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I'm doing an exercise about k-NN, k-Neighbor classifier. And I don't understand the following sentence:

Show that for all x ∈ $R^d$ which have a unique nearest neighbor amongst the points in {x1, . . . , xn} there exists an $h_0 > 0$ such that for all $h < h_0$ the resulting SVM prediction is the same as the prediction made by a Nearest Neighbor (1-NN) classifier.

What is meant by unique nearest neighbor? I know what k-Neighbour classifier is, but what is the nearest neighbor?

Happy Holidays

Tommaso Bendinelli
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  • The nearest neighbor... is the neighbor that is nearest. Seriously, if you know what a $k-$(nearest)-neighbor classifier is, you should know what a nearest neighbor is. I'm nor sure what is your doubt. – leonbloy Dec 25 '18 at 15:39

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Sometimes it is possible to have neighbors that are equidistance.

The question is describing points of which there is exactly one nearest neighbors, those points do not have two neighbors that share the minimum distance from it.

Siong Thye Goh
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