Partial Robust M-regression Research Articles

Comparing data driven soft independent class analogy (DD-SIMCA) and one class partial least square (OC-PLS) to authenticate sacha inchi (Plukenetia volubilis L.) oil using portable NIR spectrometer

Sacha Inchi (SI) oil is valuable due to high content of omega-3 and omega-6, which are important in human diet, thus being susceptible to adulteration. In this work, a low-cost and portable Near Infrared (NIR) spectrometer was used to authenticate pure sacha inchi oil from adulterated one with cheaper oils. Principal component analysis (PCA) was applied as screening technique and showed a good class separation between pure SI oil and blends, with significant impact of unsaturated fatty acids present in SI oil. Data Driven Soft Independent Class Analogy (DD-SIMCA) provided better results when compared to One Class Partial Least Square (OC-PLS) for data analysis. DD-SIMCA was implemented in rigorous approach, and it reached Sensitivity (SEN) = 89.8 % and Specificity (SPE) = 93 % using α = 0.05 and 4 PCs, while ordinary OC-PLS required 10 LVs to reach SEN = 87.8 % and SPE = 84.3 %, performing better than Gaussian radial basis function (GRBF-OCPLS) and partial robust M-regression (PRM) approaches. Results indicate that low-cost NIR spectrometer coupled to one-class classifiers could be used to authenticate pure SI oil.

Monitoring the concentrations of Cd, Cu, Pb, Ni, Cr, Zn, Mn and Fe in cultivated Haplic Luvisol soils using near-infrared reflectance spectroscopy and chemometrics

This study illustrates the successful application of near-infrared reflectance spectroscopy extended with chemometric modeling to profile Cd, Cu, Pb, Ni, Cr, Zn, Mn, and Fe in cultivated and fertilized Haplic Luvisol soils. The partial least-squares regression (PLSR) models were built to predict the elements present in the soil samples at very low contents. A total of 234 soil samples were investigated, and their reflectance spectra were recorded in the spectral range of 1100–2500 nm. The optimal spectral preprocessing was selected among 56 different scenarios considering the root mean squared error of prediction (RMSEP). The partial robust M-regression method (PRM) was used to handle the outlying samples. The most promising models were obtained for estimating the amount of Cu (using PRM) and Pb (using the classic PLS), leading to RMSEP expressed as a percentage of the response range, equal to 9.63% and 11.5%, respectively. The respective coefficients of determination for validation samples were equal to 0.86 and 0.58, respectively. Assuming similar variability of model residuals for the model and test set samples, coefficients of determination for validation samples were 0.94 and 0.89, respectively. Moreover, the favorable PLS models were also built for Zn, Mn, and Fe with coefficients of determinations equal to 0.87, 0.87, and 0.79.

Introducing an interesting and novel strategy based on exploiting first-order advantage from spectrofluorimetric data for monitoring three toxic metals in living cells

In this work, we did our best to develop a novel and interesting analytical method based on coupling of spectrofluorimetry with first-order multivariate calibration techniques for simultaneous determination of lead (Pd), zinc (Zn) and cadmium (Cd) in HeLa cells. To achieve this goal, quenching of the emission of graphene (GR) was individually investigated in the presence of Pb, Zn and Cd and then, according to the linear ranges obtained from individual calibration graphs, a multivariate calibration model was developed based on modeling of the quenching of the emission of GR in the presence of the mixtures of Pb, Zn and Cd. First-order multivariate calibration models were constructed by partial least squares (PLS), principal component regression (PCR), orthogonal signal correction-PLS (OSC-PLS), continuum power regression (CPR), robust continuum regression (RCR) and partial robust M-regression (PRM) and their performances were evaluated and statistically compared. Finally, the OSC-PLS was chosen as the best model with the best practical performance for analytical purposes.

A novel robust PLS regression method inspired from boosting principles: RoBoost-PLSR

The calibration of Partial Least Square regression (PLSR) models can be disturbed by outlying samples in the data. In these cases the models can be unstable and their predictive potential can be depreciated. To address this problem, some robust versions of the PLSR Algorithm were proposed. These algorithms rely on the downweighting of these outliers during calibration. To this end, it is necessary to estimate an inconsistency measurement between the samples and the model. However, this estimation is not trivial in high dimensions. This paper proposes a novel robust PLSR algorithm inspired from the principles of boosting: RoBoost-PLSR. This method consists of realising a series of one latent variable weighted PLSR. RoBoost-PLSR is compared with the PLSR algorithm calibrated with and without outliers and also with Partial Robust M-regression (PRM), a reference robust method. This evaluation is conducted on the basis of three simulated datasets and a real dataset. Finally Roboost-PLSR proves to be resilient to the tested outliers, and can achieve the performances of the reference PLSR calibrated without any outlier.

