Abstract
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.