Internal Coordinates and Chemical Fragments

The key question that now remains is which particular subset of internal coordinates should we select for a particular analysis Obviously this selection is intimately related to the nature of the chemical fragment (see Chapter 1.1), and to the type of analysis we wish to perform. Here we must be guided by our prior chemical and structural knowledge, and also by our preconceptions of the type of results that we hope to obtain. In practice, we should also be guided by intermediate stages of analysis, which may indicate modifications to the initial selection of parameters, or changes to the specification of the chemical fragment. 

The relationship between chemical and structural search specifications and parameter selection is an important one. Chapter 3 shows that it is possible to impose geometrical, as well as chemical, constraints on the fragments retrieved in a search. 

Despite the indications given above, it will often be impossible to reduce the number of standard parameters significantly, or to visualize suitable linear combinations of parameters that may help in this aim. We are then left with a truly multivariate problem. However, one of the aims of multivariate analysis is the reduction of dimensionality, i.e. the detection of a subset of parameters or, more often, of linear combinations thereof, that best describe the total variance in the data set. In effect, the techniques are trying to detect automatically the set of axes in parameter space that are most useful for visualizing the data. We return to this topic in some depth in Section 4.6.3. 

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