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This article is part of the supplement: Computational Intelligence in Bioinformatics and Biostatistics: new trends from the CIBB conference series

Open Access Research

Finding reproducible cluster partitions for the k-means algorithm

Paulo JG Lisboa, Terence A Etchells, Ian H Jarman* and Simon J Chambers

Author Affiliations

School of Computing and Mathematical Sciences, Byrom Street, Liverpool John Moores University, Liverpool L3 3AF, UK

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BMC Bioinformatics 2013, 14(Suppl 1):S8  doi:10.1186/1471-2105-14-S1-S8

Published: 14 January 2013


K-means clustering is widely used for exploratory data analysis. While its dependence on initialisation is well-known, it is common practice to assume that the partition with lowest sum-of-squares (SSQ) total i.e. within cluster variance, is both reproducible under repeated initialisations and also the closest that k-means can provide to true structure, when applied to synthetic data. We show that this is generally the case for small numbers of clusters, but for values of k that are still of theoretical and practical interest, similar values of SSQ can correspond to markedly different cluster partitions.

This paper extends stability measures previously presented in the context of finding optimal values of cluster number, into a component of a 2-d map of the local minima found by the k-means algorithm, from which not only can values of k be identified for further analysis but, more importantly, it is made clear whether the best SSQ is a suitable solution or whether obtaining a consistently good partition requires further application of the stability index. The proposed method is illustrated by application to five synthetic datasets replicating a real world breast cancer dataset with varying data density, and a large bioinformatics dataset.