Weighted mean of a pair of clusterings

In this paper, we introduce the weighted mean of a pair of clusterings. Given two clusterings C (1) and C (2), the weighted mean of C (1) and C (2) is a clustering C (w) that has distances d(C (1), C (w) ) and d(C (w) , C (2)) to C (1) and C (2), respectively, such that d(C (1), C (w) ) + d(C (w) , C (2)) = d(C (1), C (2)) holds for some clustering distance function d. C (w) is defined such that the sum of the distances d(C (1), C (w) ) and d(C (w) , C (2)) is equal to the distance between C (1) and C (2). 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.