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Cross validation (CV) is by far one of the most commonly used methods to estimate model complexity for partial least squares (PLS). In this study, stochastic cross validation (SCV) was proposed as a novel CV strategy, where the percent of left-out objects (PLOO) was defined as a changeable random number. We proposed two SCV strategies, namely, SCV with uniformly distributed PLOO (SCV-U) and SCV with normally distributed PLOO (SCV-N). SCV-U is actually a hybrid of leave-one-out CV (LOOCV), k -fold CV and Monte Carlo CV (MCCV). The rationale behind SCV-N is that the probability of large perturbations of the original training set will be small. SCV is expected to provide more flexibility for data splitting to explore and learn from the data set and evaluate internally a built model. SCV-U and SCV-N were used for PLS calibrations of three real data sets as well as a simulated data set and they were compared with LOOCV, k -fold CV and MCCV. Given a training and external validation set, different CV techniques were repeatedly used to evaluate the optimal model complexity and the prediction results were compared. The results indicate that SCV-U and SCV-N could provide useful alternatives to the traditional CV methods and SCV is less sensitive to the values of PLOO. [ABSTRACT FROM AUTHOR]

A particle swarm optimization (PSO) based sparse regression (PSO-SR) strategy was proposed to study the quantitative structure-selectivity relationship (QSSR) of a biomimetic catalytic system, where the selectivity in the mild oxidation of o -nitrotoluene to o -nitrobenzaldehyde was related to the molecular descriptors of 48 metalloporphyrin catalysts. PSO was used to obtain an optimal variable combination for linear or nonlinear models. For nonlinear modeling, a set of 44 nonlinear transforms were developed for each single descriptor. To enable model interpretability and reduce the risk of overfitting, the total descriptors were divided into subclasses and the selected variables were forced to be sparsely distributed in each subclass. Model complexity was controlled by adjusting the maximum total number of variables included. Accurate linear and nonlinear PSO-SR models were developed using multiple linear regression (MLR) and partial least squares (PLS) and validated by randomly and repeatedly splitting the data into training and test objects for 500 times. The best predictions were obtained with 10 variables with linear ( Q 2 =0.9460) and nonlinear ( Q 2 =0.9505) models. The results indicate PSO-SR could provide an effective and useful strategy for modeling and interpreting complex QSSR problems. The proposed nonlinear modeling method could provide more information for model interpretation by probing and catching the unknown nonlinear relationship between a descriptor and the observed selectivity. [ABSTRACT FROM AUTHOR]

Large-class-number classification (LCNC) would bring new challenges to pattern recognition due to increased data complexity and class overlapping. In this study, a novel ensemble strategy (ES) was proposed to tackle LCNC problems. By combining the One-Versus-Rest (OVR) and One-Versus-One (OVO) strategies to design a set of classifiers with reduced class numbers, ES assigns a new object to the class receiving the most votes. When two or more classes obtain the most votes, an additional OVR model is developed to discriminate them. ES, OVR, OVO and the softmax function were investigated to discriminate the geographical origins of 25 green tea samples using near-infrared (NIR) spectroscopy and Partial Least Squares Discriminant Analysis (PLSDA). Using the Standard Normal Variate (SNV) as a spectral scatter correction technique, the total accuracy was 0.6468 for OVR-PLSDA, 0.8494 for OVO-PLSDA, 0.9299 for PLSDA-softmax, and 0.9377 for ES-PLSDA, respectively. Using other preprocessing methods and multiple random splitting of the data sets obtained the similar results. The poor performance of OVR can be attributed to the increased possibility of class overlapping and high sub-model complexity. OVO was less influenced by LCNC because it is based on a set of relatively simpler two-class classifiers. PLSDA-softmax could overcome the class overlapping by nonlinear transformations. ES was demonstrated to be capable of extracting more useful information from sub-models and achieved improved performance in LCNC. [ABSTRACT FROM AUTHOR]

The accurate estimation of the underlying number of components in complex samples is critical in data analysis. A new chemometric strategy was developed in this study to determine accurately the number of underlying components in complex samples. First, discrete Fourier transformation was used to project the eigenvectors from the singular value decomposition to the frequency space. A robust statistical analysis based on iterative t -test was then employed to eliminate the outliers in the Fourier coefficients of each eigenvector. Finally, ANOVA was used to differentiate the meaningful components from noise. Simulated and published fluorescence datasets were used to demonstrate the strategy. Results indicate that the proposed strategy accurately and efficiently estimated the number of underlying components in the analyzed dataset. Moreover, the performance of the proposed method was comparable with the well-known core consistency diagnostic and Monte Carlo simulation coupled with frequency location methods. The new technique coupled with second-order calibration was successfully used to resolve the problem of seriously overlapped fluorescence spectra in the accurate quantification of fluoroquinolone antibiotics in tap water samples. Second-order advantage was achieved. [ABSTRACT FROM AUTHOR]

