Guaranteed Recovery of Unambiguous Clusters

TL;DR

This paper introduces an information-theoretic framework to determine when a clustering is unambiguous and proposes an algorithm that guarantees recovery of such clusters, especially in complex scenarios with density variations and separated high-density regions.

Contribution

It provides a formal characterization of clustering ambiguity and develops an algorithm that guarantees recovery of unambiguous clusters, improving performance on complex datasets.

Findings

Algorithm effectively recovers unambiguous clusters

Requires minimal parameter tuning

Outperforms existing methods on many datasets

Abstract

Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation in density among different clusters, and clusters have multiple relatively separated regions of high density. In this paper we propose an information-theoretic characterization of when a $K$-clustering is ambiguous, and design an algorithm that recovers the clustering whenever it is unambiguous. This characterization formalizes the situation when two high density regions within a cluster are separable enough that they look more like two distinct clusters than two truly distinct clusters in the $K$-clustering. The algorithm first identifies $K$ partial clusters (or "seeds") using a density-based approach, and then adds unclustered points to the initial $K$ partial clusters in a greedy manner to form a complete clustering. We implement and test a version of the algorithm that is modified to effectively handle overlapping clusters, and observe that it requires little parameter selection and displays improved performance on many datasets compared to widely used algorithms for non-convex cluster recovery.