Estimation of cluster centroids in presence of noisy observations

This paper considers the problem of clustering vector-valued datasets whose replicate observations are contaminated by weighted additive zero-mean white measurement noise. A corresponding error model of the cluster centroid is developed. Subsequently, an optimal iterative algorithm is proposed for updating cluster centroids obtained by using the k-means algorithm implemented on each set of noisy observations. The gain of the proposed algorithm aims for periteration minimization of the mean square estimate error. Three other methods are considered for performance evaluation. A numerical toy example is presented in order to illustrate the performance capabilities of the proposed method.