Near-optimal sample compression for nearest neighbors
  We present the first sample compression algorithm for nearest neighbors with non-trivial performance guarantees. We complement these guarantees by demonstrating almost matching hardness lower bounds, which show that our bound is nearly optimal. Our result yields new insight into margin-based nearest neighbor classification in metric spaces and allows us to significantly sharpen and simplify existing bounds. Some encouraging empirical results are also presented. 
Lee-Ad Gottlieb and Aryeh Kontorovich and Pinhas Nisnevitch
cs.LG cs.CC