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

Remote sensing of foliar chemistry

Partial least-squares (PLS) methods for quantitative spectral analyses are compared with classical least-squares (CLS) and principal component regression (PCR) methods by using simulated data and infrared spectra from bulk seven-component, silicate-based glasses. Analyses of the simulated data sets show the effect of data pretreatment, base-line variations, calibration design, and constrained mixtures on PLS and PCR prediction errors and model complexity. Analyses of the simulated data sets also illustrate some qualitative differences between PSL and PCR. PLS and PCR predicted concentration errors from the simulated data sets and a set of the Fourier transform infrared spectra of silicate-based glasses (S-glass) show that prediction errors are not statistically different between these two methods for these individual data sets with limited numbers of samples. However, PLS and PCR are both superior to CLS methods in the case of the analysis of S-glass where only one analyte is known in the calibration samples and the components of unknown concentration overlap all the spectral features of the analyte components. CLS analysis precision significantly improves when the three known analyte concentrations (B/sub 2/O/sub 3/, P/sub 2/O/sub 5/, and OH) are used in the calibration. In this latter case, PLS and PCR concentration predictions are unchanged, andmore » although they each still yield a lower standard error of prediction than the CLS method, there is no longer strong statistical evidence that these differences between PLS or PCR and CLS are outside experimental error for the B/sub 2/O/sub 3/ component. The ability of CLS and PLS methods to provide chemically useful estimates of the pure-component spectra is also demonstrated.« less

Partial least-squares methods for spectral analyses. 2. Application to simulated and glass spectral data

The characteristics of a biological fluid sample having an analyte are determined from a model constructed from plural known biological fluid samples. The model is a function of the concentration of materials in the known fluid samples as a function of absorption of wideband infrared energy. The wideband infrared energy is coupled to the analyte containing sample so there is differential absorption of the infrared energy as a function of the wavelength of the wideband infrared energy incident on the analyte containing sample. The differential absorption causes intensity variations of the infrared energy incident on the analyte containing sample as a function of sample wavelength of the energy, and concentration of the unknown analyte is determined from the thus-derived intensity variations of the infrared energy as a function of wavelength from the model absorption versus wavelength function.

Method of and apparatus for determining the similarity of a biological analyte from a model constructed from known biological fluids

The remote-sensing approach, using satellite and airborne sensors, is rapidly entering the field of environmental sciences as a complementary tool for studying natural processes. This is mainly because the approach enables an overview of large areas simultaneously, using multiple spectral information that correlates with most of the common land cover compositions, on a temporal basis and in a cost-effective way. In soil science, this technique has shown a potential for determining soil groups, the soil genesis process, and soil degradation, and reflects some soil environment interactions as well. Apparently, the limited spectral information provided by the former sensor did not allow the quantitative remote sensing of soils, and thus it could not be used to benefit the future of such endeavors as “precision agriculture”. Recent technological developments using remote sensing for monitoring the environment have produced a new approach that is able to provide quantitative rather than qualitative information regarding soil status. This approach, namely, hyper spectroscopy imaging (HSR), is characterized by many spectral channels, which expand the spectral information of the sensed material to be analyzed under quantitative approaches. This technique uses a image spectrometer that has been mounted onboard an aircraft and is able to receive discrete information regarding a sensed target from orbit. It has been successfully used in many disciplines, including geology and marine and vegetative studies. Because this technique holds new capabilities, it opens new frontiers in soil applications as well. The capability of soil spectral information to predict several important soil properties has already been demonstrated under laboratory conditions. Under noncontrolled (field) conditions, difficulties associated with the far-distant position of the sensors relative to the target and with the limited ability to sense only the upper soil crust currently prevent the HSR approach from being simply applied to soils. Only a well-designed HSR approach will be able to provide quantitative soil property maps from such far distances. This paper provides a detailed description of the quantitative (spectral-based)approach for assessing soil properties, using the reflectance radiation across the sun 's illumination range along with an extensive discussion of the obstacles (and their possible solutions)preventing this approach from being a pure laboratory equivalent. Also provided is a detailed review of recent work that has concentrated on quantitative soil remote sensing along with a discussion of the future availability of this technology in terms of cost, physical specifications, and possible applications.

