... Semi-supervised learning finds its way also to cluster-ing tasks. In this case,labeled data are used as constraints in the form of must-linksand cannot-links. In other words, the clustering task ... weighted by ki. Our goal now is to choosethe partitioning regions Rjso that the average riskr ϭM k 1r k P( k )ϭMiϭ1RiM k 1kip(x| k )P( k )dx (2.16)is minimized. ... espe-cially indebted to Kostas Berberidis, Velissar is Gezerlis, Xaris Georgion, KristinaGeorgoulakis, Leyteris Kofidis, Thanassis Liavas, Michalis Mavroforakis, AggelosPikrakis,Thanassis Rontogiannis,...