Partial Least Squares Regression Algorithm Research Articles

Structural Equation Modeling with Factors and Composites

Recent methodological developments building on partial least squares (PLS) techniques and related ideas have significantly contributed to bridging the gap between factor-based and composite-based structural equation modeling (SEM) methods. PLS-SEM is extensively used in the field of e-collaboration, as well as in many other fields where multivariate statistical analyses are employed. The author compares results obtained with four methods: covariance-based SEM with full information maximum likelihood (FIML), factor-based SEM with common factor model assumptions (FSEM1), factor-based SEM building on the PLS Regression algorithm (FSEM2), and PLS-SEM employing the Mode A algorithm (PLSA). The comparison suggests that FSEM1 yields path coefficients and loadings that are very similar to FIML's; and that FSEM2 yields path coefficients that are very similar to FIML's and loadings that are very similar to PLSA's.

Erratum to: Rapid discrimination of F1 hybrid seeds from their parental lines and selection of protein-rich corn lines for silage corn breeding using FT-IR spectroscopy combined by multivariate analysis

This study aims to establish the discrimination of F1 hybrid seeds from their parental lines and rapid selection of proteinrich lines from inbreeding lines of corn using FT-IR spectroscopy combined by multivariate analysis. Eight individual seeds from the maternal and paternal lines of Gwangpyeongok and their F1 progeny seeds were subjected to FT-IR spectroscopy. A total of 176 corn inbreeding lines including commercial corn cultivars were subjected to FT-IR spectroscopy. To establish the prediction model for total protein content from corn seed, 33 corn inbreeding lines out of 176 were randomly selected and total seed protein contents using Bradford assay were examined. PLS-DA (partial least square regression discriminant analysis) could clearly discriminate F1 hybrid seeds from their parental lines. PC (principal component) loading values show that 1,700 – 1,500 cm−1 and 1,200 – 900 cm−1 regions of FT-IR spectra are significantly important for discrimination of corn lines. The prediction model for total protein contents was established by PLS (partial least square regression) algorithm, and its accuracy was confirmed by cross-validation test (R2 = 0.94). After external validation fromexternal 25 corn inbreeding lines, regression coefficient (R2) was 0.78 which indicated that the prediction model had relatively good accuracy. Thus, considering these results we suggest that FT-IR combined with multivariate analysis could be applied as a novel tool for high-throughput screening of F1 hybrid seeds from their parental lines and protein-rich lines for breeding of silage corn cultivar.

A methodology for modeling and monitoring of centrifugal casting process

Purpose – The purpose of this paper is to build a monitoring scheme in order to detect and subsequently eliminate abnormal behavior of the concerned casting process so as to produce worm wheels with good quality characteristics. Design/methodology/approach – In this a study, a process monitoring strategy has been devised for a centrifugal casting process using data-based multivariate statistical technique, namely, partial least squares regression (PLSR). Findings – Based on a case study, the PLSR model constructed for this study seems to mimic the actual process quite well which is evident from the various performance criteria (predicted and analysis of variance results). Practical implications – The practical implication of the study involves development of a software application with a back-end database which would be interfaced with a computer program based on PLSR algorithm for estimation of model parameters and the control limit for the monitoring chart. It would help in easy and real-time detection of faults. Originality/value – This study concerns the application of a PLSR-based monitoring strategy to a centrifugal casting process engaged in the production of worm wheel.