Genetic robust kernel sample selection for chemometric data analysis

AbstractIn this work, we propose a new algorithm to improve existing techniques used in the field of spectroscopic data regression analysis. In particular, it combines the power of nonlinear kernel regressors (kernel ridge regression [KRR], kernel principal component regression [KPCR], and Gaussian process regression [GPR]) with an optimization based on nondominated sorting multi‐objective genetic algorithm (NSGAII) to filter the residual outliers in the prediction space and leverage points in the features space. The proposed algorithm, contrary to most existing robust algorithms, simultaneously optimizes many complementary objectives for an automatic adaptation and thus a better outliers detection. It is well known that the elimination of outliers greatly improves the regression model. It is thus the aim of this work to develop a new robust regression algorithm. It has been applied on five different datasets, and the results are compared to both classical nonlinear regression methods and the commonly used robust regression methods robust continuum regression (RCR), partial robust M‐regression (PRM), robust principal component regression (RPCR), robust PLSR (RSIMPLS), and locally weighted regression (LWR). They show that the proposed algorithm outperforms the classical nonlinear regression methods and is a promising competitor to the robust methods outperforming most of them. Even though the results obtained are only from five datasets, this algorithm can be considered an interesting contribution for improving data analysis in the field of chemometrics.

Extreme Learning Machine Based on Calculating the Output Weight of Partial Robust M-regression

In order to improve the nonlinear mapping capability and learning performance of extreme learning machine (ELM), a new learning algorithm called extreme learning machine based on calculating the output weight of partial robust M-regression is proposed. This algorithm introduces the partial robust M-regression into the extreme learning machine algorithm. Firstly, the hidden layer output matrix H is calculated by extreme learning machine. Secondly, the matrix H and vector Y are weighted by weighted strategy. Then, PRM algorithm is used to establish the regression model between the weighted matrix Hw and vector Yw, and calculate its regression coefficient, namely output weight of the ELM Algorithm. The proposed method predicts the Mackay’s robot arm regression and sediment concentration of the Yellow River Basin to verify the effectiveness of the method. The simulation results show that the proposed PRMELM algorithm is superior to the original extreme learning machine algorithm in prediction accuracy and generalization performance.

A lifecycle operating performance assessment framework for hot strip mill process based on robust kernel canonical variable analysis

In the modern hot strip mill process (HSMP), the operating performance may deteriorate because of wear of equipment, mode transitions, and random disturbances. If the process is not adjusted and maintained, faults may occur, resulting in greater economic losses and potential safety hazards. Therefore, it is of great practical significance to carry out comprehensive operating performance assessment. In this paper, a lifecycle operating performance assessment framework based on robust kernel canonical variable analysis (RKCVA) is proposed to deal with automation hierarchy, nonlinearity, and outliers in the plant-wide HSMP. First, the HSMP is divided into upstream, midstream, and downstream in real-time control level (L1). Then, based on kernel canonical variable analysis (KCVA) and partial robust M-regression (PRM), the RKCVA models are developed for each stream and process control level (L2). Based on the Bayesian inference, statistical fusion is implemented to judge whether the process is in normal or faulty operating condition. After that, according to different evaluation rules of different operating conditions, the lifecycle operating performance assessment is realized. Finally, the framework is illustrated with a case study on a real HSMP. The assessment results show that the accuracy of the RKCVA is more than 10% higher than that of the KCVA.

Partial Robust M-Regression Estimator in the Presence of Multicollinearity and Vertical Outliers

The objective of using regression is to explain the variation in one or more response variables by associating the variation with proportional variation in one or more explanatory variables. However, if the number of independent variables is multiple, they tend to be highly collinear and this contributes to multicollinearity problem. For instance, Ridge Regression (RR), Principal Component Regression (PCR), and Partial Least Squares Regression (PLSR) are some of the prediction methods used to handle dataset with multicollinearity. In addition, another problem that arises is the existence of outlying objects in a dataset. The effect of outlying data points in the presence of multicollinearity problem could be reduced with the implementation of robust regression method. A recently studied robust PLSR, which is called Partial Robust M-Regression (PRM) is found to be able in dealing with multicollinearity and outliers simultaneously. This method was employed in this study. Throughout this study, five methods of regression were chosen; OLS, RR, PCR, PLSR, and PRM, to compare which is the best method in their predictive ability. To compare these five regression methods, a simulation study had been conducted, and the mean square error of β estimate (MSE(β)) was calculated. The simulation results show that PRM outperforms other method in the presence of multicollinearity, outliers and leverage points.

