-out procedure has been performed to determine the optimal number of latent variables and the wavenumber selection; and k-one-out procedure (2/3, 1/3) to calibrate and to cross-validate the models. Excellent predictions were achieved for quality traits (pH, TA, SSC) with R2-greater than 0.90, except for TA prediction in the second validation steps where R2-value decreased to 0.61. Predictions of reducing sugars and sucrose were also excellent with R2-values above 0.95 in both validation steps. Models aiming at to predict bioactive compounds presented lower performances than sugar models. They remain acceptable and promising for vitamin C and phenolics (R2 ≥ 0.65; RMSECV ≤ 12%). Finally, the validation of anthocyanins prediction model did not give satisfactory results.

A new strategy to prevent over-fitting in partial least squares models based on model population analysis

Partial least squares (PLS) is one of the most widely used methods for chemical modeling. However, like many other parameter tunable methods, it has strong tendency of over-fitting. Thus, a crucial step in PLS model building is to select the optimal number of latent variables (nLVs). Cross-validation (CV) is the most popular method for PLS model selection because it selects a model from the perspective of prediction ability. However, a clear minimum of prediction errors may not be obtained in CV which makes the model selection difficult. To solve the problem, we proposed a new strategy for PLS model selection which combines the cross-validated coefficient of determination (Qcv2) and model stability (S). S is defined as the stability of PLS regression vectors which is obtained using model population analysis (MPA). The results show that, when a clear maximum of Qcv2 is not obtained, S can provide additional information of over-fitting and it helps in finding the optimal nLVs. Compared with other regression vector based indictors such as the Euclidean 2-norm (B2), the Durbin Watson statistic (DW) and the jaggedness (J), S is more sensitive to over-fitting. The model selected by our method has both good prediction ability and stability.

Using Short Wave Visible–Near Infrared Reflectance Spectroscopy to Predict Soil Properties and Content

ABSTRACT In this study, short wave visible–near infrared reflectance spectroscopy was evaluated for prediction of diverse soil properties related to four different soil series of several regions in Jiangxi, China. A total of 240 soil samples were collected for the calibration (n = 168) and prediction (n = 72) sets. The used wavelength range of short wave visible–near infrared reflectance spectroscopy is 325–1075 nm. Partial least squares regression and back propagation neural network were used to develop models for soil properties such as organic matter and extractable forms of calcium, magnesium, and potassium. Performance of these models was also compared and analyzed. The input of back propagation neural network was the first six principal components resulted from the principal component analysis and the optimal number of latent variables obtained from partial least squares regression. The overall results showed that the performance of partial least squares regression model was inferior to all back propagation neural network models. The best prediction was obtained with latent variables as input of back propagation neural network model for organic matter (determination coefficient = 0.84 and relative predictive determinant = 2.38), which was classified as very good model predictions. The prediction of calcium, magnesium, and potassium was classified as fair (determination coefficient = 0.56–0.68 and relative predictive determinant = 1.51–1.61), where quantitative predictions were considered possible. It is recommended to adopt latent variables as input for back propagation neural network model predicting soil properties with short wave visible–near infrared reflectance spectroscopy. In conclusion, short wave visible–near infrared reflectance spectroscopy was variably successful in estimating soil properties and showed potential for substituting laboratory analyses.

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.

A simple ensemble strategy of uninformative variable elimination and partial least-squares for near-infrared spectroscopic calibration of pharmaceutical products

Based on uninformative variable elimination (UVE) and partial least squares (PLS), a simple ensemble strategy, named EUVEPLS, is proposed for multivariate calibration of near-infrared spectroscopy. In such a strategy, different calibration sets are first formed by randomly selecting a fixed number of objects from the available calibration data, with replacement, in this manner, different PLS models can be obtained, as in the jackknife procedure. Then, the UVE is used to shrink the original variable space into a specific subspace, in which a PLS model with the optimal number of latent variables is determined by cross-validation. This process is repeated until a fixed number of candidate models, and therefore the same number of subspaces, are obtained. Finally, those models with better performance are used to produce an ensemble model by simple/weighted average. Two NIR spectral datasets concerning the pharmaceutical products are used to verify the accuracy and robustness of the proposed EUVEPLS. The results confirmed the superiority of EUVEPLS to two single model reference methods (UVEPLS and full-spectrum PLS).

Deriving vegetation leaf water content from spectrophotometric data with orthogonal signal correction-partial least square regression

