Partial Explanations for Interpretable Clustering

Algorithms for clustering problems typically create models which give little insight into the features or values which distinguish one cluster from another. Recent work on interpretable clustering has sought to address this issue by using decision tree algorithms to explain a reference clustering, while also allowing for critical insight into the decision making process. The following study builds upon this line of work by introducing the partial interpretable clustering perspective and problem, forgoing the requirement that every point must be explained by the interpretable model. Whereas decision trees naturally partition their entire input space, our study designs and tests an efficient \emph{decision set} clustering algorithm, which uses more generally structured collections of rules. In doing so, we find partial clusterings with large coverage, more concise descriptions, and improved robustness to noise — showing that our explanations are strongly tied to the core of the cluster they are intended to describe.