Imbalanced　classification　is　a　challenging　problem.　Re-sampling　and　cost-sensitive　learning　are　global　strategies　for　generality-oriented　algorithms　such　as　the　decision　tree,　targeting　inter-class　imbalance.　We　research　local　strategies　for　the　specificity-oriented　learning　algorithms　like　the　k　Nearest　Neighbour　(KNN)　to　address　the　within-class　imbalance　issue　of　positive　data　sparsity.　We　propose　an　algorithm　k　Rare-class　Nearest　Neighbour,　or　KRNN,　by　directly　adjusting　the　induction　bias　of　KNN.　We　propose　to　form　dynamic　query　neighbourhoods,　and　to　further　adjust　the　positive　posterior　probability　estimation　to　bias　classification　towards　the　rare　class.　We　conducted　extensive　experiments　on　thirty　real-world　and　artificial　datasets　to　evaluate　the　performance　of　KRNN.　Our　experiments　showed　that　KRNN　significantly　improved　KNN　for　classification　of　the　rare　class,　and　often　outperformed　re-sampling　and　cost-sensitive　learning　strategies　with　generality-oriented　base　learners.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.