NEAREST NEIGHBOR PROBLEMS

Suppose E is a set of labeled points (examples) in some metric space. A subset C of E is said to be a consistent subset of E if it has the property that for any example e E E, the label of the closest example in C to e is the same as the label of e. We consider the problem of computing a minimum cardinality consistent subset. Consistent subsets have applications in pattern classification schemes that are based on the nearest neighbor rule. The idea is to replace the training set of examples with as small a consistent subset as possible so as to improve the efficiency of the system while not significantly affecting its accuracy. The problem of finding a minimum size consistent subset of a set of examples is shown to be NP-complete. A special case is described and is shown to be equivalent to an optimal disc cover problem. A polynomial time algorithm for this optimal disc cover problem is then given.