Evolutionary factor analysis

There are a large number of named methods in the literature, but they are based mainly around certain main principles of evolutionary factor analysis, whereby factors corresponding to individual compounds evolve in time (or any other sequential parameter such as pH). 

A.K. Elbergali and R.G. Brereton, Influence of Noise, Peak Position and Spectral Similarities on Resolvability of Diode-Array High-Performance Liquid Chromatography by Evolutionary Factor Analysis, Chemometrics Intelligent Laboratory Systems 23 (1994), 97-106. 

Overlapping bands can become a problem when, for example, there are two consecutive electron-transfer reactions [137]. One solution is to look at the time-or potential-resolved spectra [138], Overlapping bands are often responsible for nonlinear Nemstian plots in OTTLE studies [139]. There are only a few examples of the use of differentiating the absorbance [134], least-squares analysis [140], of the latest chemometric techniques [141]. In the latter study, evolutionary factor analysis of the spectra arising from the reduction of E. coli reductase hemoprotein (SiR-HP ) in which three species are present and the reduction of the [Cl2FeS2MoS2FeCl2] (four species present). The most challenging part of the work was the determination of the transformation matrix. 

The application of evolutionary factor analysis (FA) methods to spectroscopic problems is reviewed by Malinowski. Evolutionary FA methods offer solutions to the problem of analyzing totally unknown complex mixtures. These are mixtures containing unknown quantities of an unknown number of unknown components. No model for peak shape is required for these methods to work, that is, they are self-modeling. Deconvolution of overlapped peaks in HPLC is the type of data analyzed. 

E. R. Malinowski, in Computer-Enhanced Analytical Spectroscopy, H. L. C. Meuzelaar and T. L. Isenhour, Eds., Plenum, New York, 1987. Evolutionary Factor Analysis in Analytical Spectroscopy. 

Basically, we make a distinction between methods which are carried out in the space defined by the original variables (Section 34.4) or in the space defined by the principal components. A second distinction we can make is between full-rank methods (Section 34.2), which consider the whole matrix X, and evolutionary methods (Section 34.3) which analyse successive sub-matrices of X, taking into account the fact that the rows of X follow a certain order. A third distinction we make is between general methods of factor analysis which are applicable to any data matrix X, and specific methods which make use of specific properties of the pure factors. 

There are many chemometric methods to build initial estimates some are particularly suitable when the data consists of the evolutionary profiles of a process, such as evolving factor analysis (see Figure 11.4b in Section 11.3) [27, 28, 51], whereas some others mathematically select the purest rows or the purest columns of the data matrix as initial profiles. Of the latter approach, key-set factor analysis (KSFA) [52] works in the FA abstract domain, and other procedures, such as the simple-to-use interactive self-modeling analysis (SIMPLISMA) [53] and the orthogonal projection approach (OPA) [54], work with the real variables in the data set to select rows of purest variables or columns of purest spectra, that are most dissimilar to each other. In these latter two methods, the profiles are selected sequentially so that any new profile included in the estimate is the most uncorrelated to all of the previously selected ones. 

Malinowski, E.R., Automatic window factor analysis a more efficient method for determining concentration profiles from evolutionary spectra, J. Chemom., 10, 273-279, 1996. 

Problem 6.2 Evolutionary and Window Factor Analysis in the Detection of an Embedded Peak... 

All these data indicate the possibility of adaptive evolution. Certainly, the formation of such adaptations are in all stages of the life cycle. However, as shown by the results, the factor analysis carried by us, according on the results of experiments with cross-coupling conditions for the development of tadpoles, response to exposure to the environment occurs individually for each clutch in each year of analysis (Severtsova, 2009). Consequently, the evolutionary transformation will occur at the level of change in the way of individual development of each clutch, driving changes in the way of development of each trait (West-Eberhard, 2003). 

On-line investigation methods for statistical analysis are used when the performances of a continuous process carried out in a pilot unit or in an apparatus, have to be improved. The Evolutionary Operation Process (EVOP) method [5.7, 5.27, 5.28, 5.31] is the most famous method for on-line process analysis. The name of this method comes from its analogy with biological evolution. This analogy is based on the observation of the natural selection process in which a small variation in independent life factors is responsible for genetic mutations and thus for the evolution of species. 

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