Convex group clustering of large geo-referenced data sets

Clustering partitions a data set S = fs1; : : : ; sng < into groups of nearby points. Distance-based clustering methods use optimisation criteria to de ne the quality of a partition. Formulations using representatives (means or medians of groups) have received much more attention than minimisation of the total within group distance (TWGD). However, this non-representative approach has attractive properties while remaining distance-based. While representative approaches produce partitions with non-overlapping clusters, TWGD does not. We investigate the restriction of TWGD to producing convex-hull disjoint groups and show that this problem is NP-complete in the Euclidean case as soon as m 2. Nevertheless we provide e cient algorithms for solving it approximately.