Meaning “unique nearest neighbour” (k-NN)












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










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












$begingroup$


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










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










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






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










1 Answer
1






active

oldest

votes


















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









$endgroup$














    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3052204%2fmeaning-unique-nearest-neighbour-k-nn%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    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

        104k1468120




        104k1468120






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3052204%2fmeaning-unique-nearest-neighbour-k-nn%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            Popular posts from this blog

            Bundesstraße 106

            Verónica Boquete

            Ida-Boy-Ed-Garten