Conceptual Meaning of Clusters

Abstract: The interpretation of cluster analysis solutions in the case of objectattribute data can be supported by methods of Formal Concept Analysis leading to a conceptual understanding of the "meaning " of clusters, partitions and dendrograms. The central idea is the embedding of a given cluster in a conceptual scale which represents the user's granularity with respect to the values of attributes in the original data. This method is demonstrated using data from ALLBUS 1996. 1 Interpretation of Cluster Analysis Solutions In this article we deal with the interpretation of cluster analysis solutions (Jardine, Sibson (1971), Bock (1974)) in the case that the data are given as an object-attribute table | formally described as a many-valued context (Ganter, Wille (1996)). Suchaninterpretation should relate the given cluster analysis solution with some suitable information given in the original data. We are not interested in discussing indices of cluster analysis solutions like homogeneity, stability etc. The cluster analysis solutions are mainly represented as a hierarchical tre