Normal chemometrics

Crowley et al. performed some interesting work with Pichia pastoris in a fed-batch process.19 The complex mixture was measured using a multibounce attenuated total reflectance (HATR) cell. The authors developed models for glycerol, methanol, and the product, a heterologous protein. The results are reported somewhat differently from normal chemometric results. The authors used root-mean square error (RMSE) for the product as a performance index and measured a percent difference for the methanol and glycerol. 

An attempt was made to find robust calibration equations for sugar content and acidity by MLR, PCR, and PLS, where the optical parameters were employed as explanatory variables. Normally, chemometrics by NIR spectra employs the absorbance as the explanatory variable, where only wavelength-dependent characteristics of the materials can be considered. In this case, it is very difficult to precisely evaluate the small amount of a constituent such as acid content in a fruit. On the other hand, chemometrics by TOF-NIRS would be related to both wavelength- and time-dependent characteristics as the explanatory variables, where the light absorption and light scattering phenomena in a sample are included. It may therefore be possible to detect the acid content in a fruit on the basis of this new optical concept. The statistical results are summarized in Tables 4.2.1 and 4.2.2. Figure 4.2.9 shows the PLS analysis in a optimum model for acidity in apple. In the case of normal analysis by second-derivative NIR spectra, standard error of calibration (SEC) and correlation coefficient between measured and predicted acidity r were limited to 0.048% and... 

Response Above, I described the situation as we see it, regarding the traps that both experienced and novice users of these very sophisticated algorithms can fall into. Keep in mind the pedagogy involved as well as the chemometrics by suitable choice of values for the constituent , the peaks at the nonlinear wavelengths could have been made to appear equally spaced, and the linear wavelengths appear stretched out at the higher values. The clarity of the nonlinearity is due to the presentation, not to any fundamental property of the data, and this clarity does not normally exist in real data. How is someone to detect this, especially if not looking for it Attempts to address this issue have been made in the past (see [5]) with results that in our opinion are mixed, at best. And that simulated data was also noise-free. 

To highlight and explain the quantitative chemical differences between the pitches found in the two archaeological sites, a chemometric evaluation of the GC/MS data (normalized peak areas) by means of principal component analysis (PCA) was performed. The PCA scatter plot of the first two principal components (Figure 8.6) highlights that the samples from Pisa and Fayum are almost completely separated into two clusters and that samples from Fayum form a relatively compact cluster, while the Pisa samples are... 

A total of 185 emission lines for both major and trace elements were attributed from each LIBS broadband spectrum. Then background-corrected, summed, and normalized intensities were calculated for 18 selected emission lines and 153 emission line ratios were generated. Finally, the summed intensities and ratios were used as input variables to multivariate statistical chemometric models. A total of 3100 spectra were used to generate Partial Least Squares Discriminant Analysis (PLS-DA) models and test sets. 

In chemometrics, the letter p is widely used for loadings in PCA (and partial least-squares [PLS]). It is common in chemometrics to normalize the lengths of loading vectors to 1 that means p p = 1 m is the number of variables. The corresponding... 

Barnes, R. J., Dhanoa, M. S., Lister, S. J. Appl. Spectrosc. 43,1989, 772-777. Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra. Barnes, R. J., Dhanoa, M. S., Lister, S. J. J. Near Infrared Spectrosc. 1, 1993, 185-186. Correction of the description of standard normal variate (SNV) and De-Trend transformations in practical spectroscopy with applications in food and beverage analysis. Brereton, R. G. Chemometrics—Data Analysis for the Laboratory and Chemical Plant. Wiley, Chichester, United Kingdom, 2006. 

In the worse case, where either sample temperature, pressure or reactor integrity issues make it impossible to do otherwise, it may be necessary to consider a direct in situ fiber-optic transmission or diffuse reflectance probe. However, this should be considered the position of last resort. Probe retraction devices are expensive, and an in situ probe is both vulnerable to fouling and allows for no effective sample temperature control. Having said that, the process chemical applications that normally require this configuration often have rather simple chemometric modeling development requirements, and the configuration has been used with success. 

Kohler, A., Zimonja, M., Segtnan, V., and Martens, H. (2009). Standard normal variate, multiplicative signal correction and extended multiplicative signal correction preprocessing in biospectroscopy. In "Comprehensive Chemometrics", (S. D. Brown, R. Tauler, and B. Walczak, Eds), Vol. 2, pp. 139-162. Elsevier, Amsterdam. 

