A simulation study of the weighted k-means cluster procedure

Given a data set ,the k-means cluster procedure together with a weight function w ε of the form fixed, can be used to obtain a k(n)∊ℕ which can be looked upon as the number of clusters present in the data set: Considering the as an independent sample from a k-modal distribution P(k) on ℝ l the sequence turns out to be strongly consistent for k. In this paper we illustrate how this weighted k-means cluster procedure works and demonstrate the consistency result by giving some examples. Moreover we discuss the effect of the choice of e on the estimate k(n) and use the bootstrap procedure in order to approximate the distribution of k(n).