Quantitative remote sensing of soil properties

In near-infrared reflectance analysis (NIRA), a computer is trained to recognize and quantitate the relationship between the near-infrared spectrum of a sample and the concentrations of one or more of the sample constituents. During this training process the computer implicitly generates the spectrum of the constituents in question, although this spectrum is ordinarily not available for operator inspection. In the present study, a method for displaying this implicit information is developed and evaluated. The resulting "reconstructed spectrum" can be of a specific chemical constituent in a sample or can be a composite spectrum of those components that collectively contribute to specific sample properties such as material strength or processing temperature, or to sensory characteristics such as the "hotness" of peppers. A comparison is made of this new spectral reconstruction technique to established methods such as spectral stripping and factor analysis.

A New Method for Obtaining Individual Component Spectra from Those of Complex Mixtures

A method is described and tested for improving the training sample set in near-infrared diffuse-reflectance analysis (NIRA). Utilizing linear algebra techniques similar to spectral subtraction, this method selects the most spectrally unique samples from those in a larger pool. Upon being analyzed, these spectrally unique samples are found to have a significantly larger variation in their chemical compositions than the pool of samples from which they were selected. When the spectrally unique samples are incorporated into a NIRA training set, the resulting calibration is improved in two ways: first, the larger variations in sample composition help to make a NIRA calibration more robust and less subject to unexpected variations in the sample matrix; second, use of the spectrally unique samples reduces the time and effort involved in developing a NIRA method of analysis. 13 references, 2 figures, 7 tables.

Unique-sample selection via near-infrared spectral subtraction.

Near-infrared reflectance analysis is an analytical technique that uses the near-infrared diffuse reflectance of a sample at several discrete wavelengths to predict the concentration of one or more of the chemical species in that sample. However, because near-infrared bands from solid samples are both abundant and broad, the reflectance at a given wavelength usually contains contributions from several sample components, requiring extensive calculations on overlapped bands. In the present study, these calculations have been performed using an approach similar to that employed in multi-component spectrophotometry, but with Gauss-Jordan linear algebra serving as the computational vehicle. Using this approach, correlations for percent protein in wheat flour and percent benzene in hydrocarbons have been obtained and are evaluated. The advantages of a linear-algebra approach over the common one employing stepwise regression are explored.

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Near-Infrared Reflectance Analysis by Gauss-Jordan Linear Algebra

The physical properties of a sample are typically measured one at a time using appropriate testing methods. The use of a calorimeter to determine heats of formation and a viscometer to determine molecular weights are examples of physical tests that have been developed to measure specific physical properties. In the present study, near-infrared spectrometric analysis and chemometric learning algorithms have been combined to deduce automically and simultaneously the physical properties of a sample. Specifically, the new combination enables the heat of formation, molecular weight, and the number of methyl groups per molecule to be determined in hydrocarbon mixtures directly from their near-infrared spectra. 15 references, 3 figures, 2 tables.

Near-Infrared Determination of Several Physical Properties of Hydrocarbons

Near-infrared reflectance spectroscopy uses a learning algorithm to derive a set of weighting coefficients from the reflectance spectra of a reference sample set. These coefficients, when applied to the reflectance values of an unknown sample at specific wavelengths, can be used to calculate constituent concentrations. Having enough samples in the training set and enough wavelengths in the calculation procedures is essential, but there are severe drawbacks to picking too large a number. This paper describes the principles and implementation of a working procedure for objectively calculating the minimum number of training samples required.

D. E. Honigs

Papers

A New Method for Obtaining Individual Component Spectra from Those of Complex Mixtures

Unique-sample selection via near-infrared spectral subtraction.

Near-Infrared Reflectance Analysis by Gauss-Jordan Linear Algebra

Near-Infrared Determination of Several Physical Properties of Hydrocarbons

Number of Samples and Wavelengths Required for the Training Set in Near-Infrared Reflectance Spectroscopy