Abstract. Clustering method is one of the most important tools in statistics. In a graph theory model, clustering is the process of finding all dense subgraphs. In this paper, a new clustering method is introduced. One of the most significant differences between the new method and other existing methods is that this new method constructs a much smaller hierarchical tree, which clearly highlights meaningful clusters. Another important feature of the new method is the feature of overlapping clustering or multi-membership. "· · · problems related to robustness, uniqueness, and optimality of linear ordering which complicates the interpretation of the resulting hierarchical relationships" and issues of "how to determine the optimal number of clusters" (Lukashin and Fuchs, 2001 [7] p.405); Concerns that "none of these algorithms can, in general, rigorously guarantee to produce a globally optimal clustering for non-trivial objective functions" (Xu, Olman and Xu, 2002 [15] p.536); Regarding the need for efficient clustering methods that allow for multimembership, Shepard and Arabie (1979 [13] p.91) write that "the requirement of having the clusters hierarchically nested seems to be unduly limiting".
Especially in 2007, Ou and Zhang REF proposed a new clustering method with the feature of hierarchical tree and overlapping clusters, the complexity of this method is (ℎ 2 log ) where ℎ denotes the height of the hierarchical structure.
A new multimembership clustering method
Journal of Industrial and Management Optimization
Mathematics