A novel initialisation based on hospital-resident assignment for the k-modes algorithm

TL;DR

This paper introduces a novel initialisation method for the k-modes clustering algorithm based on hospital-resident assignment, which improves performance especially on low-density data and when the number of clusters is optimized.

Contribution

The paper proposes a new initialisation technique for k-modes using the Hospital-Resident Assignment Problem, offering fairness and better data leverage compared to existing methods.

Findings

Outperforms existing initialisations on benchmark datasets

Shows superior results on artificial datasets with low-density data

More effective when the number of clusters is optimized

Abstract

This paper presents a new way of selecting an initial solution for the k-modes algorithm that allows for a notion of mathematical fairness and a leverage of the data that the common initialisations from literature do not. The method, which utilises the Hospital-Resident Assignment Problem to find the set of initial cluster centroids, is compared with the current initialisations on both benchmark datasets and a body of newly generated artificial datasets. Based on this analysis, the proposed method is shown to outperform the other initialisations in the majority of cases, especially when the number of clusters is optimised. In addition, we find that our method outperforms the leading established method specifically for low-density data.