Optimal cluster numbers of unsupervised classification in Minkowski spaces

Unsupervised classification needs no prior knowledge of interested region and has less human interference that is suitable for processing messes of digital images acquired from earth observation satellites. A typical sequence for unsupervised classification might begin with the analyst specifying minimum and maximum numbers of categories to be generated by the classification algorithm. Usually, a larger cluster number is assigned in advance for the initial clustering. Then, several classified clusters are merged into a larger group so that the number of clusters can be reduced. The selection of an appropriate cluster number is up to the analyst´s experience. This paper illustrates the convergence of cluster-center optimization and the optimal cluster number varying with the dimension in Minkowski space. One of the simplest and most popular is Euclidean distance while Minkowski distance is measured in two dimensions. The experiment was executed on several digital images by a classifier employing Genetic Algorithm as a searching tool and Davies-Bouldin index as a cluster validity measure. The results show that a smaller dimension, e.g. one-, two-, and infinity dimensions, in Minkowski space derives less clusters, while the assignment of a larger dimension results in a larger cluster number with a more detailed segmentation.