Application of Multivariate Techniques

The application of these methods has been examined in a series of field studies and multispecies toxicity tests. These examinations have demonstrated the power and usefulness of multivariate techniques in elucidating patterns in biological communities of varying complexity. 

Several researchers have attempted to employ multivariate methods to the description of ecosystems and the impacts of chemical stressors. Perhaps the best developed approaches have been those of K. Kersting, A.R. Johnson, and a new approach developed by Matthews et al. 

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Bieber, A. M., D. W. Brooks, G. Harbottle, and E. V. Sayre (1976), Application of multivariate techniques to analytical data on Aegean ceramics, Archaeometry 18, 59-74. 

DRIFT-IR) spectroscopy was also used for polymorphic characterization. The authors detail the application of multivariate techniques, multivariate statistical process control (MSPC), PC A and PLS, to the spectroscopic data for a simple yet powerful, rapid evaluation of the given crystalhzation process. ... 

A data matrix produced by compositional analysis commonly contains 10 or more metric variables (elemental concentrations) determined for an even greater number of observations. The bridge between this multidimensional data matrix and the desired archaeological interpretation is multivariate analysis. The purposes of multivariate analysis are data exploration, hypothesis generation, hypothesis testing, and data reduction. Application of multivariate techniques to data for these purposes entails an assumption that some form of structure exists within the data matrix. The notion of structure is therefore fundamental to compositional investigations. 

Landis, W.G., G.B. Matthews, R.A. Matthews, and A. Sergeant. 1994. Application of multivariate techniques to endpoint determination, selection, and evaluation in ecological risk assessment. Environ. Toxicol. Chem. 13 1917-1927. 

With pseudo 2D NMR data consisting of a series of ID profiles, analysis by multivariate techniques is obvious, since the large number of potentially overlapping variables makes visual analysis very difficult and improved methods of analysis are already called for. Analysis of real 2D NMR data by multivariate techniques is less obvious, since a lot of information can already be extracted from the 2D Fourier-transformed data. However, if real 2D NMR data from a series of samples needs to be compared, the application of multivariate techniques is an obvious possibility. 

Vandeginste, B. G. M., Massart, D. L., Buydens, L. M. C., De Jong, S., Lewi, P. L. and Smeyers-Verbecke, J. 1998. Handbook of Chemometrics and Qualimetrics Part B, Elsevier, Amsterdam. (A detailed and comprehensive account of the application of multivariate techniques in analytical chemistry.)... 

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. 

Multivariate chemometric methods have claimed considerable attention in the last few decades because of their inherent capacity for resolving multicomponent, complex systems. Applications of multivariate methods in different electrochemical techniques have been recently reported by several authors [192-194],... 

Sediment analyses are useful for characterization of pollution over a long period [MULLER, 1981]. Assessment of the state of a river and of the interactions between the components can be made by application of multivariate statistical methods only, because the strongly scattering territorial and temporal courses [FORSTNER and MULLER, 1974 FORSTNER and WITTMANN, 1983] are not compatible with many univariate techniques. FA shall serve as a tool for the recognition of variable structures and for the differentiated evaluation of the pollution of both river water and sediment [GEISS and EINAX, 1991 1992],... 

Other frequency domain techniques which have been proposed include the commutative controller (31), sequential return difference (32), and the direct Nyquist array (33). In chemical pro-ess control, a number of recent applications of multivariable frequency response methods include distillation columns (34), (35), and reactors (36). 

The use of multivariate spectral information is particularly advantageous where quantification of a particular metabolite in a complex biological background is being attempted and application of the technique necessitates the use of chemometric processing techniques for quantification of components. 

Classification and discriminant analysis algorithms are available with all multivariate statistical software packages. New or modified procedures are regularly being introduced and the application of such techniques and methods in analytical science is growing. 

Abstract This chapter introduces an application of multivariate curve resolution (MCR) technique based on a factor analysis. Not only series of IR spectra but also two-dimensional data (series of nuclear magnetic resonance (NMR), mass spectrometry (MS), and X-ray diffraction (XRD)) can deal with same manner (further more two-dimensional data generated by hyphenated techniques such as gas chromatography/mass spectrometry (GC/MS) and liquid chromatography/ultravi-olet (LC/UV) analysis, which combine two functions based on different principles, namely, chromatography, which has a separating function, and spectrometry, which provides information related to molecular structure). By using MCR techniques appropriately, the mixture data is resolved into some essential elements (chemical components, transient states and phases). The results can reveal a true chemical characteristic in your study. 

Multivariate display methods are very useful techniques for the inspection of high-dimensional data sets. They allow us to examine the relationships between points (compounds, samples, etc.) in both training and test sets, and between descriptor variables. Linear and non-linear methods are available, both with advantages and disadvantages, which have proved useful in numerous chemical applications. The linear approach (PCA) forms the basis of a variety of multivariate techniques as described later in this book. Finally, it is not possible to say in advance which, if any, is the best approach to use. 

A variety of different types of models can be used for the prediction. Choosing an appropriate model type is dependent upon the application to be controlled. The model can be based upon first-principles or it can be an empirical model. Also, the supplied model can be either linear or nonlinear, as long as the model predictive control software supports this type of model. Most industrial applications of MPC have relied on linear empirical models, because they can more easily be identified and solved and approximate most processes fairly well. Also, many MPC implementations change set points in order to move the plant to a desired steady state the actual control changes are implemented by PID controllers in response to the set points. There are over 1000 applications of MPC techniques in oil refineries and petrochemical plants around the world. Thus, MPC has had a substantial impact and is currently the method of choice for difficult constrained multivariable control problems in these industries (Qin and BadgweU, 2003). 

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