Evaluation of the prediction precision capability of partial least squares regression approach for analysis of high alloy steel by laser induced breakdown spectroscopy

Laser induced breakdown spectroscopy (LIBS) was applied for elemental characterization of high alloy steel using partial least squares regression (PLSR) with an objective to evaluate the analytical performance of this multivariate approach. The optimization of the number of principle components for minimizing error in PLSR algorithm was investigated. The effect of different pre-treatment procedures on the raw spectral data before PLSR analysis was evaluated based on several statistical (standard error of prediction, percentage relative error of prediction etc.) parameters. The pre-treatment with “NORM” parameter gave the optimum statistical results. The analytical performance of PLSR model improved by increasing the number of laser pulses accumulated per spectrum as well as by truncating the spectrum to appropriate wavelength region. It was found that the statistical benefit of truncating the spectrum can also be accomplished by increasing the number of laser pulses per accumulation without spectral truncation. The constituents (Co and Mo) present in hundreds of ppm were determined with relative precision of 4–9% (2σ), whereas the major constituents Cr and Ni (present at a few percent levels) were determined with a relative precision of ~2%(2σ).

Chemometrics-Assisted UV Spectrophotometric Method for Determination of Metformin Hydrochloride and Glyburide in Pharmaceutical Tablets

This study aims to estimate simultaneously metformin hydrochloride (MET) and glyburide (GLY) in a multicomponent tablets dosage form by spectrophotometric method using chemometric approaches such as principal component regression (PCR) and partial least-squares regression (PLS). Because of highly overlapped in UV spectra and difference proportions of two active ingredients, the conventional univariate calibration methods was not allowed without previous separation. The linearity ranges used to construct the calibration matrix were selected in the ranges from 40.00 to 200.00 mg L-1for MET and from 1.00 to 10.00 mg L-1for GLY. The absorbances were measured in the wavelength range of 200-400 nm, using ethanol as solvent. The resulting UV spectra were subjected to PCR and PLS algorithms and the optimum numbers of principal components (PCs) were selected according to prediction residual error sum of squares (PRESS) values of leave-one out cross-validation. The number of PCs for MET and GLY were found to be 5, 3 by PCR and 5, 3 by PLS, respectively. A set of synthetic mixtures was employed to verify the models and the performance of the models were shown in the values of the root mean square error in prediction (RMSEP). RMSEP values of MET and GLY were 1.806, 0.256 for PCR and 1.802, 0.185 for PLS, respectively. The suitable calibration models were applied to the analysis of these compounds in pharmaceutical formulation.

In situ measurement of some soil properties in paddy soil using visible and near-infrared spectroscopy.

In situ measurements with visible and near-infrared spectroscopy (vis-NIR) provide an efficient way for acquiring soil information of paddy soils in the short time gap between the harvest and following rotation. The aim of this study was to evaluate its feasibility to predict a series of soil properties including organic matter (OM), organic carbon (OC), total nitrogen (TN), available nitrogen (AN), available phosphorus (AP), available potassium (AK) and pH of paddy soils in Zhejiang province, China. Firstly, the linear partial least squares regression (PLSR) was performed on the in situ spectra and the predictions were compared to those with laboratory-based recorded spectra. Then, the non-linear least-square support vector machine (LS-SVM) algorithm was carried out aiming to extract more useful information from the in situ spectra and improve predictions. Results show that in terms of OC, OM, TN, AN and pH, (i) the predictions were worse using in situ spectra compared to laboratory-based spectra with PLSR algorithm (ii) the prediction accuracy using LS-SVM (R2>0.75, RPD>1.90) was obviously improved with in situ vis-NIR spectra compared to PLSR algorithm, and comparable or even better than results generated using laboratory-based spectra with PLSR; (iii) in terms of AP and AK, poor predictions were obtained with in situ spectra (R2<0.5, RPD<1.50) either using PLSR or LS-SVM. The results highlight the use of LS-SVM for in situ vis-NIR spectroscopic estimation of soil properties of paddy soils.

