About estimation of quality of clustering results via its stability

Abstract

We know that there are many clustering methods for the case of a known/unknown number of clusters. Clustering is a result of fulfillment of some stopping criterion. Usually, optimisation of some quality criterion is performed or iterative processes are accomplished. How to estimate the quality of clustering obtained by some method? Is the obtained clustering result corresponding to the objective reality or some stopping criterion of the algorithm is made and we have obtained only some partition? Here, a practical approach and the common general criteria based on an estimation of the stability of clustering are submitted. The criterion does not use any probabilistic assumptions or distances in feature space. For some well-known clustering algorithms, efficient methods for computing the introduced stability criteria according to the training set are obtained. Some illustrative real and artificial examples for various situations are shown.