scholarly journals A Numerical Procedure for Multivariate Calibration Using Heteroscedastic Principal Components Regression

Processes ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1686
Author(s):  
Alessandra da Rocha Duailibe Monteiro ◽  
Thiago de Sá Feital ◽  
José Carlos Pinto
Keyword(s):  
Covariance Matrix ◽  
Measurement Errors ◽  
Near Infrared ◽  
Multivariate Calibration ◽  
Numerical Procedure ◽  
Principal Component Regression ◽  
Principal Component ◽  
Analytical Framework ◽  
Multivariate Techniques ◽  
Different Temperatures

Many methods have been developed to allow for consideration of measurement errors during multivariate data analyses. The incorporation of the error structure into the analytical framework, usually described in terms of the covariance matrix of measurement errors, can provide better model estimation and prediction. However, little effort has been made to evaluate the effects of heteroscedastic measurement uncertainties on multivariate analyses when the covariance matrix of measurement errors changes with the measurement conditions. For this reason, the present work describes a new numerical procedure for analyses of heteroscedastic systems (heteroscedastic principal component regression or H-PCR) that takes into consideration the variations of the covariance matrix of measurement fluctuations. In order to illustrate the proposed approach, near infrared (NIR) spectra of xylene and toluene mixtures were measured at different temperatures and stirring velocities and the obtained data were used to build calibration models with different multivariate techniques, including H-PCR. Modeling of available xylene–toluene NIR data revealed that H-PCR can be used successfully for calibration purposes and that the principal directions obtained with the proposed approach can be quite different from the ones calculated through standard PCR, when heteroscedasticity is disregarded explicitly.

Nondestructive NIR and NIT Determination of Protein, Fat, and Water in Plastic-Wrapped, Homogenized Meat

1992 ◽  
Vol 46 (11) ◽  
pp. 1685-1694 ◽  
Author(s):  
Tomas Isaksson ◽  
Charles E. Miller ◽  
Tormod Næs
Keyword(s):  
Diffuse Reflectance ◽  
Near Infrared ◽  
Multivariate Calibration ◽  
Principal Component Regression ◽  
Principal Component ◽  
Prediction Errors ◽  
Optimal Test ◽  
Meat Samples ◽  
Water Contents

In this work, the abilities of near-infrared diffuse reflectance (NIR) and transmittance (NIT) spectroscopy to noninvasively determine the protein, fat, and water contents of plastic-wrapped homogenized meat are evaluated. One hundred homogenized beef samples, ranging from 1 to 23% fat, wrapped in polyamide/polyethylene laminates, were used. Results of multivariate calibration and prediction for protein, fat, and water contents are presented. The optimal test set prediction errors (root mean square error of prediction, RMSEP), obtained with the use of the principal component regression method with NIR data, were 0.45, 0.29 and 0.50 weight % for protein, fat, and water, respectively, for plastic-wrapped meat (compared to 0.40, 0.28 and 0.45 wt % for unwrapped meat). The optimal prediction errors for the NIT method were 0.31, 0.52 and 0.42 wt % for protein, fat, and water, respectively, for plastic-wrapped meat samples (compared to 0.27, 0.38, and 0.37 wt % for unwrapped meat). We can conclude that the addition of the laminate only slightly reduced the abilities of the NIR and NIT method to predict protein, fat, and water contents in homogenized meat.

Comparison of Multivariate Calibration and Discriminant Analysis in Evaluating NIR Spectroscopy for Determination of Meat Tenderness

1997 ◽  
Vol 51 (3) ◽  
pp. 350-357 ◽  
Author(s):  
Tormod Næs ◽  
Kjell Ivar Hildrum
Keyword(s):  
Discriminant Analysis ◽  
Reference Values ◽  
Near Infrared ◽  
Multivariate Calibration ◽  
Principal Component Regression ◽  
Nir Spectroscopy ◽  
Principal Component ◽  
Meat Tenderness ◽  
Intermediate Group ◽  
Calibration Methods