Estimation of Arsenic Contamination in Reclaimed Agricultural Soils Using Reflectance Spectroscopy and ANFIS Model

Heavy metal contamination from anthropogenic sources is a threat to human health. To assess the feasibility of predicting surface soil arsenic (As) concentration from hyperspectral reflectance measurement, three different regression algorithms are compared in this paper, i.e., multiple linear regression (MLR), partial least squares regression (PLSR), and adaptive neural fuzzy inference system (ANFIS) modeling. Soil samples were taken from three study sites in mining/agricultural areas after reclamation. As concentration was determined by hydride generation atomic fluorescence spectrometry (HG-AFS) analysis, and the reflectance was measured with an analytical spectral devices (ASD) field spectrometer covering the spectral region of 350–2500 nm. First, after preprocessing of the original reflectance spectroscopy, the correlation coefficients between the As concentration and spectral reflectance measurement were derived. Characteristic bands were then chosen for the quantitative retrieval model. Finally, all of the 30 samples were divided into a calibration set and a validation set of 18 and 12 samples, respectively. When compared with the MLR and PLSR algorithms, the ANFIS model was the best retrieval model, with a coefficient of determination ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\bf R}^{\bf 2}$</tex> </formula> ) of 0.94 and a root-mean-square error (RMSE) of 0.88. ANFIS model and reflectance spectroscopy therefore have the potential to map the spatial distribution of As abundance, with the aim of improving public health.

Classification and quantification analysis of peach kernel from different origins with near-infrared diffuse reflection spectroscopy.

Background:Peach kernels which contain kinds of fatty acids play an important role in the regulation of a variety of physiological and biological functions.Objective:To establish an innovative and rapid diffuse reflectance near-infrared spectroscopy (DR-NIR) analysis method along with chemometric techniques for the qualitative and quantitative determination of a peach kernel.Materials and Methods:Peach kernel samples from nine different origins were analyzed with high-performance liquid chromatography (HPLC) as a reference method. DR-NIR is in the spectral range 1100-2300 nm. Principal component analysis (PCA) and partial least squares regression (PLSR) algorithm were applied to obtain prediction models, The Savitzky-Golay derivative and first derivative were adopted for the spectral pre-processing, PCA was applied to classify the varieties of those samples. For the quantitative calibration, the models of linoleic and oleinic acids were established with the PLSR algorithm and the optimal principal component (PC) numbers were selected with leave-one-out (LOO) cross-validation. The established models were evaluated with the root mean square error of deviation (RMSED) and corresponding correlation coefficients (R2).Results:The PCA results of DR-NIR spectra yield clear classification of the two varieties of peach kernel. PLSR had a better predictive ability. The correlation coefficients of the two calibration models were above 0.99, and the RMSED of linoleic and oleinic acids were 1.266% and 1.412%, respectively.Conclusion:The DR-NIR combined with PCA and PLSR algorithm could be used efficiently to identify and quantify peach kernels and also help to solve variety problem.

Correlation between the Plasma Characteristics and the Surface Chemistry of Plasma-Treated Polymers through Partial Least-Squares Analysis

We investigated the effect of various plasma parameters (relative density of atomic N and H, plasma temperature, and vibrational temperature) and process conditions (pressure and H2/(N2 + H2) ratio) on the chemical composition of modified poly(tetrafluoroethylene) (PTFE). The plasma parameters were measured by means of near-infrared (NIR) and UV-visible emission spectroscopy with and without actinometry. The process conditions of the N2-H2 microwave discharges were set at various pressures ranging from 100 to 2000 mTorr and H2/(N2+H2) gas mixture ratios between 0 and 0.4. The surface chemical composition of the modified polymers was determined by X-ray photoelectron spectroscopy (XPS). A mathematical model was constructed using the partial least-squares regression algorithm to correlate the plasma information (process condition and plasma parameters as determined by emission spectroscopy) with the modified surface characteristics. To construct the model, a set of data input variables containing process conditions and plasma parameters were generated, as well as a response matrix containing the surface composition of the polymer. This model was used to predict the composition of PTFE surfaces subjected to N2-H2 plasma treatment. Contrary to what is generally accepted in the literature, the present data demonstrate that hydrogen is not directly involved in the defluorination of the surface but rather produces atomic nitrogen and/or NH radicals that are shown to be at the origin of fluorine atom removal from the polymer surface. The results show that process conditions alone do not suffice in predicting the surface chemical composition and that the plasma characteristics, which cannot be easily correlated with these conditions, should be considered. Process optimization and control would benefit from plasma diagnostics, particularly infrared emission spectroscopy.