Abstract Cross-validation (CV) is widely used to estimate model complexity or the number of significant latent variables (LVs) for multivariate calibration methods like partial least squares (PLS). A basic consideration when developing and validating multivariate calibration models is that both the training and validation sets should be representative and distributed in the experimental space as uniformly as possible. Motivated by this idea, we proposed a new CV method called representative splitting cross-validation (RSCV). In RSCV, firstly, the DUPLEX algorithm was used to sequentially divide the original training set into k (in this work, k = 2, 4, 8 and 16) equal parts. Secondly, a series of k-fold (k = 2, 4, 8 and 16) CVs were performed based on the above data splitting. Finally, the pooled root mean squared error of CV (RMSECV) was used to estimate model complexity. Five real multivariate calibration data sets were investigated and RSCV was compared with leave-one-out CV (LOOCV), 10-fold CV and Monte Carlo CV (MCCV). With a maximum k of 16, RSCV was shown to be a useful and stable method to select PLS LVs, and can obtain simpler models with acceptable computational burden. Highlights • Representative splitting cross validation (RSCV) was proposed. • The DUPLEX algorithm was used to split the raw data set. • RSCV is a fusion of serial k -fold cross validations. • RSCV is stable and can obtain simpler models when necessary. [ABSTRACT FROM AUTHOR]

Complex datasets can be routinely produced from modern analytical platforms in metabonomics surveys, which brings enormous challenges to existing chemometrics tools. In the current study, inspired by the characteristic of classification tree (CT) in automatically selecting the most informative variables and measuring their importance, the potential of bagging in improving the reliability and robustness of a single model, and the promising modeling performance of radial basis function network (RBFN), we designed a new chemometrics tool, i.e., bagging classification tree-radial basis function network (BAGCT-EBFN), for metabonomics data analysis. In BAGCT-RBFN, a series of parallel CT models were firstly established based on the idea of bagging (BAGCT). The informative variables can be successfully spied via inspecting the variable importance values over all CTs in BAGCT. Then, RBFN was utilized to relate the identified informative variables to the class memberships. To demonstrate the practical application of BAGCT-RBFN in metabonomics, an H-1 NMR-based metabonomics dataset associated with lung cancer was applied. The results showed that BAGCT-RBFN can find a shortlist of discriminatory variables with reliability while attain more satisfactory classification accuracy than traditional CT and RBFN. [ABSTRACT FROM AUTHOR]

Abstract: This study presented a new version of the nonlinear partial least-squares method on the optimized radial basis function network transformation by particle swarm optimization (PSORBFPLS). This algorithm firstly transformed the training inputs into the hidden outputs using the nonlinear transformation carried by a radial basis function network (RBFN), and then employed linear partial least-squares (PLS) to relate the outputs of the hidden layer to the bioactivities. The widths and centers involved in RBF transformation were optimized by particle swarm optimization (PSO) with the minimized model error via PLS modeling as the criterion. The number of latent variables associated with PLS modeling was automatically identified by F-statistic. Two QSAR data sets were used to evaluate the performance of the newly proposed PSORBFPLS. Results of these two data sets demonstrated that PSORBFPLS offers substantially enhanced capacities in modeling nonlinearity while circumvents overfitting frequently encountered in nonlinear modeling. [Copyright &y& Elsevier]

Abstract: A new method, “advanced chemometric algorithm coupled to subspace projection technique between original and pseudo samples (ACA-SPOPS)”, is proposed for the first time for chemical rank estimation of three-way data arrays. In ACA-SPOPS, self-weighted alternating trilinear decomposition (SWATLD) algorithm is used to create pseudo samples to produce a pseudo array. Singular value decomposition (SVD) is then performed on the unfolded matrices of both pseudo array and original array. The chemical rank can be accordingly determined via the subspace projection technique. The performance of ACA-SPOPS has been demonstrated by both simulated and experimental data arrays. By comparing with four other widely used methods, namely core consistency diagnostic (CORCONDIA) test, ADD-ONE-UP truncating and fitting (ADD-ONE-UP), two-mode subspace comparison (TMSC) and subspace projection of pseudo high-way data array (SPPH), the results showed that this new method possessed better analytical performance than many other ones, in terms of noise, collinearity, concentration and computation speed. Moreover, the ACA-SPOPS method may be further applied for processing higher-order data arrays by accordingly extending the SWATLD algorithm to higher dimensions. [Copyright &y& Elsevier]