Estimation of the number of clusters and influence zones

Whereas estimating the number of clusters is directly involved in the first steps of unsupervised classification procedures, the problem still remains topical. In our attempt to propose a solution, we focalize on procedures that do not make any assumptions on the cluster shapes. Indeed the classification approach we use is based on the estimation of the probability density function (PDF) using the Parzen–Rosenblatt method. The modes of the PDF lead to the construction of influence zones which are intrinsically related to the number of clusters. In this paper, using different sizes of kernel and different samplings of the data set, we study the effects they imply on the relation between influence zones and the number of clusters. This ends up in a proposal of a method for counting the clusters. It is illustrated in simulated conditions and then applied on experimental results chosen from the field of multi-component image segmentation.