Spatially-Aware Comparison and Consensus for Clusterings

TL;DR

This paper introduces a spatially-aware distance metric for clusterings, leveraging Hilbert space representations to improve consensus clustering, with demonstrated efficiency and quality through experiments.

Contribution

It presents a novel spatially-aware clustering distance metric and a consensus clustering method based on Hilbert space representations, enhancing clustering comparison and aggregation.

Findings

The proposed metric effectively captures spatial information in clusterings.

The consensus clustering method is simple, efficient, and applicable to soft and hard clusterings.

Experimental results show improved clustering quality and computational efficiency.

Abstract

This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a combination of the representations of their constituent points. We use this representation and the underlying metric to design a spatially-aware consensus clustering procedure. This consensus procedure is implemented via a novel reduction to Euclidean clustering, and is both simple and efficient. All of our results apply to both soft and hard clusterings. We accompany these algorithms with a detailed experimental evaluation that demonstrates the efficiency and quality of our techniques.