Algorithms multivariate

Algorithms, multivariate techniques, quality control, and experimental design [King, Srinivasan et al., 2001 Booth, Isenhour et al., 2003 Eriksson, Antti et al., 2003 Hemmer, 2003 Leardi,... 

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. 

One important class of nonlinear programming techniques is called quadratic programming (QP), where the objective function is quadratic and the constraints are hnear. While the solution is iterative, it can be obtained qmckly as in linear programming. This is the basis for the newest type of constrained multivariable control algorithms called model predic tive control. The dominant method used in the refining industiy utilizes the solution of a QP and is called dynamic matrix con-... 

D. Jouan-Rimbaud, D.L. Massart, R. Leardi, et al.. Genetic algorithms as a tool for wavelength selection in multivariate calibration. Anal. Chem., 67 (1995) 4295 301. 

J. Zhang, J.-H. Jiang, P. Liu, Y.-Z. Liang and R.-Q. Yu, Multivariate nonlinear modelling of fluorescence data by neural network with hidden node pruning algorithm. Anal. Chim. Acta, 344(1997) 29 0. 

Manne R (1987) Analysis of two partial-least-squares algorithms for multivariate calibration. Chemom Intell Lab Syst 2 187... 

In our next chapter we will look at the problem of representing higher dimensional space with fewer dimensions it will be a precursor to discussions of the dimensional aspects of multivariate algorithms. 

Discriminant Analysis (DA) is a multivariate statistical method that generates a set of classification functions that can be used to predict into which of two or more categories an observation is most likely to fall, based on a certain combination of input variables. DA may be more effective than regression for relating groundwater age to major ion hydrochemistry and well construction because it can account for complex, non-continuous relationships between age and each individual variable used in the algorithm while inherently coping with uncertainty in the age values used for... 

If an MLR equation needs more than five wavelengths, it is often better to apply one of the other multivariate algorithms mentioned above. Since the information which an analyst seeks is spread throughout the sample, methods such as PLS and PCA use much or all of the NIR spectra to determine the information sought. 

Consider now multivariate data, e.g. measurements at many wavelengths instead of only one, say kinetics followed by a diode-array spectrophotometer. Assume the instrument records the spectra at 1024 wavelengths. Compared with monovariate data (single wavelength), there is a dramatic increase in the number of parameters to be fitted. In addition to the rate constant, there are now 1024 molar absorptivities for each reacting component that need to be fitted. The algorithm devised so far cannot cope with that number of parameters. 

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