Adaptive knot selection for B-spline fitting.











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When fitting a B-spline for regression purposes I've seen a lot of cases where knots are fixed uniformly ,but in some situations this could lead to poor estimations because the behaviour of the curve is not uniform. Knots should be denser when function changes rapidly to capture those "high frequency" moves. I've read some papers that propose different methods to fit adaptive knots, by pruning knots , by fitting multi-resolution basis, etc.
My idea (it's just that, an idea) is to use the short time Fourier transform to determine the intervals where higher frequencies are present, and hence to fix denser knots in these, and on the other hand to figure out where the low frequencies are more important and hence to fix more sparse knots.
Is this theoretically correct? Maybe it's already been done , but honestly I didn't find anything online.
Any hint or suggestions will be greatly appreciated.










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    When fitting a B-spline for regression purposes I've seen a lot of cases where knots are fixed uniformly ,but in some situations this could lead to poor estimations because the behaviour of the curve is not uniform. Knots should be denser when function changes rapidly to capture those "high frequency" moves. I've read some papers that propose different methods to fit adaptive knots, by pruning knots , by fitting multi-resolution basis, etc.
    My idea (it's just that, an idea) is to use the short time Fourier transform to determine the intervals where higher frequencies are present, and hence to fix denser knots in these, and on the other hand to figure out where the low frequencies are more important and hence to fix more sparse knots.
    Is this theoretically correct? Maybe it's already been done , but honestly I didn't find anything online.
    Any hint or suggestions will be greatly appreciated.










    share|cite|improve this question
























      up vote
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      down vote

      favorite









      up vote
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      down vote

      favorite











      When fitting a B-spline for regression purposes I've seen a lot of cases where knots are fixed uniformly ,but in some situations this could lead to poor estimations because the behaviour of the curve is not uniform. Knots should be denser when function changes rapidly to capture those "high frequency" moves. I've read some papers that propose different methods to fit adaptive knots, by pruning knots , by fitting multi-resolution basis, etc.
      My idea (it's just that, an idea) is to use the short time Fourier transform to determine the intervals where higher frequencies are present, and hence to fix denser knots in these, and on the other hand to figure out where the low frequencies are more important and hence to fix more sparse knots.
      Is this theoretically correct? Maybe it's already been done , but honestly I didn't find anything online.
      Any hint or suggestions will be greatly appreciated.










      share|cite|improve this question













      When fitting a B-spline for regression purposes I've seen a lot of cases where knots are fixed uniformly ,but in some situations this could lead to poor estimations because the behaviour of the curve is not uniform. Knots should be denser when function changes rapidly to capture those "high frequency" moves. I've read some papers that propose different methods to fit adaptive knots, by pruning knots , by fitting multi-resolution basis, etc.
      My idea (it's just that, an idea) is to use the short time Fourier transform to determine the intervals where higher frequencies are present, and hence to fix denser knots in these, and on the other hand to figure out where the low frequencies are more important and hence to fix more sparse knots.
      Is this theoretically correct? Maybe it's already been done , but honestly I didn't find anything online.
      Any hint or suggestions will be greatly appreciated.







      fourier-transform change-of-basis spline






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      asked Dec 1 at 13:00









      Ramiro Scorolli

      62813




      62813






















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          If I properly remember, around $1978$, Carl de Boor published a book "A Practical Guide to Splines" in which is described the optimal knot sequence for splines. This was implemented in subroutine $BSOPK$ in $IMSL$ which I used in the past.



          On the other side, I just found this document "Spline Regression with Automatic Knot Selection" which appeared in $2018$.



          I hope and wish this could be of some help to you.






          share|cite|improve this answer





















          • I've read this article, in any case what I wanted to do is to propose some new method in order to find optimal knots. Thanks for your answer.
            – Ramiro Scorolli
            9 hours ago











          Your Answer





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          up vote
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          down vote













          If I properly remember, around $1978$, Carl de Boor published a book "A Practical Guide to Splines" in which is described the optimal knot sequence for splines. This was implemented in subroutine $BSOPK$ in $IMSL$ which I used in the past.



          On the other side, I just found this document "Spline Regression with Automatic Knot Selection" which appeared in $2018$.



          I hope and wish this could be of some help to you.






          share|cite|improve this answer





















          • I've read this article, in any case what I wanted to do is to propose some new method in order to find optimal knots. Thanks for your answer.
            – Ramiro Scorolli
            9 hours ago















          up vote
          1
          down vote













          If I properly remember, around $1978$, Carl de Boor published a book "A Practical Guide to Splines" in which is described the optimal knot sequence for splines. This was implemented in subroutine $BSOPK$ in $IMSL$ which I used in the past.



          On the other side, I just found this document "Spline Regression with Automatic Knot Selection" which appeared in $2018$.



          I hope and wish this could be of some help to you.






          share|cite|improve this answer





















          • I've read this article, in any case what I wanted to do is to propose some new method in order to find optimal knots. Thanks for your answer.
            – Ramiro Scorolli
            9 hours ago













          up vote
          1
          down vote










          up vote
          1
          down vote









          If I properly remember, around $1978$, Carl de Boor published a book "A Practical Guide to Splines" in which is described the optimal knot sequence for splines. This was implemented in subroutine $BSOPK$ in $IMSL$ which I used in the past.



          On the other side, I just found this document "Spline Regression with Automatic Knot Selection" which appeared in $2018$.



          I hope and wish this could be of some help to you.






          share|cite|improve this answer












          If I properly remember, around $1978$, Carl de Boor published a book "A Practical Guide to Splines" in which is described the optimal knot sequence for splines. This was implemented in subroutine $BSOPK$ in $IMSL$ which I used in the past.



          On the other side, I just found this document "Spline Regression with Automatic Knot Selection" which appeared in $2018$.



          I hope and wish this could be of some help to you.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 2 days ago









          Claude Leibovici

          117k1156131




          117k1156131












          • I've read this article, in any case what I wanted to do is to propose some new method in order to find optimal knots. Thanks for your answer.
            – Ramiro Scorolli
            9 hours ago


















          • I've read this article, in any case what I wanted to do is to propose some new method in order to find optimal knots. Thanks for your answer.
            – Ramiro Scorolli
            9 hours ago
















          I've read this article, in any case what I wanted to do is to propose some new method in order to find optimal knots. Thanks for your answer.
          – Ramiro Scorolli
          9 hours ago




          I've read this article, in any case what I wanted to do is to propose some new method in order to find optimal knots. Thanks for your answer.
          – Ramiro Scorolli
          9 hours ago


















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