Weighted mean of a pair of clusterings

In this paper, we introduce the weighted mean of a pair of clusterings. Given two clusterings C1 and C2, the weighted mean of C1 and C2 is a clustering Cw that has distances d(C1, Cw) and d(Cw, C2) to C1 and C2, respectively, such that d(C1, Cw) + d(Cw, C2) = d(C1, C2) holds for some clustering distance function d. Cw is defined such that the sum of the distances d(C1, Cw) and d(Cw, C2) is equal to the distance between C1 and C2. An algorithm for its computation will be presented. Experimental results on both synthetic and real data will be shown to illustrate the usefulness of the weighted mean concept. In particular, it gives a tool for the cluster ensemble techniques.