Meaning “unique nearest neighbour” (k-NN)












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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?



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  • $begingroup$
    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.
    $endgroup$
    – leonbloy
    Dec 25 '18 at 15:39
















0












$begingroup$


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






machine-learning







share|cite|improve this question









$endgroup$












  • $begingroup$
    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.
    $endgroup$
    – leonbloy
    Dec 25 '18 at 15:39














0












0








0





$begingroup$


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






machine-learning







share|cite|improve this question









$endgroup$




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






machine-learning




machine-learning






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 25 '18 at 15:33









Tommaso BendinelliTommaso Bendinelli

14110




14110












  • $begingroup$
    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.
    $endgroup$
    – leonbloy
    Dec 25 '18 at 15:39


















  • $begingroup$
    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.
    $endgroup$
    – leonbloy
    Dec 25 '18 at 15:39
















$begingroup$
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.
$endgroup$
– leonbloy
Dec 25 '18 at 15:39




$begingroup$
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.
$endgroup$
– 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.






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    1 Answer
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    1 Answer
    1






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    active

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    1












    $begingroup$

    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.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      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.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        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.






        share|cite|improve this answer









        $endgroup$



        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 25 '18 at 15:49









        Siong Thye GohSiong Thye Goh

        102k1466118




        102k1466118






























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