Estimations of Clustering Quality via Evaluation of Its Stability

Currently, there are many clustering algorithms for the case of a known/unknown number of clusters. Typically, clustering is a result of optimisation of some quality criterion or iterative process. How to estimate the quality of clustering obtained by some method? Is the clustering result corresponding to the objective reality or just a stopping criterion of the method is made and obtained some partition? In this paper, a practical approach and the general criteria based on an estimation of the stability of clustering are proposed. For the well-known clustering methods, efficient algorithms for computing the introduced stability criteria according to the training set are obtained. We give illustrative examples.