A method to estimate the statistical confidence of cluster separation

Cluster analysis contains several multivariate methods for the separation of patterns (clusters). The definition of the optimum or universally best cluster analysis is an unresolved issue. Three methods are of special importance: 1. The statistical confidence of cluster separation. 2. The definition of the optimal number of clusters. 3. 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. This method solves problems one and two. Using a newly developed special rank-sum analysis, a solution to the third problem is possible. An example shows the practicability of the proposed procedures.