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Home Multivariate Data Modeling Classification and Discrimination Cluster Analysis Minimal Spanning Tree  
See also: agglomerative clustering  
Minimal Spanning TreeAll agglomerative clustering algorithms based on the LanceWilliams equation have the drawback that the full distance matrix has to be calculated during the cluster analysis. This can take considerable computing power and requires high amounts of memory. A remedy to this can be found in a graphtheoretical approach, which is called the minimal spanning tree. Unfortunately, the minimal spanning tree algorithm can be applied only to single linkage clustering. However, in the case of large data sets, this algorithm can be orders of magnitude faster. A minimal spanning tree is a graph which meets the following requirements:
There is a simple algorithm described by Prim how to determine the
minimal spanning tree. The resulting minimal spanning tree is equal to
the results of a single linkage cluster analysis:
1. select an arbitrary object as the starting vertex of a partial graph M


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