Programmable clustering

Sreenivas Gollapudi, Ravi Kumar, D. Sivakumar

Abstract: We initiate a novel study of clustering problems. Rather than specifying an explicit objective function to optimize, our framework allows the user of clustering algorithm to specify, via a first-order formula, what constitutes an acceptable clustering to them. While the resulting genre of problems includes, in general, NP-complete problems, we highlight three specific first-order formulae, and provide efficient algorithms for the resulting clustering problems.