CAsee Cluster Analysis

Figure 8.39 shows a three-dimensional scatter plot of the first three PC scores obtained from a PCA analysis of 987 calibration spectra that were collected for a specific on-line analyzer calibration project. In this case, cluster analysis was done using the first six PCs (all of which cannot be displayed in the plot ) in order to select a subset of 100 of these samples for calibration. The three-dimensional score plot shows that the selected samples are well distributed among the calibration samples, at least when the first three PCs are considered. 

Beauchaine, T. P., Beauchaine, R. J. (2002). A comparison of maximum covariance and k-means cluster analysis in classifying cases into known taxon groups. Psychological Methods, 7, 245-261. 

Figure 12.24 Dendrograms obtained from hierarchical cluster analysis (HCA) of the NIR. spectra of the poly(urethane) foam samples (shown in Figure 12.16), (A) using the first two PCA scores as input, (B) using the first five PCA scores as input. In both cases, the Mahalanobis distance measure and the nearest-neighbor linkage rule were used.

There are two main types of clustering techniques hierarchical and nonhierarchical. Hierarchical cluster analysis may follow either an agglomerative or a divisive scheme agglomerative techniques start with as many clusters as objects and, by means of repeated similarity-based fusion steps, they reach a final situation with a unique cluster containing all of the objects. Divisive methods follow exactly the opposite procedure they start from an all-inclusive cluster and then perform a number of consecutive partitions until there is a bijective correspondence between clusters and objects (see Fig. 2.12). In both cases, the number of clusters is defined by the similarity level selected. 

In principle, the features describing the objects can also be subjected to cluster analysis. In this case one may think immediately of the correlation coefficient, r, or the coefficient of determination, COD, as a measure of the similarity of each pair of features. Accordingly, 1 - r or 1 - COD is useful as a measure of distance. 

Analysis of variance in general serves as a statistical test of the influence of random or systematic factors on measured data (test for random or fixed effects). One wants to test if the feature mean values of two or more classes are different. Classes of objects or clusters of data may be given a priori (supervised learning) or found in the course of a learning process (unsupervised learning see Section 5.3, cluster analysis). In the first case variance analysis is used for class pattern confirmation. 

In a study of the fluorescence properties of the Brazil Block seam (Parke Co., IN), a somewhat different approach was used. In this case, about a hundred individual spectra were taken on a variety of fluorescing liptinite macerals. Although the macerals from which the spectra were tkane were not identified at the time of measurement, photomicrographs in both normal white-light and fluorescent light were taken for documentation. The spectral parameters for each spectrum were calculated and these data were subjected to cluster analysis to test the degree to which the... 

The principal component plot of the objects allows a visual cluster analysis. The distances between data points in the projection, however, may differ considerably from the actual distance values. This will be the case when variances of the third and following principal components cannot be left out of consideration. A serious interpretation should include the application of at least another cluster analysis method (ref. 11,12). 

The second cluster analysis involved attaching twice as much importance to the interaction term than to any of the other 12 attributes. We obtained basically the same cluster tree as with the first method, with only a few modifications some cluster breakups were more severe than before, indicating more cluster-to-cluster distinctiveness, and some were less severe. Inspection of the tree indicated that there were either two clusters, in which case one cluster was approximately twice as big as the other cluster, or there were three clusters, with the larger cluster subdivided into two clusters. (See Figure 4.) Further examination of spatial plots revealed no clear separation of cluster, whether the number of clusters was designated two or three (Figures 5a and b),... 

Kmeans Clustering. Type of partitioning cluster analysis in which an object, such as a chemical structure, is placed into one of K clusters, based on how similar the structure is to the average value (or centroid) of each cluster. The average of the cluster may be an actual structure itself, in which case the technique is referred to as K-medoids clustering. 

Similarity Search. A type of "fuzzy" structure searching in which molecules are compared with respect to the degree of overlap they share in terms of topological and/or physicochemical properties. Topological descriptors usually consist of substructure keys or fingerprints, in which case a similarity coefficient like the Tanimoto coefficient is computed. In the case of calculated properties, a simple correlation coefficient may be used. The similarity coefficient used in a similarity search can also be used in various types of cluster analysis to group similar structures. 

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