On a new naturally indexed quick clustering method with a global objective function

A new clustering method is presented which proposes a class of objective functions and an algorithm which sub-optimizes the objective functions over the whole space of partitions. The objective functions have a global nature, encompassing both the cluster contents and the cluster number. However, the accompanying suboptimization algorithm works according to a simple progressive merger scheme. The algorithmic scheme produces in a quite natural way an indexed hierarchy. The hierarchy index is not just tacked on to the method—see Diday and Moreau¹—on the contrary, the algorithm refers directly to its values which measure, depending upon the particular formulation, either the relative affinity or the relative difference of the two clusters merged at a given level of hierarchy. In this way, the scale of hierarchy and hierarchy-wise validity of clusters can easily be established, which is of great importance in analysing unstructured data sets whose generating process is unknown and can only be hypothesized after an initial structure had been established, e.g. owing to clustering, as is the case in pattern recognition—see Kaminuma².