Quasi-optimality under pseudo F statistic in clustering data

Pseudo F statistic is often used in deciding the number of clusters. A set of clusters having the largest pseudo F value is selected as the optimum set of clusters. This paper proposes the quasi-optimum set of clusters, whose pseudo F value is larger than those of other sets of clusters, whose numbers are around the number of clusters in the quasi-optimum set. The before and behind (BB) difference of pseudo F values is proposed to find the number of clusters in the quasi-optimum set. The relative BB difference of pseudo F values, which is the ratio of the BB difference of pseudo F values to the pseudo F value itself, is also proposed to find it when the pseudo F value severely varies. This paper shows some examples to demonstrate that the BB differences of pseudo F values and the relative ones work well in finding quasi-optimum sets of clusters.