Measures for the structure of clustering and admissibilities of its algorithm

The problem of selecting a clustering algorithm from the myriad of algorithms has been discussed in recent years. Many researchers have attacked this problem by using the concept of admissibility (e.g. Fisher and Van Ness, 1971, Yadohisa, et al., 1999). We propose a new criterion called the structured ratio for measuring the clustering results. It includes the concept of the well-structured admissibility as a special case, and represents some kind of goodness-of-fit of the clustering result. New admissibilities of the clustering algorithm and a new agglomerative hierarchical clustering algorithm are also provided by using the structured ratio. Details of the admissibilities of the eight popular algorithms are discussed.