Comparison of Different PLS Algorithms for Simultaneous Determination of Cd(II), Cu(II), Pb(II), and Zn(II) by Anodic Stripping Voltammetry at Bismuth Film Electrode

AbstractIn this work we evaluated the use of different variable selection techniques combined with partial least‐squares regression (PLS) – genetic algorithm PLS (GA‐PLS), interval PLS (iPLS), and synergy interval PLS (siPLS) – in the simultaneous determination of Cd(II), Cu(II), Pb(II) and Zn(II) by anodic stripping voltammetry at a bismuth film. Generally, variable selection provided an improvement in prediction results when compared to full‐voltammogram PLS. The use of interval selection based algorithms have shown to be most adequate than the selection of discrete variables by GA. Excellent analytical performances were obtained despite the inherent complexity of the simultaneous determination.

Abstract C124: Proteomic and phenotype derived model for selection of combinations of targeted therapies in ovarian cancer.

Abstract Combinations of molecular targeted therapies may be more effective due to collective inhibition at multiple points within a signaling network, but selecting the right targets has been elusive. We have used a partial least squares regression (PLS) statistical model to identify key functional proteins in four ovarian cancer cell lines (HEYA8, OVCAR8, CAOV3, SKOV3). We measured the changes in 85 proteins by reverse phase protein arrays (RPPA) when these four cell lines were treated with seven different kinase inhibitors (AZD6244, XL147, vandetinib, dasatinib, rapamycin, PF0573228, sunitinib). We also measured how these drugs modulated five different phenotypic endpoints: (1) a novel optimized co-culture differentiation assay with tumor cells and primary human microvascular endothelial cells (HMVECs), (2) mitochondrial activity as a surrogate for cytotoxicity using an XTT assay, and the production of (3) VEGF, (4) bFGF, and (5) EGF by tumor cells. We then applied PLS regression to the relationship between the proteins measured by RPPA and in vitro phenotypes to define important driver signaling proteins. We identified 14 proteins in this analysis: EGFR, p27, mTOR, p38, HER3, ERalpha, JNK, PRAS40, CHK2, TAZ, YAP, CHK1, AKT, and AMPK. Nine of these proteins have readily available inhibitors in various stages of clinical development: EGFR (BIBW2992), mTOR (MLN0128), p38 (SB203580), HER3 (AZD8931), ERalpha (tamoxifen), JNK (SP600125), CHK2 (AZD7762), CHK1 (LY2603618), AKT (MK2206). We examined these nine agents against all four cell lines with XTT assays. The mean IC50 was significantly less for the inhibitors targeting PLS selected driving proteins when compared to the original seven inhibitors tested across all four cell lines (Mean IC50 2.2x10−5M vs. 3.2 x 10−4M, p=0.0025). Similarly, while TORC1 inhibition with temsirolimus has been clinically tested in ovarian cancer, the PLS algorithm suggested that inhibitors targeting both TORC1 and TORC2 signaling might be more effective. MLN0128 (TORC1/2 inhibitor) was significantly more effective than sirolimus in HEYA8 (&amp;gt;5x10−4M vs. 8.9x10−7M, p=0.002), SKOV3 (1.4x10−5M vs 1.4 x10−8M, p=0.0006), CAOV3 (5.2x10−6M vs. 8.3x10−8M, p=0.018) and OVCAR8 (8.8x10−7M vs. 5.8x10−8M, p=0.0012) cell lines when comparing IC50 values for an XTT assay. The four most active compounds (MLN0128, AZD7762, LY2603618 and MK2206) across all four cell lines were selected for further testing. These compounds demonstrate good single agent activity as well as pair-wise synergism in all four cell lines. The PLS method provides a unique and predictive algorithm to examine interactions between proteomics and phenotypic endpoints and has yielded driver signaling events that will guide novel target combinations for phase I examination in ovarian cancer. Citation Information: Mol Cancer Ther 2013;12(11 Suppl):C124. Citation Format: John L. Hays, Eric C. Polley, Jason J. David, Joyce Lu, Anna M. Leone, Saawan Mehta, Elise C. Kohn. Proteomic and phenotype derived model for selection of combinations of targeted therapies in ovarian cancer. [abstract]. In: Proceedings of the AACR-NCI-EORTC International Conference: Molecular Targets and Cancer Therapeutics; 2013 Oct 19-23; Boston, MA. Philadelphia (PA): AACR; Mol Cancer Ther 2013;12(11 Suppl):Abstract nr C124.

