Weighted Distance Nearest Neighbor Condensing
Lee-Ad Gottlieb Timor Sharabi Roi Weiss
The problem of nearest neighbor condensing has enjoyed a long history of
study, both in its theoretical and practical aspects. In this paper, we
introduce the problem of weighted distance nearest neighbor condensing, where
one assigns weights to each point of the condensed set, and then new points are
labeled based on their weighted distance nearest neighbor in the condensed set.
  We study the theoretical properties of this new model, and show that it can
produce dramatically better condensing than the standard nearest neighbor rule,
yet is characterized by generalization bounds almost identical to the latter.
We then suggest a condensing heuristic for our new problem. We demonstrate
Bayes consistency for this heuristic, and also show promising empirical
results.