The effects of different weight functions on partial robust M-regression performance: A simulation study

Partial Robust M (PRM) is a partial robust regression estimator using robust M-estimators. The aim of this study is to see the effects of using alternative Iteratively Reweighted Least Squares (IRLS) weight functions instead of Fair weight function used in original robust Partial Least Squares Regression (PLSR) method PRM, furthermore, is to examine the effects of soft, semi-hard and hard weightings on this algorithm in terms of efficiency, goodness of fit and prediction. Hence, classical SIMPLS, original PRM algorithm using Fair weight function and four alternative PRM algorithms named as PRMBSQR, PRMCHY, PRMHBR, PRMTLWRTH (obtained using Bisquare, Cauchy, Huber and Talworth weight functions) are compared. The simulation results and a real data application show the original PRM and PRMCHY, both of using soft weighting functions, are the leading algorithms in terms of efficiency and prediction for both low and high dimensional data sets in case of moderate outliers existence. However, when the proportion of outliers is getting higher, semi-hard weighting PRMBSQR or a hard weighting PRMTLWRTH could be good alternatives. Moreover, real data application showed that generally original PRM and PRMCHY, PRMBSQR and PRMTLWRTH algorithms have better performances in terms of outlier detection than both PRMHBR and classical SIMPLS algorithms.

The Comparison of Robust Partial Least Squares Regression Methods (RSIMPLS, PRM) with Robust Principal Component Regression for Predicting Tourist Arrivals to Turkey

Tourism is one of the most important component in the economic development strategy of many developing countries such as Turkey. The annual data set of Turkey (1986 - 2013), including the six factors affecting the tourist arrivals, is examined. The aim of this study is modelling the tourist arrivals to Turkey in cases of both multicollinearity and outlier existence in the data set by using a robust Principal Component Regression method: RPCR, two robust Partial Least Squares Regression methods: RSIMPLS and Partial Robust M-Regression (PRM). Hence, the best model giving the best predictions of tourist arrivals is selected and the most important factors are determined.

Effects of sewage sludge application on unfertile tropical soils evaluated by multiple approaches: A field experiment in a commercial Eucalyptus plantation

Sewage sludge (SS) reuse in forest plantation as soil fertilizer/amendment has tremendously increased in recent years. However, SS may have high concentrations of potentially toxic elements (PTE), representing a potential risk for soil and the whole ecosystem. This paper was aimed to assess the toxicity of PTE in unfertile tropical soils amended with SS in a commercial Eucalyptus plantation, with an integrated multiple approaches combining: i) the use of a battery of bioassays (Daphnia magna, Pseudokcrichirella subcapitata, Lactuca sativa, and Allium cepa); and ii) the evaluation of some PTE (Cd, Cr, Cu, Fe, Mn, Ni, Pb, and Zn) and their availability into the pedoenvironment. Differences in total and available PTE between SS doses and time of treatments were evaluated using ANOVA; correlations between PTE and bioassays by a sparse partial robust M-regression (SPRM), while multiple correlations among parameters were performed by principal factor analysis (PFA). Results show that PTE contents in soils tended to increase with SS application doses. However this cannot be assumed as a general rule since in all the investigated treatments the PTE concentrations were consistently below both soil natural background concentrations and quality reference values. Bioassays showed a generalized low eco- and genotoxicity of SS with an increase in toxicity at increasing SS doses but with a clear decreasing trend as time went by. A. cepa was the most sensitive bioassay followed by P. subcapitata > D. magna > L. sativa. Overall, the results indicate that in realistic open field conditions SS risk may be lower than expected due to dynamic decrease in PTE toxicity with time after application. This study has an important implication that open-field trials should be strongly encouraged for evaluating environmental risk of SS application in forestry.

Advanced spectrophotometric chemometric methods for resolving the binary mixture of doxylamine succinate and pyridoxine hydrochloride.

The prediction power of partial least squares (PLS) and multivariate curve resolution-alternating least squares (MCR-ALS) methods have been studied for simultaneous quantitative analysis of the binary drug combination - doxylamine succinate and pyridoxine hydrochloride. Analysis of first-order UV overlapped spectra was performed using different PLS models - classical PLS1 and PLS2 as well as partial robust M-regression (PRM). These linear models were compared to MCR-ALS with equality and correlation constraints (MCR-ALS-CC). All techniques operated within the full spectral region and extracted maximum information for the drugs analysed. The developed chemometric methods were validated on external sample sets and were applied to the analyses of pharmaceutical formulations. The obtained statistical parameters were satisfactory for calibration and validation sets. All developed methods can be successfully applied for simultaneous spectrophotometric determination of doxylamine and pyridoxine both in laboratory-prepared mixtures and commercial dosage forms.