Quantitative Analysis of Mixtures Using Terahertz Time-Domain Spectroscopy and Different PLS Algorithms

This paper attempted the feasibility to determine component concentrations in multicomponent mixtures with terahertz time-domain spectroscopy (THz-TDS) combined with different partial least-squares regression (PLS) algorithms. First, THz absorbance spectra for 75 ternary mixtures of anhydrous theophylline, lactose monohydrate and magnesium stearate were investigated using THz-TDS in the frequency range from 0.1 to 3.0 THz, then four different PLS methods, including interval PLS (iPLS), backward interval PLS (biPLS), synergy interval PLS (siPLS) and moving window PLS (mwPLS), were employed to perform quantitative analysis of anhydrous theophylline concentrations in ternary mixtures. The performance of mwPLS model is the best in contrast to other PLS models and full spectrum PLS. The optimal model was achieved with higher correlation coefficient for calibration (RC) of 0.9842, higher correlation coefficient for prediction (RP) of 0.9851, lower root mean square error of cross-validation (RMSECV) of 3.8241, and lower root mean square error of prediction (RMSEP) of 4.1540. Experimental results demonstrate that THz spectroscopy combined with PLS algorithms could be successfully applied as an effective nondestructive tool for the quantitative analysis of component concentrations in multicomponent mixtures, and mwPLS is an ideal method for reducing the complexity and improving the performance of the model.

Continuous Wavelet Transform Based Partial Least Squares Regression for Quantitative Analysis of Raman Spectrum

Quantitative analysis of Raman spectra using surface-enhanced Raman scattering (SERS) nanoparticles has shown the potential and promising trend of development in in vivo molecular imaging. Partial least square regression (PLSR) methods have been reported as state-of-the-art methods. However, the approaches fully rely on the intensities of Raman spectra and can not avoid the influences of the unstable background. In this paper we design a new continuous wavelet transform based PLSR (CWT-PLSR) algorithm that uses mixing concentrations and the average CWT coefficients of Raman spectra to carry out PLSR. We elaborate and prove how the average CWT coefficients with a Mexican hat mother wavelet are robust representations of Raman peaks, and the method can reduce the influences of unstable baseline and random noises during the prediction process. The algorithm was tested using three Raman spectra data sets with three cross-validation methods in comparison with current leading methods, and the results show its robustness and effectiveness.

Forecasting and Discussing of the Fouling Characteristic of the Plain Tube

A fouling experimental system was built to measure the following parameters: wall temperatures, input and output temperature, etc. The model was set up based on the partial least-squares regression (PLS) to predict the fouling characteristics of the plain tube, in which there were five input vectors, which were the wall temperature, the inlet and outlet temperature and one output vectors, which was the fouling resistance. The prediction model was validated by the second operation cycle. By comparison of the predicted and experimental results, the maximal relative error of the model was in 8.5%, so, the partial least-squares regression algorithm of fouling model is reasonable and feasible. It provides an effective method for the design and operation personnel to anticipate the heat exchanger fouling characteristics under conditions of known water quality environmental parameters. The four-variable optimization model was obtained by analyzing the impact of each single independent variable on the prediction model, to increase the precision of the model. In addition, analysis of the impact of flow rate, etc. on the prediction model was also given.

