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Thread Subject:
Thin-plate splines?

Subject: Thin-plate splines?

From: dpdoughe@my-deja.com

Date: 6 Sep, 2000 16:36:11

Message: 1 of 3

In order to determine the optimal smoothing parameter for 1D data using
the spline toolbox I can minimize the leave-one-out prediction error
using any number of iterative optimization approachs (fminsearch, etc).

The problem here is that this is very slow _and_ due to the requirement
that input be gridded (see csaps), I can not use this approach for 2D
surface splines.

Does anyone know of matlab code for doing thin-plate splines? I am
looking for code that uses generalized cross-validation to determine the
optimal smoothing parameter quickly for data surfaces.

Although spaps allows smoothing constrained on the maximum interpolation
error I don't think this is general enough for the many automated
numerical tasks that smoothing splines can be used for (e.g. unbiased
derivative estimation,...)

Thanks.



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Before you buy.

Subject: Thin-plate splines?

From: Matthew C Roberts

Date: 7 Sep, 2000 15:44:31

Message: 2 of 3

<dpdoughe@my-deja.com> wrote in message news:8p5rpp$rsq$1@nnrp1.deja.com...
> In order to determine the optimal smoothing parameter for 1D data using
> the spline toolbox I can minimize the leave-one-out prediction error
> using any number of iterative optimization approachs (fminsearch, etc).
>
> The problem here is that this is very slow _and_ due to the requirement
> that input be gridded (see csaps), I can not use this approach for 2D
> surface splines.
Check out
  author = "P. J. Green and B. W. Silverman",
  title = "Nonparametric Regression and Generalized Linear Models",
  publisher = "Chapman and Hall",
  year = "1994",
  volume = "58",
  series = "Monographs on Statistics and Probability",
  address = "London, UK"
it has a description of a an analytical approach to determining the
smoothing parameter by GCV. I haven't implemented the whole thing (I can't
use OLS in my problems), but I have implemented code that generates most of
the matrices involved.

I think that it is actually included in the ML spline toolbox, too, but I
don't know this for certain.
Let me know if I can be of any more help.

>
> Does anyone know of matlab code for doing thin-plate splines? I am
> looking for code that uses generalized cross-validation to determine the
> optimal smoothing parameter quickly for data surfaces.
>
> Although spaps allows smoothing constrained on the maximum interpolation
> error I don't think this is general enough for the many automated
> numerical tasks that smoothing splines can be used for (e.g. unbiased
> derivative estimation,...)

--
Matthew C Roberts
Graduate Student
Department of Economics
NC State University

iday_amspay@DIESPAMDIEhotmail.com
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Subject: Thin-plate splines?

From: G. Anthony Reina

Date: 11 Sep, 2000 10:59:05

Message: 3 of 3



>
> > Does anyone know of matlab code for doing thin-plate splines? I am
> > looking for code that uses generalized cross-validation to determine the
> > optimal smoothing parameter quickly for data surfaces.
> >
> > Although spaps allows smoothing constrained on the maximum interpolation
> > error I don't think this is general enough for the many automated
> > numerical tasks that smoothing splines can be used for (e.g. unbiased
> > derivative estimation,...)
>

I'm not familiar with the term "thin-plate" but I have a spline that does GCV.
The algorithm was created by Herman Woltring and has been implemented in
MATLAB as a mex function.

http://isb.ri.ccf.org/software/gcvspl/reina/

-Tony Reina

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