Simultaneously detection of calcium and magnesium in various samples by calmagite and chemometrics data processing

The current study describes results of the application of radial basis function-partial least squares (RBF-PLS), partial robust M-regression (PRM), singular value decomposition (SVD), evolving factor analysis (EFA), multivariate curve resolution with alternating least squares (MCR-ALS) and rank annihilation factor analysis (RAFA) methods for the purposes of simultaneous determination of trace amounts calcium (Ca2+) and magnesium (Mg2+) and exploratory analysis based on their colored complexes formation with 1-(1-hydroxy-4-methyl-2-phenylazo)-2-naphthol-4-sulfonic acid (calmagite) as chromomeric reagent. The complex formation Ca2+ and Mg2+ with calmagite was investigated under pH10.20. The performance of RBF-PLS model in detection of minerals was compared with PRM as a linear model. The pure concentration and spectral profiles were obtained using MCR-ALS. EFA and SVD were used to distinguish the number species. The stability constants of the complexes were derived using RAFA. Finally, RBF-PLS was utilized for simultaneous determination of minerals in pharmaceutical formulation and various vegetable samples.

Investigating the discrimination potential of linear and nonlinear spectral multivariate calibrations for analysis of phenolic compounds in their binary and ternary mixtures and calculation pKa values

Vanillin (VA), vanillic acid (VAI) and syringaldehyde (SIA) are important food additives as flavor enhancers. The current study for the first time is devote to the application of partial least square (PLS-1), partial robust M-regression (PRM) and feed forward neural networks (FFNNs) as linear and nonlinear chemometric methods for the simultaneous detection of binary and ternary mixtures of VA, VAI and SIA using data extracted directly from UV-spectra with overlapped peaks of individual analytes. Under the optimum experimental conditions, for each compound a linear calibration was obtained in the concentration range of 0.61–20.99 [LOD=0.12], 0.67–23.19 [LOD=0.13] and 0.73–25.12 [LOD=0.15] μgmL−1 for VA, VAI and SIA, respectively. Four calibration sets of standard samples were designed by combination of a full and fractional factorial designs with the use of the seven and three levels for each factor for binary and ternary mixtures, respectively. The results of this study reveal that both the methods of PLS-1 and PRM are similar in terms of predict ability each binary mixtures. The resolution of ternary mixture has been accomplished by FFNNs. Multivariate curve resolution-alternating least squares (MCR-ALS) was applied for the description of spectra from the acid-base titration systems each individual compound, i.e. the resolution of the complex overlapping spectra as well as to interpret the extracted spectral and concentration profiles of any pure chemical species identified. Evolving factor analysis (EFA) and singular value decomposition (SVD) were used to distinguish the number of chemical species. Subsequently, their corresponding dissociation constants were derived. Finally, FFNNs has been used to detection active compounds in real and spiked water samples.

A MPRM-based approach for fault diagnosis against outliers

In practice industrial applications, the training dataset collected from production process usually contain some outliers. This is a difficult case for partial least squares (PLS) regression which is sensitive to outliers. In order to solve this problem, the paper presents a multivariate statistical process monitoring and diagnosis method based on modified partial robust M-regression (MPRM). MPRM can eliminate the effects of the outliers in the raw data and establish accurate model by down-weighting the outliers strategy. In industry application, the key performance indicator related prediction and fault diagnosis are important to ensure the product quality and enhance economic benefits. Although, the standard PLS is one kind of the most widely used method, it performs an oblique projection to the input space, and thus cannot well distinguish quality-related faults from quality-unrelated ones. To overcome this drawback, the paper proposes to use the singular value decomposition (SVD) on coefficient matrix to decompose input data into quality-related part and quality-unrelated part. Then, robust monitoring statistics and control limits are derived for process monitoring purposes. A numerical example illustrates that the proposed method shows superior process monitoring performance in comparison with standard PLS when the modeling dataset contains outliers.

Novel robust approach for constructing Mamdani-type fuzzy system based on PRM and subtractive clustering algorithm

A novel approach for constructing robust Mamdani fuzzy system was proposed, which consisted of an efficiency robust estimator (partial robust M-regression, PRM) in the parameter learning phase of the initial fuzzy system, and an improved subtractive clustering algorithm in the fuzzy-rule-selecting phase. The weights obtained in PRM, which gives protection against noise and outliers, were incorporated into the potential measure of the subtractive cluster algorithm to enhance the robustness of the fuzzy rule cluster process, and a compact Mamdani-type fuzzy system was established after the parameters in the consequent parts of rules were re-estimated by partial least squares (PLS). The main characteristics of the new approach were its simplicity and ability to construct fuzzy system fast and robustly. Simulation and experiment results show that the proposed approach can achieve satisfactory results in various kinds of data domains with noise and outliers. Compared with D-SVD and ARRBFN, the proposed approach yields much fewer rules and less RMSE values.