A New Model of Predicting the Hydrogen Element in Coal-Fired

A new model was built to predict hydrogen element in coal-fired based on partial least squares regression algorithm, in which there were 4 input vectors, which were the moisture, ash content, volatile matter and low calorific value, and one output vectors, which was the hydrogen element. By comparison of the predicted and experimental results of test samples, the maximal relative error of the model was less than 10.0%, so, the partial least-squares regression algorithm model is reasonable and feasible. It provides an effective method for the operation personnel to anticipate the hydrogen element under conditions of known coal industrial analysis component.

Development and Optimization of an HPLC Analysis of Citalopram and Its Four Nonchiral Impurities Using Experimental Design Methodology

In this study, the RP-HPLC method was investigated for the separation of citalopram and its four impurities by use of statistical experimental design. Initially, the influence of different experimental conditions (buffer pH, flow rate, and column temperature) on the chromatographic behavior of citalopram and its four impurities was investigated by use of partial least squares regression (PLSR) and multilayer perceptron (MLP) artificial neural networks (ANNs) trained by back-propagation. The developed models and the corresponding response surface plots were used to select the optimal HPLC conditions, buffer pH 7.0, flow rate 1.0 mL/ min, and column temperature 25 degrees C, for an efficient separation of citalopram and its four impurities. The elaborated HPLC method was found to be linear, specific, sensitive, precise, accurate, and robust. Retention times of citalopram and its impurities, obtained with the developed HPLC method, and the computed molecular parameters of the examined compounds were used in a quantitative structure retention relationship (QSRR) study. The PLSR and ANN algorithms were applied for the development of the QSRR methods. The MLP-two layers-ANN-QSRR model with root mean square error of prediction 0.105 and r(2) (observed versus predicted) 0.978 was selected. Since many different reaction conditions are applied for the synthesis of citalopram, different impurities and degradation products can be formed. Therefore, the developed QSRR model can be extended to the prediction of the retention times with the other citalopram impurities, degradation products, and metabolites.

Simultaneous Spectraphotometric Kinetic Determination of Manganese, Silver and Iron by a Hybrid Chemometric Method

This paper proposes a hybrid chemometric method named DOSC-WPT-PLS, which is based on partial least squares (PLS) regression combined with direct orthogonal signal correction (DOSC) and wavelet packet transform (WPT) as pre-processing tools for the simultaneous spectrophotometric kinetic determination of Mn (II), Ag (I) and Fe (III). This method combined with kinetic approach is used for the first time and no past reference has been found for this determination. The improved PLS regression algorithm was developed by adding a preprocessor based on DOSC and WPT to enhance the prediction ability. The kinetic chemometric approach that combines kinetic-catalytic method with DOSC-WPTPLS does not require a detailed kinetic model of the chemical system to obtain the order of reaction and rate constants. The relative standard errors of prediction (RSEP) obtained for all components using DOSC-WPT-PLS, WPTPLS and PLS were compared for evaluating their predictive capability. Results obtained from the DOSC-WPT-PLS method were significantly better, and proved that it outperformed the WPTPLS and PLS methods.

Partitioned partial least squares regression with application to a batch fermentation process

