[Scilab-users] Surface smoothing in Scilab, immune to outliers

[Calixte Denizet]

Hi Rafael,

you are right: when the magnitude of the outliers is too large, 
lsq_splin is not always good. But if you increase the number of points, 
you could have something better (with the same example (ie 50 rather 
than 5) replace x by x = %pi * [-1:0.01:1]').

Best regards

Calixte

On 05/03/2013 04:15, Rafael Guerra wrote:
>
> Hi Calixte,
>
> Thanks for your feedback, the beatiful example and very useful script.
>
> The weighted least squares cubic spline fitting function (lsq_splin) 
> seems to work very well for outliers of moderate magnitude. However, 
> it seems to fail for larger outliers:
>
> // Replace for instance the three outliers defined in your script by:
>
> z(10,10)=50;
>
> z(30,20)=50;
>
> z(10,40)=50;
>
> Sinha and Schunck (1992) address this problem using a two-stage 
> procedure, where a robust local algorithm MLMS (moving least median of 
> squares of error) is run first to get rid of the outliers. Thereafter, 
> weighted least squares cubic splines are used. MLMS seems very 
> computationally intensive.
>
> A different approach is the Loess method - see for instance W.G. 
> Jacoby (2000).
>
> Best regards,
>
> Rafael G.
>
> -----Original Message-----
> From: users-bounces at lists.scilab.org 
> [mailto:users-bounces at lists.scilab.org] On Behalf Of Calixte Denizet
> Sent: Monday, March 04, 2013 4:01 PM
> To: users at lists.scilab.org
> Subject: Re: [Scilab-users] Surface smoothing in Scilab, immune to 
> outliers
>
> Hi Rafael,
>
> You can try to use lsq_splin along the axes x and y.
>
> It seems to work on the following example:
>
> x = %pi * [-1:0.05:1]';
>
> z = sin(x)*cos(x)';
>
> f = gcf();
>
> f.color_map = jetcolormap(32);
>
> subplot(131);
>
> xtitle("Exact values");
>
> plot3d(x, x, z, 70, 70);
>
> e=gce();
>
> e.color_flag = 1;
>
> z = z + 0.5*rand(z);
>
> z(10,10)=5;
>
> z(30,20)=5;
>
> z(10,40)=5;
>
> subplot(132);
>
> xtitle("Perturbated values");
>
> plot3d(x, x, z, 70, 70);
>
> e=gce();
>
> e.color_flag = 1;
>
> zz=zeros(z);
>
> w=linspace(-%pi,%pi,5)';
>
> for i=1:size(z,'r')
>
> [y,d]=lsq_splin(x', z(i,:), w);
>
> zz(i,:)=interp(x', w, y, d);
>
> end
>
> for i=1:size(zz,'c')
>
> [y,d]=lsq_splin(x, zz(:,i), w);
>
> zz(:,i)=interp(x, w, y, d);
>
> end
>
> subplot(133);
>
> xtitle("Smoothed values");
>
> plot3d(x, x, zz, 70, 70);
>
> e=gce();
>
> e.color_flag = 1;
>
> Best regards
>
> Calixte
>
> On 04/03/2013 04:36, Rafael Guerra wrote:
>
> > Hello,
>
> >
>
> > Does somebody know if there are Scilab functions capable of replacing
>
> > outliers via some local robust fitting in 2D, i.e., that smooths
>
> > experimental data z=f(x,y) and is immune to strong outliers.
>
> >
>
> > PS: CASCI in Atoms has a lowess function which does this via local
>
> > robust linear fitting but for functions of one variable only.
>
> >
>
> > Thanks and regards,
>
> > Rafael Guerra
>
> >
>
> >
>
> >
>
> >
>
> > --
>
> > View this message in context:
>
> > http://mailinglists.scilab.org/Surface-smoothing-in-Scilab-immune-to-o
>
> > utliers-tp4026119.html Sent from the Scilab users - Mailing Lists
>
> > Archives mailing list archive at Nabble.com.
>
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>
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>
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>
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> --
>
> Calixte Denizet
>
> Software Development Engineer
>
> -----------------------------------------------------------
>
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>
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> http://www.scilab-enterprises.com
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-- 
Calixte Denizet
Software Development Engineer
-----------------------------------------------------------
Scilab Enterprises
143bis rue Yves Le Coz - 78000 Versailles, France
http://www.scilab-enterprises.com

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