Condensed and Edited Nearest Neighbor Rules

Abstract

Condensing is the process by which we eliminate data points, yet keep the same behavior. For example, in the nearest neighbor rule, by condensing we might mean the reduction of (X ₁, Y ₁,...,(X _n , Y _n to (X´₁, Y´₁),...,(X´ _m , Y´ _m ) such that for all x ∈ R ^d, the 1-nn rule is identical based on the two samples. This will be called pure condensing. This operation has no effect on L _n , and therefore is recommended whenever space is at a premium. The space savings should be substantial whenever the classes are separated. Unfortunately, pure condensing is computationally expensive, and offers no hope of improving upon the performance of the ordinary 1-nn rule.