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| Can not make Penalized regression spline flexible enought http://forum.alglib.net/viewtopic.php?f=2&t=292 |
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| Author: | mamitko [ Fri Feb 04, 2011 8:57 am ] |
| Post subject: | Can not make Penalized regression spline flexible enought |
Hello, Sergey. Some time ago you advised me to use penalized regression splines http://forum.alglib.net/viewtopic.php?f=2&t=73 It was not implemented at that time but now it has been . I'm trying to buld a spline using spline1dfitpenalized() and getting "not enought flexible" spline even with very small Rho value. (m = n*3 as you advised). Generally origin points are quite "spased" but there are "ranges" where they are close. And there are no cases when the are making smth like a "cloud". Is there any way to make this spline more flexible? If it metters I'm trying to build a "2D spline". I have 2D points, make two series of points (L, X) and (L, Y) where L is polyline length from start of 2D points series. Then I build to splines using spline1dfitpenalized() routine. Any way, thank you and sorry for horrible English in your forum. |
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| Author: | Sergey.Bochkanov [ Fri Feb 04, 2011 8:58 pm ] |
| Post subject: | Re: Can not make Penalized regression spline flexible enough |
You can't build 2D spline as combination of two 1D splines. That is the root of your problem. Even with very flexible spline you won't get good results - just because you can't decompose general 2D function into sum of two 1D functions. Your problem with penalized spline is a consequence of what was said above. Points which are close at one axis (X or Y) are in fact far away from each other at the XY-plane, and you will always have problems with wild oscillations in the function. P.S. As for English - it is OK, my English isn't perfect too. |
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| Author: | mamitko [ Sat Feb 05, 2011 3:14 am ] |
| Post subject: | Re: Can not make Penalized regression spline flexible enough |
I used a cubic smoothing spline from this book before exactly the same way (two slines for X and for Y coordinates of origin 2D) and got relativle good results. The problems were: (1) spline was sensitive to "frequency" of points and local single deviations. (2) I could not find fast way to solve system of linear equations with "pentadiagonal" matrix. I'm not trying to cast a doubt on your message before, but could you explane a "nature" of difference in this two cases? ("wrong way" of using Smoothed cubic and Regression splines) And could you advise smth to read about how to build smoothing 2D splines? Thank you! |
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| Author: | mamitko [ Sat Feb 05, 2011 11:07 am ] |
| Post subject: | Re: Can not make Penalized regression spline flexible enough |
I'm realy sorry. I was using small "m" value (not n*3 as I wrote). Now it works relativle fine. Thank you for greate library. Could you advise somthing about fast solving system of linear equations with 5 non-zero diagonals (the main one and 2 above and below)? |
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| Author: | Sergey.Bochkanov [ Mon Feb 07, 2011 9:41 am ] |
| Post subject: | Re: Can not make Penalized regression spline flexible enough |
If you need direct algorithm, you can take a look at LAPACK. It contains functions for factorization of band matrices. Another solution is to use linear conjugate gradient, but it can be less precise than direct algo. |
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