The instance easiness of supervised learning for cluster validity

Abstract

"The statistical problem of testing cluster validity is essentially unsolved" [5]. We translate the issue of gaining credibility on the output of un-supervised learning algorithms to the supervised learning case. We introduce a notion of instance easiness to supervised learning and link the validity of a clustering to how its output constitutes an easy instance for supervised learning. Our notion of instance easiness for supervised learning extends the notion of stability to perturbations (used earlier for measuring clusterability in the un-supervised setting). We follow the axiomatic and generic formulations for cluster-quality measures. As a result, we inform the trust we can place in a clustering result using standard validity methods for supervised learning, like cross validation. © 2012 Springer-Verlag.