While there will be much more extensive discussions in later chapters on the topic of analyzer calibration, I will try to give you a quick snapshot here on how NIR analysis is done. The first step is to have a valid sample set, normally 30-50 samples covering the range of interest. The spectra are collected and a correlation is built between the wavelengths and their corresponding absorbencies and the reference analysis of these samples. The chemometric tools used in developing calibrations are discussed in Chapter 8. This is just the first step in developing a calibration but many people make the mistake of... 

A third and often neglected reason for the need for care fill application of chemometric methods is the problem of the type of distribution of environmental data. Most basic and advanced statistical methods are based on the assumption of normally distributed data. But in the case of environmental data, this assumption is often not valid. Figs. 1-7 and 1-8 demonstrate two different types of experimentally found empirical data distribution. Particularly for trace amounts in the environment, a log-normal distribution, as demonstrated for the frequency distribution of N02 in ambient air (Fig. 1-7), is typical. 

The remaining chapters of the book introduce some of the advanced topics of chemometrics. The coverage is fairly comprehensive, in that these chapters cover some of the most important advanced topics. Chapter 6 presents the concept of robust multivariate methods. Robust methods are insensitive to the presence of outliers. Most of the methods described in Chapter 6 can tolerate data sets contaminated with up to 50% outliers without detrimental effects. Descriptions of algorithms and examples are provided for robust estimators of the multivariate normal distribution, robust PC A, and robust multivariate calibration, including robust PLS. As such, Chapter 6 provides an excellent follow-up to Chapters 3, 4, and 5. 

However, it is not just the presence or absence of an element that is useful (as most elements will be present at some concentration), but it is the relative variation in the trace element profile that is the parameter that provides the major discriminatory power. McHard et al. [16] were possibly some of the first researchers to apply a normalization procedure to multielement data in order to maximize the differences between two sets of samples. Their approach, which is now accepted as being a standard tool for use in chemometric investigations, was to identify an element whose concentration was constant, irrespective of the geographical origin of the samples, and then to normalize all other elemental data against it. In McHard s study on fruit juice, they used Zn. The authors of this chapter used Ca in an egg authenticity study, where eggshells were used as the sample matrix (unpublished data) and Mg was used in a study of Welsh onions [14]. 

Like many classical methods of data analysis, the normal probability plot has limitations. It is only useful if there are several factors, and clearly will not be much use in the case of two or three factors. It also assumes that a large number of the factors are not significant, and will not give good results if there are too many significant effects. However, in certain cases it can provide useful preliminary graphical information, although probably not much used in modern computer based chemometrics. 

In calibration it is normal to use several concentration levels to form a model. Indeed, for information on lack-of-fit and so predictive ability, this is essential. Hence two level factorial designs are inadequate and typically four or five concentration levels are required for each compound. However, chemometric techniques are most useful for multicomponent mixtures. Consider an experiment earned out in a mixture of methanol and acetone. What happens if the concentrations of acetone and methanol in a training set are completely correlated If the concentration of acetone increases, so does that of methanol, and similarly with a decrease. Such an experimental arrangement is shown in Figure 2.25. A more satisfactory design is given in Figure 2.26, in which the two... 

Chromatograms and spectra are normally considered to consist of a series of peaks, or lines, superimposed upon noise. Each peak arises from either a characteristic absorption or a characteristic compound. In most cases the underlying peaks are distorted for a variety of reasons such as noise, blurring, or overlap with neighbouring peaks. A major aim of chemometric metiiods is to obtain the underlying, undistorted, information. 

Some of the classical applications of chemometrics are to evolutionary data. Such a type of information is increasingly common, and normally involves simultaneously recording spectra whilst a physical parameter such as time or pH is changed, and signals evolve during the change of this parameter. 

D. A. Whitman, T. R Weber, and J. A. Blackwell, Chemometric characterization of Lewis base-modified zirconia for normal phase chromatography, J. Chromatogr. A 691 (1995), 205-212. 

The multivariate methods of data analysis, like discriminant analysis, factor analysis and principal component analysis, are often employed in chemometrics if the multiple regression method fails. Most popular in QSRR studies is the technique of principal component analysis (PCA). By PCA one reduces the number of variables in a data set by finding linear combinations of these variables which explain most of the variability [28]. Normally, 2-3 calculated abstract variables (principal components) condense most (but not all) of the information dispersed within the original multivariable data set. 

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