Clustering to the Fewest Clusters Under Intra-Cluster Dissimilarity Constraints

TL;DR

This paper defines the equiwide clustering problem, which seeks the fewest clusters satisfying intra-cluster dissimilarity constraints, without relying on density or predefined class counts, emphasizing error bounds and optimization strategies.

Contribution

It introduces the novel equiwide clustering problem, analyzes its properties, and evaluates algorithms to balance cluster count and dissimilarity constraints.

Findings

Equiwide clustering ensures an upper bound on object replacement error.

The problem is related to and distinct from existing clustering optimization problems.

Various algorithms offer trade-offs between cluster count and computational efficiency.

Abstract

This paper introduces the equiwide clustering problem, where valid partitions must satisfy intra-cluster dissimilarity constraints. Unlike most existing clustering algorithms, equiwide clustering relies neither on density nor on a predefined number of expected classes, but on a dissimilarity threshold. Its main goal is to ensure an upper bound on the error induced by ultimately replacing any object with its cluster representative. Under this constraint, we then primarily focus on minimizing the number of clusters, along with potential sub-objectives. We argue that equiwide clustering is a sound clustering problem, and discuss its relationship with other optimization problems, existing and novel implementations as well as approximation strategies. We review and evaluate suitable clustering algorithms to identify trade-offs between the various practical solutions for this clustering problem.