Symmetric Submodular Clustering with Actionable Constraint

TL;DR

This paper introduces a new actionable constraint for symmetric submodular clustering, addressing the challenge of partitioning with approximation guarantees in practical applications.

Contribution

It proposes a novel constraint to make symmetric submodular clustering actionable, expanding the applicability of efficient clustering methods.

Findings

Symmetric submodular functions include common practical functions like graph cuts and mutual information.

Introducing the actionable constraint poses new challenges for approximation guarantees.

Further work is needed to develop algorithms with provable guarantees for the constrained problem.

Abstract

Clustering with submodular functions has been of interest over the last few years. Symmetric submodular functions are of particular interest as minimizing them is significantly more efficient and they include many commonly used functions in practice viz. graph cuts, mutual information. In this paper, we propose a novel constraint to make clustering actionable which is motivated by applications across multiple domains, and pose the problem of performing symmetric submodular clustering subject to this constraint. We see that obtaining a $k$ partition with approximation guarantees is a non-trivial task requiring further work.