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 t hat do not make any assumptions on the cluster shapes. Indeed the classific ation approach we use is based on the estimation of the probability density function (PDF) using the Parzen-Rosenblatt method. The modes of the PDF le ad to the construction of influence zones which are intrinsically related t o the number of clusters. In this paper, using different sizes of kernel an d different samplings of the data set, we study the effects they imply on t he relation between influence zones and the number of clusters. This ends u p 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. (C) 2001 Published by Else vier Science B.V.