Often the primary goal of analytical measurement tasks is not to find good estimates of continuous reference values but rather to determine whether a sample belongs to one of a number of categories or subgroups. In this paper the potential of different statistical techniques in the classification of raw beef samples in tenderness subgroups was studied. The reference values were based on sensory analysis of beef tenderness of 90 samples from bovine M. longissimus dorsi muscles. The sample set was divided into three categories—very tough, intermediate, and very tender—according to degree of tenderness. A training set of samples was used to find the relationship between category and near-infrared (NIR) spectroscopic measurements. The study indicates that classical discriminant analysis has advantages in comparison to multivariate calibration methods [i.e., principal component regression (PCR)], in this application. One reason for this observation seems to be that PCR underestimates high measurement values and overestimates low values. In this way most samples are assigned to the intermediate group of samples, causing a small number of erroneous classifications for the intermediate subgroup, but a large number of errors for the two extreme groups. With the use of PCR the number of correct classifications in the extreme subgroups was as low as 23%, while the use of discriminate analysis increased this number to almost 60%. The number of classifications in correct or neighbor subgroup for the two extreme subgroups was equal to 97%. A “bias-correction” was also attempted for PCR, and this gave results comparable to the best results obtained by discriminant analysis methods. Test sets used NIR analysis of fresh, raw beef samples with different processing. While this spectroscopic approach had previously been shown to be useful with frozen products, it appears unsuitable at this time for fresh beef. However, its marginal analytical utility proved useful in evaluating the two classification approaches employed in this study.

A New Method for Multivariate Calibration

2005 ◽  
Vol 13 (5) ◽  
pp. 241-254 ◽  
Author(s):  
Ralf Marbach
Keyword(s):  
Near Infrared ◽  
Multivariate Calibration ◽  
Low Cost ◽  
Classical Model ◽  
Principal Component Regression ◽  
Principal Component ◽  
New Method ◽  
Data Set ◽  
Pharmaceutical Tablets ◽  
K Matrix

A new method for multivariate calibration is described that combines the best features of “classical” (also called “physical” or “K-matrix”) calibration and “inverse” (or “statistical” or “P-matrix”) calibration. By estimating the spectral signal in the physical way and the spectral noise in the statistical way, so to speak, the prediction accuracy of the inverse model can be combined with the low cost and ease of interpretability of the classical model, including “built-in” proof of specificity of response. The cost of calibration is significantly reduced compared to today's standard practice of statistical calibration using partial least squares or principal component regression, because the need for lab-reference values is virtually eliminated. The method is demonstrated on a data set of near-infrared spectra from pharmaceutical tablets, which is available on the web (so-called Chambersburg Shoot-out 2002 data set). Another benefit is that the correct definitions of the “limits of multivariate detection” become obvious. The sensitivity of multivariate measurements is shown to be limited by the so-called “spectral noise,” and the specificity is shown to be limited by potentially existing “unspecific correlations.” Both limits are testable from first principles, i.e. from measurable pieces of data and without the need to perform any calibration.

scholarly journals Prediction of Total Phenolic Content in Extracts of Prunella Species from HPLC Profiles by Multivariate Calibration

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Saliha Sahin ◽  
Esra Isik ◽  
Cevdet Demir
Keyword(s):  
High Performance ◽  
Multivariate Calibration ◽  
Principal Component Regression ◽  
Principal Component ◽  
Total Phenol ◽  
Total Phenolic ◽  
Total Phenol Content ◽  
Phenol Content ◽  
Calibration Methods ◽  
Hplc Profiles

The multivariate calibration methods—principal component regression (PCR) and partial least squares (PLSs)—were employed for the prediction of total phenol contents of four Prunella species. High performance liquid chromatography (HPLC) and spectrophotometric approaches were used to determine the total phenol content of the Prunella samples. Several preprocessing techniques such as smoothing, normalization, and column centering were employed to extract the chemically relevant information from the data after alignment with correlation optimized warping (COW). The importance of the preprocessing was investigated by calculating the root mean square error (RMSE) for the calibration set of the total phenol content of Prunella samples. The models developed based on the preprocessed data were able to predict the total phenol content with a precision comparable to that of the reference of the Folin-Ciocalteu method. PLS model seems preferable, because of its predictive and describing abilities and good interpretability of the contribution of compounds to the total phenol content. Multivariate calibration methods were constructed to model the total phenol content of the Prunella samples from the HPLC profiles and indicate peaks responsible for the total phenol content successfully.

scholarly journals Application of FTIR Spectroscopy and HPLC Combined with Multivariate Calibration for Analysis of Xanthones in Mangosteen Extracts

2020 ◽  
Vol 88 (3) ◽  
pp. 35
Author(s):  
Endjang Prebawa Tejamukti ◽  
Widiastuti Setyaningsih ◽  
Irnawati ◽  
Budiman Yasir ◽  
Gemini Alam ◽  
...  
Keyword(s):  
Quantitative Analysis ◽  
Multivariate Calibration ◽  
Principal Component Regression ◽  
Principal Component ◽  
Ethanolic Extract ◽  
Ftir Spectra ◽  
Partial Least Square ◽  
Least Square ◽  
Coefficient Of Determination ◽  
Garcinia Mangostana