A MATLAB toolbox for class modeling using one-class partial least squares (OCPLS) classifiers

One-class classifiers are widely used to solve the classification problems where control or class modeling of a target class is necessary, e.g., untargeted analysis of food adulterations and frauds, tracing the origins of a food with Protected Denomination of Origin, fault diagnosis, etc. Recently, one-class partial least squares (OCPLS) has been developed and demonstrated to be a useful technique for class modeling. For analysis of nonlinear and outlier-contaminated data, nonlinear and robust OCPLS algorithms are required.This paper describes a free MATLAB toolbox for class modeling using OCPLS classifiers. The toolbox includes ordinary, nonlinear and robust OCPLS methods. The nonlinear algorithm is based on the Gaussian radial basis function (GRBF), and the robust algorithm is based on the partial robust M-regression (PRM). The usage of the toolbox is demonstrated by analysis of a real data set.

A Partial Robust M-Regression-Based Prediction and Fault Detection Method

Due to its simplicity and easy implementation, partial least squares (PLS) serves as an efficient approach in large-scale industrial process. However, like many data-based methods, PLS is quite sensitive to outliers, which is a common abnormal characteristic of the measured process data that can significantly affect the monitoring performance of PLS. In order to develop a robust prediction and fault detection method, this paper employs the partial robust M-regression (PRM) to deal with the outliers. Moreover, to eliminate the useless variations for prediction, an orthogonal decomposition is performed on the measurable variables space so as to allow the new method to serve as a powerful tool for quality-related prediction and fault detection. The proposed method is finally applied on the Tennessee Eastman (TE) process.

Chemometrics-assisted simultaneous voltammetric determination of ascorbic acid, uric acid, dopamine and nitrite: Application of non-bilinear voltammetric data for exploiting first-order advantage

For the first time, several multivariate calibration (MVC) models including partial least squares-1 (PLS-1), continuum power regression (CPR), multiple linear regression-successive projections algorithm (MLR-SPA), robust continuum regression (RCR), partial robust M-regression (PRM), polynomial-PLS (PLY-PLS), spline-PLS (SPL-PLS), radial basis function-PLS (RBF-PLS), least squares-support vector machines (LS-SVM), wavelet transform-artificial neural network (WT-ANN), discrete wavelet transform-ANN (DWT-ANN), and back propagation-ANN (BP-ANN) have been constructed on the basis of non-bilinear first order square wave voltammetric (SWV) data for the simultaneous determination of ascorbic acid (AA), uric acid (UA), dopamine (DP) and nitrite (NT) at a glassy carbon electrode (GCE) to identify which technique offers the best predictions. The compositions of the calibration mixtures were selected according to a simplex lattice design (SLD) and validated with an external set of analytes' mixtures. An asymmetric least squares splines regression (AsLSSR) algorithm was applied for correcting the baselines. A correlation optimized warping (COW) algorithm was used to data alignment and lack of bilinearity was tackled by potential shift correction. The effects of several pre-processing techniques such as genetic algorithm (GA), orthogonal signal correction (OSC), mean centering (MC), robust median centering (RMC), wavelet denoising (WD), and Savitsky-Golay smoothing (SGS) on the predictive ability of the mentioned MVC models were examined. The best preprocessing technique was found for each model. According to the results obtained, the RBF-PLS was recommended to simultaneously assay the concentrations of AA, UA, DP and NT in human serum samples.

Comparison of statistical and machine learning methods in modelling of data with multicollinearity

Multicollinearity occurs in a dataset due to correlation between the predictors. Models derived from such data without a check on multicollinearity may lead to erroneous system analysis. This problem can be eliminated by the selection of appropriate predictors from the dataset. Variable reduction methods like B2, B4, VIF, KIF and factor analysis (FA) can be used to overcome this problem. Such methods are useful particularly when used in conjunction with modelling methods that do not automate variable selection, such as artificial neural network (ANN) and fuzzy logic. The literature reveals that the current problem is aptly described in the field of statistics but is paid little attention in the field of machine learning. In this paper, multicollinearity is presented involving the estimation of fat content inside the body. Commonly used statistical methods such as stepwise regression, radial basis function partial least squares, partial robust M-regression, ridge regression and principal component regressi...