Minimum adjusted Rand index for two clusterings of a given size
José E. Chacón, Ana I. Rastrojo
Abstract
Abstract The adjusted Rand index (ARI) is commonly used in cluster analysis to measure the degree of agreement between two data partitions. Since its introduction, exploring the situations of extreme agreement and disagreement under different circumstances has been a subject of interest, in order to achieve a better understanding of this index. Here, an explicit formula for the lowest possible value of the ARI for two clusterings of given sizes is shown, and moreover a specific pair of clusterings achieving such a bound is provided.
Topics & Concepts
Index (typography)Measure (data warehouse)MathematicsStatisticsDegree (music)Cluster (spacecraft)Value (mathematics)Rand indexEconometricsComputer scienceData miningCluster analysisPhysicsProgramming languageAcousticsWorld Wide WebAdvanced Clustering Algorithms ResearchSensory Analysis and Statistical MethodsData Management and Algorithms