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The naive algorithm for single linkage clustering is essentially the same as Kruskal's algorithm for minimum spanning trees. However, in single linkage clustering, the order in which clusters are formed is important, while for minimum spanning trees what matters is the set of pairs of points that form distances chosen by the algorithm.
Hierarchical clustering is a bottom-up approach to cluster analysis, in which the two closest data points are grouped together and are treated as a single data point for later clustering. In complete-linkage Hierarchical Clustering, this process of combining data points into clusters of increasing size is repeated until all date as part of a ...
This is a common way to implement this type of clustering, and has the benefit of caching distances between clusters. A simple agglomerative clustering algorithm is described in the single-linkage clustering page; it can easily be adapted to different types of linkage (see below).
Complete-linkage clustering is one of several methods of agglomerative hierarchical clustering. At the beginning of the process, each element is in a cluster of its own. The clusters are then sequentially combined into larger clusters until all elements end up being in the same cluster. The method is also known as farthest neighbour clustering.
Single linkage (minimum method, nearest neighbor) Average linkage ; Complete linkage (maximum method, furthest neighbor) Different studies have already shown empirically that the Single linkage clustering algorithm produces poor results when employed to gene expression microarray data and thus should be avoided. K-means clustering
Sequence clustering. In bioinformatics, sequence clustering algorithms attempt to group biological sequences that are somehow related. The sequences can be either of genomic, "transcriptomic" ( ESTs) or protein origin. For proteins, homologous sequences are typically grouped into families. For EST data, clustering is important to group ...
As with complete linkage and average distance, the difficulty of calculating cluster distances causes the nearest-neighbor chain algorithm to take time and space O(n 2) to compute the single-linkage clustering. However, the single-linkage clustering can be found more efficiently by an alternative algorithm that computes the minimum spanning ...
Ward's method. In statistics, Ward's method is a criterion applied in hierarchical cluster analysis. Ward's minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward, Jr. [1] Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing the pair ...