  Clustering is a widely used unsupervised learning method for finding
structure in the data. However, the resulting clusters are typically presented
without any guarantees on their robustness; slightly changing the used data
sample or re-running a clustering algorithm involving some stochastic component
may lead to completely different clusters. There is, hence, a need for
techniques that can quantify the instability of the generated clusters. In this
study, we propose a technique for quantifying the instability of a clustering
solution and for finding robust clusters, termed core clusters, which
correspond to clusters where the co-occurrence probability of each data item
within a cluster is at least $1 - \alpha$. We demonstrate how solving the core
clustering problem is linked to finding the largest maximal cliques in a graph.
We show that the method can be used with both clustering and classification
algorithms. The proposed method is tested on both simulated and real datasets.
The results show that the obtained clusters indeed meet the guarantees on
robustness.
