Principal Component Regression prediction

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

Y.L. Xie and J.H. Kalivas, Evaluation of principal component selection methods to form a global prediction model by principal component regression. Anal. Chim. Acta (1997) 348, 19-27. 

M. Stone and R.J. Brooks, Continuum regression cross-validated sequentially constructed prediction embracing ordinary least sqaures, partial least squares, and principal component regression. J. Roy. Stat. Soc. B52 (1990) 237-269. 

A difficulty with Hansch analysis is to decide which parameters and functions of parameters to include in the regression equation. This problem of selection of predictor variables has been discussed in Section 10.3.3. Another problem is due to the high correlations between groups of physicochemical parameters. This is the multicollinearity problem which leads to large variances in the coefficients of the regression equations and, hence, to unreliable predictions (see Section 10.5). It can be remedied by means of multivariate techniques such as principal components regression and partial least squares regression, applications of which are discussed below. 

Principal component regression Linear projection Fixed shape, linear a, maximum variance of projected inputs (3, minimum output prediction error... 

Principal component regression (PCR) is an extension of PCA with the purpose of creating a predictive model of the Y-data using the X or measurement data. For example, if X is composed of temperatures and pressures, Y may be the set of compositions that results from thermodynamic considerations. Piovoso and Kosanovich (1994) used PCR and a priori process knowledge to correlate routine pressure and temperature measurements with laboratory composition measurements to develop a predictive model of the volatile bottoms composition on a vacuum tower. 

Faber K, Kowalski BR (1997b) Propagation of measurement errors for the validation of predictions obtained by principal component regression and partial least squares. J Chemom 11 181... 

This chapter ends with a short description of the important methods, Principal Component Regression (PCR) and Partial Least-Squares (PLS). Attention is drawn to the similarity of the two methods. Both methods aim at predicting properties of samples based on spectroscopic information. The required information is extracted from a calibration set of samples with known spectrum and property. 

Fourier transform infrared (FTIR) spectroscopy of coal low-temperature ashes was applied to the determination of coal mineralogy and the prediction of ash properties during coal combustion. Analytical methods commonly applied to the mineralogy of coal are critically surveyed. Conventional least-squares analysis of spectra was used to determine coal mineralogy on the basis of forty-two reference mineral spectra. The method described showed several limitations. However, partial least-squares and principal component regression calibrations with the FTIR data permitted prediction of all eight ASTM ash fusion temperatures to within 50 to 78 F and four major elemental oxide concentrations to within 0.74 to 1.79 wt % of the ASTM ash (standard errors of prediction). Factor analysis based methods offer considerable potential in mineral-ogical and ash property applications. 

Experience in this laboratory has shown that even with careful attention to detail, determination of coal mineralogy by classical least-squares analysis of FTIR data may have several limitations. Factor analysis and related techniques have the potential to remove or lessen some of these limitations. Calibration models based on partial least-squares or principal component regression may allow prediction of useful properties or empirical behavior directly from FTIR spectra of low-temperature ashes. Wider application of these techniques to coal mineralogical studies is recommended. 

R. Marbach and H. M. Heise, Calibration modeling by partial least-squares and principal component regression and its optimisation using an improved leverage correction for prediction testing, Chemom. Intell. Lab. Syst., 9(1), 1990, 45-63. 

Tablet hardness is a property that, when measured, destroys the sample. The destructive nature of the test, coupled with the variability of the test itself does not contribute to an incentive to test a large number of samples. Morisseau and Rhodes99 correlated the diffuse reflectance NIR spectra of tablets pressed at different pressures and subsequently tested the tablet hardness with an Erweka Hardness Tester. The tablet hardness, as predicted by the NIR method, was at least as precise as the laboratory test method. Kirsch and Drennen100 evaluated NIR as a method to determine potency and tablet hardness of Cimetidine tablets over a range of 1-20% potency and 107-kPa compaction pressure. Hardness at different potency levels was used to build calibration models using PCA/ principal component regression and a new spectral best-fit algorithm. Both methods provided acceptable predictions of tablet hardness.

Municipal solid waste Near infrared Oxidation induction time Partial least square Post-consumer recyclate Post-consumer waste Principal component analysis Principal component regression Root-mean-square error of prediction... 

Principal component regression is accomplished in two steps, a calibration step and an unknown prediction step. In the calibration step, concentrations of the constituent(s) to be quantitated in each calibration standard sample are assembled into a matrix, y, and mean-centered. Spectra of standards are measured, assembled into a matrix X, mean-centered, and then an SVD is performed. Calibration spectra are projected onto the d principal components (basis vectors) retained and are used to determine a vector of regression coefficients that can be then used to estimate the concentration of the calibrated constituent(s). 

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