Mangosteen, or Garcinia mangostana L., has merged as an emerging fruit to be investigated due to its active compounds, especially xanthone derivatives such as α -mangostin (AM), γ-mangostin (GM), and gartanin (GT). These compounds had been reported to exert some pharmacological activities, such as antioxidant and anti-inflammatory, therefore, the development of an analytical method capable of quantifying these compounds should be investigated. The aim of this study was to determine the correlation between FTIR spectra and HPLC chromatogram, combined with chemometrics for quantitative analysis of ethanolic extract of mangosteen. The ethanolic extract of mangosteen pericarp was prepared using the maceration technique, and the obtained extract was subjected to measurement using instruments of FTIR spectrophotometer at wavenumbers of 4000–650 cm−1 and HPLC, using a PDA detector at 281 nm. The data acquired were subjected to chemometrics analysis of partial least square (PLS) and principal component regression (PCR). The result showed that the wavenumber regions of 3700–2700 cm−1 offered a reliable method for quantitative analysis of GM with coefficient of determination (R2) 0.9573 in calibration and 0.8134 in validation models, along with RMSEC value of 0.0487% and RMSEP value 0.120%. FTIR spectra using the second derivatives at wavenumber 3700–663 cm−1 with coefficient of determination (R2) >0.99 in calibration and validation models, along with the lowest RMSEC value and RMSEP value, were used for quantitative analysis of GT and AM, respectively. It can be concluded that FTIR spectra combined with multivariate are accurate and precise for the analysis of xanthones.

The Effect of Multiplicative Scatter Correction (MSC) and Linearity Improvement in NIR Spectroscopy

1988 ◽  
Vol 42 (7) ◽  
pp. 1273-1284 ◽  
Author(s):  
Tomas Isaksson ◽  
Tormod Næs
Keyword(s):  
Near Infrared ◽  
Scatter Correction ◽  
Principal Component Regression ◽  
Nir Spectroscopy ◽  
Principal Component ◽  
Data Sets ◽  
Prediction Errors ◽  
Regression Methods ◽  
Multiplicative Scatter Correction ◽  
Linearity Improvement

Near-infrared (NIR) reflectance spectra of five different food products were measured. The spectra were transformed by multiplicative scatter correction (MSC). Principal component regression (PCR) was performed, on both scatter-corrected and uncorrected spectra. Calibration and prediction were performed for four food constituents: protein, fat, water, and carbohydrates. All regressions gave lower prediction errors (7–68% improvement) by the use of MSC spectra than by the use of uncorrected absorbance spectra. One of these data sets was studied in more detail to clarify the effects of the MSC, by using PCR score, residual, and leverage plots. The improvement by using nonlinear regression methods is indicated.

The Authentication of Basmati Rice Using near Infrared Spectroscopy: Some Further Analysis

1995 ◽  
Vol 3 (3) ◽  
pp. 111-117 ◽  
Author(s):  
W.J. Krzanowski
Keyword(s):  
Near Infrared ◽  
Principal Component ◽  
Basmati Rice ◽  
Multivariate Techniques ◽  
Infrared Transmission ◽  
Linear Discriminant ◽  
Canonical Variates ◽  
Rice Samples ◽  
Single Category ◽  
Pooled Samples

The feasibility of using near infrared transmission spectroscopy to discriminate between Basmati and other long-grain rice samples has been demonstrated previously by Osborne et al. In their analysis they pooled samples from different countries of origin into the single category “other” and used the multivariate techniques of principal component analysis and linear discriminant functions to arrive at their conclusions. We reanalyse here their data but without such a major pooling of samples, retaining four groups in the discrimination. Using the multivariate techniques of partial least squares, orthogonal canonical variates and a recently proposed search for “extremeness”, we demonstrate complete support for the previous conclusions.

Spectrophotometric determination of mixtures of iron(III) and manganese(II) by complexation with 3-indolylacetohydroxamic acid and principal component regression multivariate calibration

The Analyst ◽  
1994 ◽  
Vol 119 (7) ◽  
pp. 1537-1540 ◽  
Author(s):  
Mercedes Jiménez Arrabal ◽  
Pablo Valiente González ◽  
Concepción Caro Gámez ◽  
Antonio Sánchez Misiego ◽  
Arsenio Muñoz de la Peña
Keyword(s):  
Spectrophotometric Determination ◽  
Multivariate Calibration ◽  
Principal Component Regression ◽  
Principal Component
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