Sequential clustering with radius and split criteria

• Published in: Central European journal of operations research Vol. 21; no. Suppl 1; pp. 95 - 115
• Main Authors: Mladenovic, Nenad, Hansen, Pierre, Brimberg, Jack
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.06.2013; Springer; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Cluster analysis; Clustering; Clusters; Criteria; Datasets; Electronic data processing; Homogeneity; Management research; Methods; Operations research; Operations Research/Decision Theory; Original Paper; Separation; Sequential scheduling; Studies; United Kingdom; Radius; Sequential; Efficient cluster; Clustering; Split
• ISSN: 1435-246X; 1613-9178
• DOI: 10.1007/s10100-012-0258-3

Sequential clustering aims at determining homogeneous and/or well-separated clusters within a given set of entities, one at a time, until no more such clusters can be found. We consider a bi-criterion sequential clustering problem in which the radius of a cluster (or maximum dissimilarity between an entity chosen as center and any other entity of the cluster) is chosen as a homogeneity criterion and the split of a cluster (or minimum dissimilarity between an entity in the cluster and one outside of it) is chosen as a separation criterion. An O ( N 3 ) algorithm is proposed for determining radii and splits of all efficient clusters, which leads to an O ( N 4 ) algorithm for bi-criterion sequential clustering with radius and split as criteria. This algorithm is illustrated on the well known Ruspini data set.