AbstractThe performance of Partial Least Squares regression (PLS) in predicting the output with multivariate cross‐ and autocorrelated data is studied. With many correlated predictors of varying importance PLS does not always predict well and we propose a modified algorithm, Partitioned Partial Least Squares (PPLS). In PPLS the predictors are partitioned into smaller subgroups and the important subgroups with high prediction power are identified. Finally, regular PLS analysis using only those subgroups is performed. The proposed Partitioned PLS (PPLS) algorithm is used in the analysis of data from a real pharmaceutical batch fermentation process for which the process variables follow certain profiles during a specific fermentation period. We observed that PPLS leads to a more accurate prediction of the yield of the fermentation process and an easier interpretation, since fewer predictors are used in the final PLS prediction. In the application important issues such as alignment of the profiles from one batch to another and standardization of the predictors are also addressed. For instance, in PPLS noise magnification due to standardization does not seem to create problems as it might in regular PLS. Finally, PPLS is compared to several recently proposed functional PLS and PCR methods and a genetic algorithm for variable selection. More specifically for a couple of publicly available data sets with near infrared spectra it is shown that overall PPLS has lower cross‐validated error than PLS, PCR and the functional modifications hereof, and is similar in performance to a more complex genetic algorithm. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Estimation of heavy-metal contamination in soil using reflectance spectroscopy and partial least-squares regression

Lead (Pb) poisoning from anthropogenic sources continues to threaten the health of urban children. Mapping Pb distribution on a large scale is imperative to identify hotspots and reduce Pb poisoning. To assess the feasibility of using reflectance spectroscopy to map soil Pb and other heavy metal abundance, the relationship between surface soil metal concentrations and hyperspectral reflectance measurements was examined via partial least-squares regression (PLSR) modelling. Soil samples were taken from four study sites. Metal concentrations were determined by inductively coupled plasma-atomic-emission spectrometry (ICP-AES) analysis, and reflectance was measured with an ASD (Analytical Spectral Devices) field spectrometer covering the spectral region of 350–2500 nm. Pb displayed an exponential decrease as a function of distance from the roadway, demonstrating the depositional patterns from leaded gas combustion which remain on the landscape 20 years after the phase-out of leaded gasoline. Calibration samples were used to derive the PLSR algorithm, and validation samples assessed the model's predictive ability. The correlation coefficients between the lab-determined abundance and the abundance predicted from PLSR calibration for all metals except copper were at or above 0.970, with the correlation coefficient for Pb the highest of all metals (0.992). Manganese, zinc and Pb had significant coefficients of determination (0.808, 0.760 and 0.746, respectively) for the validation samples. These results suggest that Pb and other heavy metal concentrations can be retrieved from spectral reflectance at high accuracy. Reflectance spectroscopy thus has potential to map the spatial distribution of Pb abundance with the aim of improving children's health in an urban environment.

Automated estimation of stellar fundamental parameters from low resolution spectra: the PLS method

PLS (Partial Least Squares regression) is introduced into an automatic estimation of fundamental stellar spectral parameters. It extracts the most correlative spectral component to the parameters (Teff, log g and [Fe/H]), and sets up a linear regression function from spectra to the corresponding parameters. Considering the properties of stellar spectra and the PLS algorithm, we present a piecewise PLS regression method for estimation of stellar parameters, which is composed of one PLS model for Teff, and seven PLS models for log g and [Fe/H] estimation. Its performance is investigated by large experiments on flux calibrated spectra and continuum normalized spectra at different signal-to-noise ratios (SNRs) and resolutions. The results show that the piecewise PLS method is robust for spectra at the medium resolution of 0.23 nm. For low resolution 0.5 nm and 1 nm spectra, it achieves competitive results at higher SNR. Experiments using ELODIE spectra of 0.23 nm resolution illustrate that our piecewise PLS models trained with MILES spectra are efficient for O ∼ G stars: for flux calibrated spectra, the systematic offsets are 3.8%, 0.14 dex, and -0.09 dex for Teff, log g and [Fe/H], with error scatters of 5.2%, 0.44 dex and 0.38 dex, respectively; for continuum normalized spectra, the systematic offsets are 3.8%, 0.12dex, and -0.13dex for Teff, log g and [Fe/H], with error scatters of 5.2%, 0.49 dex and 0.41 dex, respectively. The PLS method is rapid, easy to use and does not rely as strongly on the tightness of a parameter grid of templates to reach high precision as Artificial Neural Networks or minimum distance methods do.