As an important element for the growth of plants, water is of great significance for real-time understanding of vegetation status, especially in the field of agricultural drought monitoring and forest fire prediction. Currently, vegetation leaf water content (LWC) estimation approaches employing remote sensing mainly include monitoring of spectral indices based on vegetation moisture feature bands and processing of continuous spectral data gained from hyperspectral remote sensing. In this article, a new approach, orthogonal signal correction-partial least square regression (OSC-PLSR), is introduced, to extract LWC from laboratory-measured reflectance spectra. Equivalent water thickness (EWT) and fuel moisture content (FMC) (based on both fresh and dry weight; FMCw and FMCd) were selected as indicators of LWC. Using the Leaf Optical Properties EXperiment (LOPEX) data set, first the relationships between LWC (EWT, FMCw and FMCd) and the spectral features of original reflectance were examined, via simple PLSR. Next, the OSC-PLSR was applied to evaluate its performance for estimating LWC (EWT, FMCw and FMCd) from reflectance spectra. Then, the vegetation moisture feature bands were derived from the analysis of OSC-PLSR latent variable loadings. According to the results, there are three major conclusions. (1) OSC-PLSR shows good performance for predicting all LWC indicators, and using only one latent variable, the OSC-PLSR model's complexity is greatly reduced compared with simple PLSR models. (2) Using both one and an optimal number of latent variables in OSC-PLSR models, FMCw sees the best prediction, followed by EWT and lastly FMCd; this order is opposite to the order of LWC data variation. (3) Through loading analysis of one-latent-variable OSC-PLSR models, the vegetation moisture feature bands can be retrieved. For EWT, the moisture-sensitive bands lie within one near-infrared (NIR) and two shortwave-infrared (SWIR) regions; for FMCw and FMCd, the moisture-sensitive bands lie within two SWIR regions. Also, the vegetation moisture-insensitive bands for EWT, FMCw and FMCd estimation are respectively acquired at around 1340, 1150 and 1330 nm.

Comparison among principal component, partial least squares and back propagation neural network analyses for accuracy of measurement of selected soil properties with visible and near infrared spectroscopy

The selection of calibration method is one of the main factors influencing the measurement accuracy with visible (vis) and near infrared (NIR) spectroscopy. This paper compared the performance of three calibration methods, namely, principal component regression (PCR), partial least squares regression (PLSR) and back propagation neural network (BPNN) analyses for the accuracy of measurement of selected soil properties, namely, organic carbon (OC) and extractable forms of potassium (K), sodium (Na), magnesium (Mg) and phosphorous (P). A total of 168 soil samples collected from Belgium and Northern France were used as the data set for the calibration–validation procedure. Optical scanning was carried out on fresh soil samples with a fibre-type, vis–NIR (LabSpec®Pro Near Infrared Analyzer, Analytical Spectral Devices, Inc, USA) with a measurement range of 350–2500 nm. The entire data set was split randomly into 3 replicates of 90% and 10% for the cross-validation set and prediction set, respectively. The input of BPNN was the first 5 principal components (PCs) resulted from the principal component analysis (PCA) and the optimal number of latent variables (LVs) obtained from PLSR. Both the leave-one-out cross validation and prediction for the three replicates showed that all BPNN-LV models outperformed PCR, PLSR and BPNN-PCs models. Furthermore, BPNN-PCs and PLSR provided, respectively, better performance than PCR. The best predictions were obtained with BPNN-LVs modelling for OC ( R pre 2 = 0.84 and residual prediction deviation (RPD) = 2.54) and Mg ( R pre 2 = 0.82 and RPD = 2.54), which were classified as excellent model predictions. The prediction of K, P and Na was classified as good ( R pre 2 = 0.68–0.74 and RPD = 1.77–1.94), where quantitative predictions were considered possible. It is recommended to adopt BPNN-LVs modelling technique for higher accuracy measurement of the selected soil properties with vis–NIR spectroscopy, in comparison with PCR, PLS and BPNN-PCs modelling techniques.

Partial Least Square Regression with Variable-Bagged Model Ensemble

A new bagging strategy, called variable-bagging, for partial least square (PLS) modelling is proposed. Variable-bagging is to bootstrap a set of spectral variables for each modelling process. Namely, Variable-bagged PLS (VBPLS) can be viewed as an ensemble of multiple PLS models built with bootstrapped molecular structure features of the analytes, for example, wavenumber. It can condense information from spectral variables broadly distributed in the wavenumber dimension and truncate the contribution of non-informative variables such as interference or simple noise. Thus, it potentially has an advantage to yield superior regression performance to conventional PLS which is based on a single model. The performance of VBPLS is demonstrated for the determination of Brix values with a set of NIR spectra collected from apples. The comparisons with other PLS techniques reveal that VBPLS yields superior regression performance, in terms of both prediction error and robustness, to conventional PLS, even with the optimal number of latent variables. Namely, VBPLS models can describe more reasonable relationships between the NIR spectra and corresponding Brix values.

Canonical correlation analysis for multivariate regression and its application to metabolic fingerprinting

Multivariate regression analysis is one of the most important tools in metabolomics studies. For regression of high-dimensional data, partial least squares (PLS) has been widely used. Canonical correlation analysis (CCA) is a classic method of multivariate analysis; it has however rarely been applied to multivariate regression. In the present study, we applied PLS and regularized CCA (RCCA) to high-dimensional data where the number of variables ( p) exceeds the number of observations ( N), N ≪ p. Using kernel CCA with linear kernel can drastically reduce the calculation time of RCCA. We applied these methods to gas chromatography–mass spectrometry (GC–MS) data, which were analyzed to resolve the problem of Japanese green tea ranking. To construct a quality-predictive model, the optimal number of latent variables in RCCA determined by leave-one-out cross-validation (LOOCV) was significantly fewer than in PLS. For metabolic fingerprinting, we successfully identified important metabolites for green tea grade classification using PLS and RCCA.