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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>Hi Calixte,<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>Thanks for your feedback, the beatiful example and very useful script.<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>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:<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>// Replace for instance the three outliers defined in your script by:<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>z(10,10)=50;<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>z(30,20)=50;<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>z(10,40)=50;<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>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.<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'> <o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>A different approach is the Loess method - see for instance W.G. Jacoby (2000).<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>Best regards,<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>Rafael G.<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText>-----Original Message-----<br>From: users-bounces@lists.scilab.org [mailto:users-bounces@lists.scilab.org] On Behalf Of Calixte Denizet<br>Sent: Monday, March 04, 2013 4:01 PM<br>To: users@lists.scilab.org<br>Subject: Re: [Scilab-users] Surface smoothing in Scilab, immune to outliers<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Hi Rafael,<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>You can try to use lsq_splin along the axes x and y.<o:p></o:p></p><p class=MsoPlainText>It seems to work on the following example:<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>x = %pi * [-1:0.05:1]';<o:p></o:p></p><p class=MsoPlainText>z = sin(x)*cos(x)';<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>f = gcf();<o:p></o:p></p><p class=MsoPlainText>f.color_map = jetcolormap(32);<o:p></o:p></p><p class=MsoPlainText>subplot(131);<o:p></o:p></p><p class=MsoPlainText>xtitle("Exact values");<o:p></o:p></p><p class=MsoPlainText>plot3d(x, x, z, 70, 70);<o:p></o:p></p><p class=MsoPlainText>e=gce();<o:p></o:p></p><p class=MsoPlainText>e.color_flag = 1;<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>z = z + 0.5*rand(z);<o:p></o:p></p><p class=MsoPlainText>z(10,10)=5;<o:p></o:p></p><p class=MsoPlainText>z(30,20)=5;<o:p></o:p></p><p class=MsoPlainText>z(10,40)=5;<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>subplot(132);<o:p></o:p></p><p class=MsoPlainText>xtitle("Perturbated values");<o:p></o:p></p><p class=MsoPlainText>plot3d(x, x, z, 70, 70);<o:p></o:p></p><p class=MsoPlainText>e=gce();<o:p></o:p></p><p class=MsoPlainText>e.color_flag = 1;<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>zz=zeros(z);<o:p></o:p></p><p class=MsoPlainText>w=linspace(-%pi,%pi,5)';<o:p></o:p></p><p class=MsoPlainText>for i=1:size(z,'r')<o:p></o:p></p><p class=MsoPlainText>[y,d]=lsq_splin(x', z(i,:), w);<o:p></o:p></p><p class=MsoPlainText>zz(i,:)=interp(x', w, y, d);<o:p></o:p></p><p class=MsoPlainText>end<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>for i=1:size(zz,'c')<o:p></o:p></p><p class=MsoPlainText>[y,d]=lsq_splin(x, zz(:,i), w);<o:p></o:p></p><p class=MsoPlainText>zz(:,i)=interp(x, w, y, d);<o:p></o:p></p><p class=MsoPlainText>end<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>subplot(133);<o:p></o:p></p><p class=MsoPlainText>xtitle("Smoothed values");<o:p></o:p></p><p class=MsoPlainText>plot3d(x, x, zz, 70, 70);<o:p></o:p></p><p class=MsoPlainText>e=gce();<o:p></o:p></p><p class=MsoPlainText>e.color_flag = 1;<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Best regards<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Calixte<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>On 04/03/2013 04:36, Rafael Guerra wrote:<o:p></o:p></p><p class=MsoPlainText>> Hello,<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Does somebody know if there are Scilab functions capable of replacing <o:p></o:p></p><p class=MsoPlainText>> outliers via some local robust fitting in 2D, i.e., that smooths <o:p></o:p></p><p class=MsoPlainText>> experimental data z=f(x,y) and is immune to strong outliers.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> PS: CASCI in Atoms has a lowess function which does this via local <o:p></o:p></p><p class=MsoPlainText>> robust linear fitting but for functions of one variable only.<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> Thanks and regards,<o:p></o:p></p><p class=MsoPlainText>> Rafael Guerra<o:p></o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>><o:p> </o:p></p><p class=MsoPlainText>> --<o:p></o:p></p><p class=MsoPlainText>> View this message in context: <o:p></o:p></p><p class=MsoPlainText>> <a href="http://mailinglists.scilab.org/Surface-smoothing-in-Scilab-immune-to-o"><span style='color:windowtext;text-decoration:none'>http://mailinglists.scilab.org/Surface-smoothing-in-Scilab-immune-to-o</span></a><o:p></o:p></p><p class=MsoPlainText>> utliers-tp4026119.html Sent from the Scilab users - Mailing Lists <o:p></o:p></p><p class=MsoPlainText>> Archives mailing list archive at Nabble.com.<o:p></o:p></p><p class=MsoPlainText>> _______________________________________________<o:p></o:p></p><p class=MsoPlainText>> users mailing list<o:p></o:p></p><p class=MsoPlainText>> <a href="mailto:users@lists.scilab.org"><span style='color:windowtext;text-decoration:none'>users@lists.scilab.org</span></a><o:p></o:p></p><p class=MsoPlainText>> <a href="http://lists.scilab.org/mailman/listinfo/users"><span style='color:windowtext;text-decoration:none'>http://lists.scilab.org/mailman/listinfo/users</span></a><o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>--<o:p></o:p></p><p class=MsoPlainText>Calixte Denizet<o:p></o:p></p><p class=MsoPlainText>Software Development Engineer<o:p></o:p></p><p class=MsoPlainText>-----------------------------------------------------------<o:p></o:p></p><p class=MsoPlainText>Scilab Enterprises<o:p></o:p></p><p class=MsoPlainText>143bis rue Yves Le Coz - 78000 Versailles, France <a href="http://www.scilab-enterprises.com"><span style='color:windowtext;text-decoration:none'>http://www.scilab-enterprises.com</span></a><o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>_______________________________________________<o:p></o:p></p><p class=MsoPlainText>users mailing list<o:p></o:p></p><p class=MsoPlainText><a href="mailto:users@lists.scilab.org"><span style='color:windowtext;text-decoration:none'>users@lists.scilab.org</span></a><o:p></o:p></p><p class=MsoPlainText><a href="http://lists.scilab.org/mailman/listinfo/users"><span style='color:windowtext;text-decoration:none'>http://lists.scilab.org/mailman/listinfo/users</span></a><o:p></o:p></p></div></body></html>