Spectral data evaluation

The selection of an optimal spectral data evaluation algorithm is essential for satisfactory system performance, but is usually not easily predictable. Apart from the chemometrical performance, the execution time of the algorithm is crucial for realtime systems. As the execution time depends mainly on the number of mathematical operations of the algorithm, expressed by the run-time complexity, a mathematically simpler method involving fewer operations is often preferable to a (potentially) more powerful method that takes longer to calculate. 

Spatially resolved material identification and classification is currently the prevalent application for SI systems. Of the many powerful spectral classifiers available, only two types, each with a number of different algorithms,14 could successfully be applied for real-time SI applications discriminant classifiers and dissimilarity-based classifiers. In addition, occasionally dedicated algorithms, such as fuzzy-classifiers, may be useful for special applications, for example, when there is no ab inito knowledge about the number and properties of the classification classes. 

1 Discriminant classifiers. The two most important discriminant classifiers for material analysis using spectroscopic imaging systems are the Fisher linear discriminant classifier (FLDC) and the quadratic discriminant classifier (QDC). Other classfiers, such as the classical linear disriminant classifier (LDC), have frequently exhibited an inferior performance. 

Prior to the actual classification, the FLDC performs a linear mapping to a lower dimensional subspace optimised for class separability, based on the between-class scatter and the within-class scatter of the training set. In classification, each sample is assigned to the class giving the highest log-likelihood using a linear classifier. 

The QDC calculates a mean and the covariance for each class, allowing the classifier to find more accurate discriminative functions. Each sample is assigned to the class with the highest log-likelihood calculated following Equation (7.2), with the class mean /x and the class covariance . 

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A.S. El-Hagrasy, F.D Amico and J.K. Drennen III, A process analytical technology approach to near-infrared process control of pharmaceutical powder blending. Part I D-optimal design for characterization of powder mixing and preliminary spectral data evaluation, J. Pharm. Sci, 95(2), 392 06 (2006). 

The chemometric approach has been applied on diverse field of mass spectral data evaluation peak resolution and quantification [64], calibration [65], instrument standardization [66], fast interpretation [67], and evaluation of rate constants [68]. 

In contrast to IR and NMR spectroscopy, the principle of mass spectrometry (MS) is based on decomposition and reactions of organic molecules on theii way from the ion source to the detector. Consequently, structure-MS correlation is basically a matter of relating reactions to the signals in a mass spectrum. The chemical structure information contained in mass spectra is difficult to extract because of the complicated relationships between MS data and chemical structures. The aim of spectra evaluation can be either the identification of a compound or the interpretation of spectral data in order to elucidate the chemical structure [78-80],... 

Other methods consist of algorithms based on multivariate classification techniques or neural networks they are constructed for automatic recognition of structural properties from spectral data, or for simulation of spectra from structural properties [83]. Multivariate data analysis for spectrum interpretation is based on the characterization of spectra by a set of spectral features. A spectrum can be considered as a point in a multidimensional space with the coordinates defined by spectral features. Exploratory data analysis and cluster analysis are used to investigate the multidimensional space and to evaluate rules to distinguish structure classes. 

Miscellaneous. NIST has a reference database of criticaUy evaluated x-ray photoelectron and Auger spectral data, which is designed to mn on PCs. It is searchable by spectral lines as weU as by element, line energy, and chemical data (82). The Nuclear Quadrapole Resonance Spectra Database at Osaka University of over 10,000 records is avaUable in an MS-DOS version (83). The NCLl system, SDBS, has esr and Raman spectra, along with nmr, ir, and ms data, as described. 

It should not be concluded that the above examples of the evaluation of qualitative and quantitative data comprise an exhaustive analysis of this particular set of LC-MS data. They have been included primarily for those not used to the analysis of mass spectral data, to show the principles involved, and to demonstrate how powerful the mass speedometer can be as a chromatographic detector. 

While the field of near-IR sensing is frequently regarded as having reached its (scientific) limits, with advances restricted to minor progress in instrumentation and data evaluation procedures, interesting developments are reported in particular in the field of near-IR spectral imaging. 

Another possibility is to immobilise enzymes either on the sensor element itself or in the vicinity of the sensing element. The operation principle is in most cases a semi-continuous spectral difference measurement in combination with a kinetic data evaluation. A sample containing the analyte of interest is recorded by the sensor immediately after contact with the sample and again after a certain time. Provided that no other changes in the composition of the sample occur over time, the spectral differences between the two measurements are characteristic for the analyte (and the metabolic products of the enzymatic reaction) and can quantitatively evaluated. Provided that suitable enzymes are available that can be immobilised, this may be a viable option to build a sensor, in particular when the enzymatic reaction can not (easily) be monitored otherwise, e.g. by production or consumption of oxygen or a change of pH. In any case, the specific properties and stumbling blocks related to enzymatic systems must be observed (see chapter 16). 

Evaluation of the Work Term from Charge Transfer Spectral Data. The intermolecular interaction leading to the precursor complex in Scheme IV is reminiscent of the electron donor-acceptor or EDA complexes formed between electron donors and acceptors (21). The latter is characterized by the presence of a new absorption band in the electronic spectrum. According to the Mulliken charge transfer (CT) theory for weak EDA complexes, the absorption maximum hv rp corresponds to the vertical (Franck-Condon) transition from the neutral ground state to the polar excited state (22). 

Even for potential energy the other approach [93] required one parameter additional to oiu-s, apart from Dq, the latter quantity, equilibrium binding energy, is stated to be based on thermochemical data, but the cited source [95] indicates a value of dissociation energy 29q <2.84eV to arise from spectral analysis. Such an upper limit must be understood to provide an asymptotic limit for V(i ) at large i in a formula of Morse type because an attempted evaluation of 29e from only infrared spectral data is unreliable. The stated reason for the choice... 

A tertiary base isolated from Thalictrum strictum was assigned a pavine structure based on the spectral data (27). Three methoxyl and one methylenedioxy functions were detected with the aid of mass spectroscopy. Structure 3 was proposed as the most probable representation for this new pavine alkaloid, which indeed is the first example of a pentasubstituted pavine base. However, when the reported aromatic proton chemical shifts (8 6.23, 6.36, and 6.54) were evaluated in the light of empirical rules about the H-NMR absorptions of pavine bases (Section V,B), and it seemed possible that the two upfield absorptions belong to H-4 and H-10 rather than to H-1 and H-10. Therefore, alternative structure 4 cannot presently be completely excluded from consideration. 

De Braekeleer, K., and Massart, D. L. (1997), Evaluation of the orthogonal projection approach (OPA) and the SIMPLISMA approach on the Windig standard spectral data sets, Chemomet. Intell. Lab. Syst., 39,127-141. 

The energy states of the gaseous S2 molecule are evaluated from the band spectral data of Christy and Naude.1 The spectrum of S2 has also been studied by Henri,3 Henri and Teves,1 Rosen,1 and Kondratjew.1 See also Jevons.1... 

Raman spectroscopy has its main strength in the combination of a fairly high chemical selectivity and a true remote sensing capability. In comparison, NIR has been used extensively in the manufacturing industry due to its ruggedness and simplicity with respect to interfacing of probes to process vessels. However, due to fairly poor spectral selectivity it has to be paired with multivariate data evaluation and is thus sometimes considered as a black box technique. Mid-IR, on the other hand, offers a high selectivity and is also well established... 

The fourth module is the control unit, consisting primarily of a state-of-the-art industry PC equipped with a suitable frame-grabber card for image frame acquisition, spectral and spatial real-time data evaluation and control of subsequent actuators or communication with process control systems. 

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