Branch-and-Bound Technique for Solving Optimal Clustering

The problem of finding optimal clustering has not been well covered in literature. Solutions can be found only for special cases, which can be solved in polynomial time. In this paper, we give solution for the general case. The method generates all possible clusterings by a series of merge steps. The clusterings are organized as a minimum redundancy search tree and the optimal clustering is found by a branch-and-bound technique. The result has theoretical interest and could also provide new insight to the problem itself.