Single link clustering methods

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... 

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) ... 

Single link (or nearest neighbour) method, d(Ci, Cj) is the smallest distance between the observations for both clusters (d(Ci,Cj) = mind(dj j),... 

Agglomerative methods, such as single link and complete link, are stepwise procedures. The formulation in (5)-(7) allows us to define the hierarchical clustering problem in terms of combinatorial optimization. To do this, however, we need an appropriate internal clustering criterion. The most obvious is squared error. 

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. 

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