Comparing clustering solutions: The use of adjusted paired indices

Article type: Research Article

Authors: Amorim, Maria José^a | Cardoso, Margarida G.M.S.^{b; *}

Affiliations: [a] Department of Mathematics of ISEL and UNIDE Lisboa, Portugal | [b] UNIDE and Department of Quantitative Methods for Management and Economics of ISCTE, Lisbon University Institute, Lisbon, Portugal

Correspondence: [*] Corresponding author: Margarida G.M.S. Cardoso, UNIDE and Department of Quantitative Methods for Management and Economics of ISCTE - Lisbon University Institute, Lisboa 1649-026, Portugal. Tel.: +351 21 7903264; E-mail:[email protected]

Abstract: In the present paper we compare clustering solutions using indices of paired agreement. We propose a new method - IADJUST - to correct indices of paired agreement, excluding agreement by chance. This new method overcomes previous limitations known in the literature as it permits the correction of any index. We illustrate its use in external clustering validation, to measure the accordance between clusters and an a priori known structure. The adjusted indices are intended to provide a realistic measure of clustering performance that excludes agreement by chance with ground truth. We use simulated data sets, under a range of scenarios - considering diverse numbers of clusters, clusters overlaps and balances - to discuss the pertinence and the precision of our proposal. Precision is established based on comparisons with the analytical approach for correction - specific indices that can be corrected in this way are used for this purpose. The pertinence of the proposed correction is discussed when making a detailed comparison between the performance of two classical clustering approaches, namely Expectation-Maximization (EM) and K-Means (KM) algorithms. Eight indices of paired agreement are studied and new corrected indices are obtained.

Keywords: Adjusted indices, indices of paired agreement, clustering evaluation, external evaluation

DOI: 10.3233/IDA-150782

Journal: Intelligent Data Analysis, vol. 19, no. 6, pp. 1275-1296, 2015