Partial leastgquares (PLS) methods for spectral analyses are related to other multlvarlate callbratlon methods such as classical least-squares (CLS), Inverse least-squares (ILS), and prlnclpal component regression (PCR) methods which have been used often In quantitative spectral analyses. The PLS method which analyzes one chemlcal component at a tbne Is presented, and the basis for each step In the algorithm Is explained. PLS callbratlon Is shown to be composed of a series of simpllfled CLS and ILS steps. This detalled understandlng of the PLS algorithm has helped to ldentlfy how chemically Interpretable qualltatlve spectral lnformatlon can be obtained from the lntennedlate steps of the PLS algorithm. These methods for extractlng qualitative Information are demonstrated by use of simulated spectral data. The qualltatlve Information directly available from the PLS analysis Is superlor to that obtained from PCR but is not as complete as that which can be generated during CLS analyses. Methods are presented for selecting optbnal numbers of loading vectors for both the PLS and PCR models In order to optimize the model while simultaneously reduclng the potential for overfittlng the caHbratlon data. Outlier detection and methods to evaluate the statlstlcal slgnlflcance of resuits obtalned from the dMerent cahatlon methods applied to the same spectral data are also discussed.

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Partial least-squares methods for spectral analyses. 1. Relation to other quantitative calibration methods and the extraction of qualitative information

A generic preprocessing method for multivariate data, called orthogonal projections to latent structures (O-PLS), is described. O-PLS removes variation from X (descriptor variables) that is not correlated to Y (property variables, e.g. yield, cost or toxicity). In mathematical terms this is equivalent to removing systematic variation in X that is orthogonal to Y. In an earlier paper, Wold et al. (Chemometrics Intell. Lab. Syst. 1998; 44: 175-185) described orthogonal signal correction (OSC). In this paper a method with the same objective but with different means is described. The proposed O-PLS method analyzes the variation explained in each PLS component. The non-correlated systematic variation in X is removed, making interpretation of the resulting PLS model easier and with the additional benefit that the non-correlated variation itself can be analyzed further. As an example, near-infrared (NIR) reflectance spectra of wood chips were analyzed. Applying O-PLS resulted in reduced model complexity with preserved prediction ability, effective removal of non-correlated variation in X and, not least, improved interpretational ability of both correlated and non-correlated variation in the NIR spectra.

Orthogonal projections to latent structures (O-PLS)

Pre-processing of near-infrared (NIR) spectral data has become an integral part of chemometrics modeling. The objective of the pre-processing is to remove physical phenomena in the spectra in order to improve the subsequent multivariate regression, classification model or exploratory analysis. The most widely used pre-processing techniques can be divided into two categories: scatter-correction methods and spectral derivatives. This review describes and compares the theoretical and algorithmic foundations of current pre-processing methods plus the qualitative and quantitative consequences of their application. The aim is to provide NIR users with better end-models through fundamental knowledge on spectral pre-processing.

Review of the most common pre-processing techniques for near-infrared spectra

The pls package implements principal component regression (PCR) and partial least squares regression (PLSR) in R (R Development Core Team 2006b), and is freely available from the Comprehensive R Archive Network (CRAN), licensed under the GNU General Public License (GPL). The user interface is modelled after the traditional formula interface, as exemplified by lm. This was done so that people used to R would not have to learn yet another interface, and also because we believe the formula interface is a good way of working interactively with models. It thus has methods for generic functions like predict, update and coef. It also has more specialised functions like scores, loadings and RMSEP, and a flexible crossvalidation system. Visual inspection and assessment is important in chemometrics, and the pls package has a number of plot functions for plotting scores, loadings, predictions, coecients and RMSEP estimates. The package implements PCR and several algorithms for PLSR. The design is modular, so that it should be easy to use the underlying algorithms in other functions. It is our hope that the package will serve well both for interactive data analysis and as a building block for other functions or packages using PLSR or PCR. We will here describe the package and how it is used for data analysis, as well as how it can be used as a part of other packages. Also included is a section about formulas and data frames, for people not used to the R modelling idioms.

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The pls Package: Principal Component and Partial Least Squares Regression in R

This chapter provides a review on the state of soil visible–near infrared (vis–NIR) spectroscopy Our intention is for the review to serve as a source of up-to-date information on the past and current role of vis–NIR spectroscopy in soil science It should also provide critical discussion on issues surrounding the use of vis–NIR for soil analysis and on future directions To this end, we describe the fundamentals of visible and infrared diffuse reflectance spectroscopy and spectroscopic multivariate calibrations A review of the past and current role of vis–NIR spectroscopy in soil analysis is provided, focusing on important soil attributes such as soil organic matter (SOM), minerals, texture, nutrients, water, pH, and heavy metals We then discuss the performance and generalization capacity of vis–NIR calibrations, with particular attention on sample pretratments, covariations in data sets, and mathematical data preprocessing Field analyses and strategies for the practical use of vis–NIR are considered We conclude that the technique is useful to measure soil water and mineral composition and to derive robust calibrations for SOM and clay content Many studies show that we also can predict properties such as pH and nutrients, although their robustness may be questioned For future work we recommend that research should focus on: (i) moving forward with more theoretical calibrations, (ii) better understanding of the complexity of soil and the physical basis for soil reflection, and (iii) applications and the use of spectra for soil mapping and monitoring, and for making inferences about soils quality, fertility and function To do this, research in soil spectroscopy needs to be more collaborative and strategic The development of the Global Soil Spectral Library might be a step in the right direction

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Visible and Near Infrared Spectroscopy in Soil Science

This paper is concerned with the quantitative analysis of multicomponent mixtures by diffuse reflectance spectroscopy. Near-infrared reflectance (NIRR) measurements are related to chemical composition but in a nonlinear way, and light scatter distorts the data. Various response linearizations of reflectance (R) are compared (R with Saunderson correction for internal reflectance, log 1/R, and Kubelka-Munk transformations and its inverse). A multi-wavelength concept for optical correction (Multiplicative Scatter Correction, MSC) is proposed for separating the chemical light absorption from the physical light scatter. Partial Least Squares (PLS) regression is used as the multivariate linear calibration method for predicting fat in meat from linearized and scatter-corrected NIRR data over a broad concentration range. All the response linearization methods improved fat prediction when used with the MSC; corrected log 1/R and inverse Kubelka-Munk transformations yielded the best results. The MSC provided simpler calibration models with good correspondence to the expected physical model of meat. The scatter coefficients obtained from the MSC correlated with fat content, indicating that fat affects the NIRR of meat with an additive absorption component and a multiplicative scatter component.

P. Geladi

Papers

Linearization and Scatter-Correction for Near-Infrared Reflectance Spectra of Meat