Data analysis methods simple

Often the goal of a data analysis problem requites more than simple classification of samples into known categories. It is very often desirable to have a means to detect oudiers and to derive an estimate of the level of confidence in a classification result. These ate things that go beyond sttictiy nonparametric pattern recognition procedures. Also of interest is the abiUty to empirically model each category so that it is possible to make quantitative correlations and predictions with external continuous properties. As a result, a modeling and classification method called SIMCA has been developed to provide these capabihties (29—31). 

Cyclodextrin-modified solvent extraction has been used to extract several PAHs from ether to an aqueous phase. Data evaluation shows that the degree of extraction is related to the size of the potential guest molecule and that the method successfully separates simple binary mixtures in which one component does not complex strongly with CDx. The most useful application of cyclodextrin-modified solvent extraction is for the simplification of complex mixtures. The combined use of CDx modifier and data-analysis techniques may simplify the qualitative analysis of PAH mixtures. 

A rather crude, but nevertheless efficient and successful, approach is the bond fluctuation model with potentials constructed from atomistic input (Sect. 5). Despite the lattice structure, it has been demonstrated that a rather reasonable description of many static and dynamic properties of dense polymer melts (polyethylene, polycarbonate) can be obtained. If the effective potentials are known, the implementation of the simulation method is rather straightforward, and also the simulation data analysis presents no particular problems. Indeed, a wealth of results has already been obtained, as briefly reviewed in this section. However, even this conceptually rather simple approach of coarse-graining (which historically was also the first to be tried out among the methods described in this article) suffers from severe bottlenecks - the construction of the effective potential is neither unique nor easy, and still suffers from the important defect that it lacks an intermolecular part, thus allowing only simulations at a given constant density. 

The collection of examples is extensive and includes relatively simple data analysis tasks such as polynomial fits they are used to develop the principles of data analysis. Some chemical processes will be discussed extensively they include kinetics, equilibrium investigations and chromatography. Kinetics and equilibrium investigations are often reasonably complex processes, delivering complicated data sets and thus require fairly complex modelling and fitting algorithms. These processes serve as examples for the advanced analysis methods. 

A great variety of different methods for multivariate classification (pattern recognition) is available (Table 5.6). The conceptually most simply one is fc-NN classification (Section 5.3.3), which is solely based on the fundamental hypothesis of multivariate data analysis, that the distance between objects is related to the similarity of the objects. fc-NN does not assume any model of the object groups, is nonlinear, applicable to multicategory classification, and mathematically very simple furthermore, the method is very similar to spectral similarity search. On the other hand, an example for a rather sophisticated classification method is the SVM (Section 5.6). 

For small data sets (n < 10), which are often encountered in chemical analysis, a simple method to determine if an outlier is rejectable is the Q test. In this test, a value for Q is calculated and compared to a table of Q values that represent a certain percentage of confidence that the proposed rejection is valid. If the calculated Q value is greater than the value from the table, then the suspect value is rejected and the mean recalculated. If the Q value is less than or equal to the value from the table, then the calculated mean is reported. Q is defined as follows ... 

These EDA methods are essentially pictorial and can often be carried out using simple pencil and paper methods. Picturing data and displaying it accurately is an aspect of data analysis which is under utilised. Unless exploratory data analysis uncovers features and structures within the data set there is likely to be nothing for confirmatory data analysis to consider One of the champions of EDA, the American statistician John W. Tukey, in his seminal work on EDA captures the underlying principle in his comment that... 

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