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

Abstract

This paper presents a new way of selecting an initialisation for the $$k$$ k -modes algorithm that allows for a notion of game theoretic fairness that classic initialisations, namely those by Huang and Cao, do not. Our new method utilises the hospital-resident assignment problem to find the set of initial cluster centroids which we compare with two classical initialisation methods for $$k$$ k -modes: the original presented by Huang and the next most popular method of Cao and co-authors. To highlight the merits of our proposed method, two stages of analysis are presented. It is demonstrated that the proposed method is often able to offer computational speed-up of the order of $$50\%$$ 50 % . Improved clustering, in terms of a commonly used cost-function, was witnessed in several cases and can be of the order of $$10\%$$ 10 % , particularly for more complex datasets.