Local Algorithms For Interactive Clustering

We study the design of interactive clustering algorithms. The user supervision that we consider is in the form of cluster split/merge requests; such feedback is easy for users to provide because it only requires a high-level understanding of the clusters. Our algorithms start with any initial clustering and only make local changes in each step; both are desirable properties in many applications. Local changes are desirable because in practice edits of other parts of the clustering are considered churn-changes that are perceived as quality-neutral or quality-negative. We show that in this framework we can still design provably correct algorithms given that our data satisfies natural separability properties. We also show that our framework works well in practice.