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1-NN learning on Hanan sets
  • Przemysław Śliwiński ,
  • Paweł Wachel ,
  • Jerzy W. Rozenblit
Przemysław Śliwiński
Wrocław University of Science and Technology

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Paweł Wachel
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Jerzy W. Rozenblit
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The output of the nearest neighbor (1-NN) classification rule, gS,q(x), depends on a given learning set SN and on a distance function ρq(x,X).
We show that transforming S_{N} into a set A_{N} whose patterns have a Hanan grid-like structure, results in the equivalence gA,q(x) = gA,p(x) that holds for any NN classifier with distance functions ‖x-X‖q and with any q ∈ (0,∞). Thanks to the equivalence, AN can be used to learn gA,q(x) to mimic a behavior of the classifier gS,p(x) based on the original set SN even when q is unknown (and varying).
Possible application of the proposed framework (inspired also by a time-varying stimuli perception phenomenon) in autism spectrum disorder (ASD) therapeutic tools design is discussed.