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Abstract:
Cluster analysis contains several multivariate methods for the separation of patterns (clusters). Definition of the optimum, or globally best, cluster analysis is an unresolved issue. Three methods are of special importance:
• The statistical security of cluster separation.
• The definition of the optimal number of clusters.
• The description of the internal cluster structure. Two new methods addressing these problems are presented.
On the basis of non-hierarchical minimum-distance cluster analysis a new method is described that allows a separation of clusters in a statistically well-founded way. With this method the outstanding problems one and two can be solved.
Using a newly developed special rank-sum analysis, a solution of the third problem is possible. An example shows the practicability of the proposed procedures.
