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Equation of relation that has mulitple y points

  1. Mar 12, 2009 #1
    Hi, well I need something close to curve fitting. But I am not sure if it could serve the purpose. The problem is as below:
    Suppose, I have the following relation X r Y. Here X is a natural number set. Suppose we have "k" sets,D1,D2,..Dk of selected datapoints over natural number, such that the intersection of all Di's is null set. Let Y be a set of all Di's.

    The relation relates every x, to a set of possible data point sets in Y.

    As an example see this, here we have k=3.

    X Y
    1 {2, 4, 5, 10, 12, 13 }
    2 { 3,7,8,9,11,14}
    3 {1,6, 15,17, 20, 22}
    4 {2, 4, 5, 10, 12, 13 }
    5 { 3,7,8,9,11,14}

    The question is to find the Smallest equation/function F that Exactly fits the given data in such a way that F(x) just outputs any one of the datapoint from the Di. I do not need the whole Di.Just any one of the value from Di.

    As an example, the F may be

    X Y
    1 2
    2 3
    3 1
    4 2
    5 3

    I need to find the relation F :)




    Well, I am looking for the smallest degree function. There is no restriction that it should be polynomial even.( May be aCos(x)+bSin(x) etc. ). What I am looking for is a technique that can take advantage of the fact that it has multiple candidate y points for each x. Many traditional curve fitting techniques tend to fit the curve around one y point.

    My hypothesis is that since we have multiple candidate y points for each x, one can exploit this redundancy, and might be able to get a function much smaller than (n-1) polynomial. How true is this ?


    If you know that I have chosen the wrong forum, please point me to the right place. Thanks
     
    Last edited: Mar 13, 2009
  2. jcsd
  3. Mar 13, 2009 #2

    HallsofIvy

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  4. Mar 13, 2009 #3
    Well, I am looking for the smallest degree function. There is no restriction that it should be polynomial even.( May be aCos(x)+bSin(x) etc. ). What I am looking for is a technique that can take advantage of the fact that it has multiple candidate y points for each x. Many traditional curve fitting techniques tend to fit the curve around one y point.

    My hypothesis is that since we have multiple candidate y points for each x, one can exploit this redundancy, and might be able to get a function much smaller than (n-1) polynomial. How true is this?
     
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