Centroid link clustering linking methods

The second approach used for linking clusters is termed the centroid link method. This method joins the centroids of the clusters instead of the nearest neighbors. The centroid is calculated as the average of the points within a cluster. Clustering using this approach with the same data as in Figure 4.8 is shown in Figure 4.10. 

The single and centroid linking methods do not always join clusters in. the same order as in the previous example. Figure 4.12 shows an example where these methods yield different dendrograms. If the single-link method is used, the clustering proceeds as follows (solid lines in Figure 4.12) ... 

This results in the dendrogram foimd in Figure 4.13 2- If the centroid-link method is used on these same data, the clustering scheme is as follows (dashed lines in Figure 4.12) ... 

Figure 4.11. Dendrogram of the data in Figure 4.10 using the centroid-link clustering method.

It is not possible to make a general statement as to whether the single- or centroid-link approach will perform better. The centroid method results in a better measure of the distance betw een clusters when the clusters are well separated. This is because it measures the distance between the centers of the clusters rather than the distances from the edges as in single link. On the other hand, the centroid method is sensitive to outliers because these unusual points... 

To generate the dendrogram, HCA methods form clusters of samples based on their nearness in row space. A common approach is to initially treat every sample as a cluster and join closest clusters together. This process is repeated until only one cluster remains. Variations of HCA use different approaches to measure distances between clusters (e.g., single vs. centroid linking, Euclidean vs. Mahalanobis distance), fhe two methods discussed below use single and centroid linking with Euclidean distances. 

In this work, classification through HCA was based on the Euclidean distance and the average group method. This method established links between samples/cluster. The distance between two clusters was computed as the distance between the average values (the mean vector or centroids) of the two clusters. The descriptors employed in HCA were the same selected in... 

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