We investigate the role of the initialization for the stability of the қ-means clusteringalgorithm. As opposed to other papers, we consider the actual қ-means algorithm (also knownas Lloyd algorithm). In particular we leverage on the property that this algorithm can getstuck in local optima of the қ-means objective function. We are interested in the actualclustering, not only in the costs of the solution. We analyze when differentinitializations lead to the same local optimum, and when they lead to different localoptima. This enables us to prove that it is reasonable to select the number of clustersbased on stability scores.
