NP-completeness of the problem of prototype selection in the nearest neighbor method

  • Authors:
  • A. V. Zukhba

  • Affiliations:
  • Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow Region, Russia 141700

  • Venue:
  • Pattern Recognition and Image Analysis
  • Year:
  • 2010

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Abstract

The problem of selecting of prototypes is to select a subset in the learning sample for which the set of minimum cardinality would provide the optimum of a given learning quality functional. In this article the problem of classification is considered in two classes, the method of classification by nearest neighbor, and three functional characteristics: the frequency of errors on the entire sample, a cross validation with one separated object, and a complete cross validation with k separated objects. It is shown that the problem of selection of prototypes in all three cases is NP-complete, which justifies the use of well-known heuristic methods for the prototype search.