Relational duals of the c-means clustering algorithms

摘要

The hard and fuzzy c-means algorithms are widely used, effective tools for the problem of clustering n objects into (hard or fuzzy) groups of similar individuals when the data is available as object data, consisting of a set of n feature vectors in RP. However, object data algorithms are not directly applicable when the n objects are implicitly described in terms of relational data, which consists of a set of n2 measurements of relations between each of the pairs of objects. New relational versions of the hard and fuzzy c-means algorithms are presented here for the case when the relational data can reasonably be viewed as some measure of distance. Some convergence properties of the algorithms are given along with a numerical example.