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1-NN learning on Hanan sets

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posted on 14.04.2022, 21:14 authored by Przemysław ŚliwińskiPrzemysław Śliwiński, Paweł Wachel, Jerzy W. Rozenblit

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.

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Email Address of Submitting Author

Przemyslaw.Sliwinski@pwr.edu.pl

ORCID of Submitting Author

0000-0003-3839-1580

Submitting Author's Institution

Wrocław University of Science and Technology

Submitting Author's Country

Poland

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