Cluster analysis group separation

It has been shown that similar conformations that belong to adjacent energy basins separated by high energy barriers are incorrectly grouped together by the straightforward cluster analysis [29]. 

In cluster analysis " each variable is considered as a point in a separate dimension, and the points so obtained are analyzed in multidimensional space. Similar points identified within this multidiniensional space are grouped together. For example, in a study of five-coordinate d metal complexes, Biirgi and Auf der Heyde showed that the coordination of the metal in crystal structures can be described by three data clusters. These are representations of a trigonal bipyramid and... 

Fig. 5. An example of a scores plot as one might obtain in a principal components analysis. Distinct clustering or grouping of NMR spectra is observed in this type of plot, where the discrimination results from the analyzed metric used (e.g., principal components). The distance between samples (r ) within groups is used by many supervised methods to further describe and improve class or group separation. There are different chemometric techniques that can be used to identify outliers, or to provide a group assignment.

To demonstrate the use and application of fuzzy clustering, a simple set of data will be analysed manually. The data in Table 4.9 represent 15 objects (A. .. O) characterized by two variables X and X2, and these data are plotted in the scatter diagram of Figure 4.15. It is perhaps not unreasonable to assume that these data represent two classes or clusters. The means of the clusters are well separated but the clusters touch about points G, H, and I. Because the apparent groups are not well separated, the results using conventional cluster analysis schemes can be misleading or ambiguous. With the data from Table... 

Cluster analysis provides a tool for separation of very similar materials, and the success of these methods is highly dependent upon the calibration techniques used to build the model. Key elements of experimental design include the selection of samples used to teach the system and the performance of their corresponding reference tests. Proper grouping of the raw materials into appropriate cluster models is also important. To separate close materials, similar materials should be grouped together and then cross-validated against the remainder of materials in the database. 

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