Subject: Re: MDS distances From: Olivier Tache <olivier.tache@xxxxxxxx> Date: Wed, 21 Jun 2006 11:54:37 +0200This is a multi-part message in MIME format. --------------080609080105050401020205 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: quoted-printable X-MIME-Autoconverted: from 8bit to quoted-printable by drizzle.cc.mcgill.ca id k5L9uGdC027864 Dear Jim, Like Jan, i would be very interested by the results of the sanity checks=20 he suggests. I have read a number of "classical" papers about MDS and auditory=20 dissimilarity (by Gordon&Grey, Grey&Moorer, Wessel) (and was wondering=20 if such experiments were still carried out). These studies usually led=20 to 3D sound spaces, so the result you report is indeed quite suprising.=20 I'm wondering what kind of sounds you are using. Do they have the same=20 length ? pitch? Do they have really different timbre? Past studies used=20 to test short sounds with equal pitches. The high number of dimension=20 you obtain might come from the fact you are using a less homogeneous set=20 of sounds. Best Regards, Olivier Jan Schnupp a =C3=A9crit : > Dear Jim, > > I think the motivation behind your MDS question is a very interesting=20 > one. To me it seems that there are two likely possibilities. > > -one is that "auditory dissimilarity" is truly quite high-dimensional,=20 > so Matlab did not manage to project the data into a low dimensional=20 > space because it simply cannot be done, and even reducing the=20 > dimensionality just a little bit from 10 to 8 leads to appreciable=20 > distoritions (i.e. "error"), > > -the other (which seems to be the possibility you are asking about) is=20 > that Matlab's algorithm doesn't work properly. However, you could=20 > quite easily "sanity check" Matlab's algorithm: Just draw ten points=20 > randomly on (2-dimensional) graph paper, measure their pairwise=20 > distances, and feed those into the Matlab MDS algorithm. If Matlab=20 > does its job right it should give you a 2 D solution with errors no=20 > larger than the measurement errors you would expect from holding your=20 > ruler up to the points on your paper. In fact, it should be easily be=20 > possible to "virtualize" and automate his sort of sanity check by=20 > letting random numbers generate points in space of any dimensionality=20 > you choose and work out relative pairwise distances using Pythagoras.=20 > Once you have automated code that does this you could run hundreds of=20 > sanity checks like that you should know pretty quickly how far you can=20 > trust Matlab's algorithm. And I hope you will let us know the answer.=20 > I, for one, would not be too surprised if it turned out that sounds=20 > could sound dissimilar on at least 8 "different dimensions". > > Best wishes, > > Jan > > On 15/06/06, *beaucham* <beaucham@xxxxxxxx=20 > <mailto:beaucham@xxxxxxxx>> wrote: > > We ran an MDS calculation (using MatLab) on a 10x10 distance > matrix based on dissimilarity judgements between all pairs of > 10 sounds, and obtained an 8-dimension solution, which gives > the coordinates of the sounds in 8-D space. The distances > between the positions of the sounds are supposed to match > the original distances. In fact, we get an rms error of 8% > and a max error of 30%. > > Is this typical? Is MatLab's program accurate? Is there a way > to improve on the MDS results? > > Jim Beauchamp > Univ. of Illinois Urbana-Champaign > jwbeauch@xxxxxxxx <mailto:jwbeauch@xxxxxxxx> > > > > > --=20 > Dr Jan Schnupp > University of Oxford > Dept. of Physiology, Anatomy and Genetics > Sherrington Building - Parks Road > Oxford OX1 3PT - UK > +44-1865-272513 > www.oxfordhearing.com <http://www.oxfordhearing.com>=20 --=20 Olivier Tache Associate Researcher - Doctorate Applicant Laboratoire Informatique et Cr=C3=A9ation Artistique INPG, 46, av. F=C3=A9lix Viallet 38031 Grenoble Cedex, France Tel. +33 (0) 476574660 Fax +33 (0) 476574889 --------------080609080105050401020205 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-MIME-Autoconverted: from 8bit to quoted-printable by drizzle.cc.mcgill.ca id k5L9uGdC027864 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content=3D"text/html;charset=3DUTF-8" http-equiv=3D"Content-Type"= > </head> <body bgcolor=3D"#ffffff" text=3D"#000000"> Dear Jim,<br> <br> Like Jan, i would be very interested by the results of the sanity checks he suggests.<br> I have read a number of "classical" papers about MDS and auditory dissimilarity (by Gordon&Grey, Grey&Moorer, Wessel) (and was wondering if such experiments were still carried out).=C2=A0 These studie= s usually led to 3D sound spaces, so the result you report is indeed quite suprising. I'm wondering what kind of sounds you are using. Do they have the same length ? pitch? Do they have really different timbre? Past studies used to test short sounds with equal pitches. The high number of dimension you obtain might come from the fact you are using a less homogeneous set of sounds. <br> <br> Best Regards,<br> <br> Olivier<br> <br> <br> Jan Schnupp a =C3=A9crit=C2=A0: <blockquote cite=3D"mid9c1a4ffb0606210211y40a45568wb428d93267e66b4@xxxxxxxx" type=3D"cite">Dear Jim,<br> <br> I think the motivation behind your MDS question is a very interesting one. To me it seems that there are two likely possibilities. <br> <br> -one is that "auditory dissimilarity" is truly quite high-dimensional, so Matlab did not manage to project the data into a low dimensional space because it simply cannot be done, and even reducing the dimensionality just a little bit from 10 to 8 leads to appreciable distoritions (i.e. "error"),<br> <br> -the other (which seems to be the possibility you are asking about) is that Matlab's algorithm doesn't work properly. However, you could quite easily "sanity check" Matlab's algorithm: Just draw ten points randomly on (2-dimensional) graph paper, measure their pairwise distances, and feed those into the Matlab MDS algorithm. If Matlab does its job right it should give you a 2 D solution with errors no larger than the measurement errors you would expect from holding your ruler up to the points on your paper. In fact, it should be easily be possible to "virtualize" and automate his sort of sanity check by letting random numbers generate points in space of any dimensionality you choose and work out relative pairwise distances using Pythagoras. Once you have automated code that does this you could run hundreds of sanity checks like that you should know pretty quickly how far you can trust Matlab's algorithm. And I hope you will let us know the answer. I, for one, would not be too surprised if it turned out that sounds could sound dissimilar on at least 8 "different dimensions". <br> <br> Best wishes,<br> <br> Jan<br> <br> <div><span class=3D"gmail_quote">On 15/06/06, <b class=3D"gmail_sendername">beaucham</b> <<a href=3D"mailto:beaucham@xxxxxxxx">beaucham@xxxxxxxx= iuc.edu</a>> wrote:</span> <blockquote class=3D"gmail_quote" style=3D"border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt = 0.8ex; padding-left: 1ex;">We ran an MDS calculation (using MatLab) on a 10x10 distance<br> matrix based on dissimilarity judgements between all pairs of<br> 10 sounds, and obtained an 8-dimension solution, which gives<br> the coordinates of the sounds in 8-D space. The distances <br> between the positions of the sounds are supposed to match<br> the original distances. In fact, we get an rms error of 8%<br> and a max error of 30%.<br> <br> Is this typical? Is MatLab's program accurate? Is there a way<br> to improve on the MDS results?<br> <br> Jim Beauchamp<br> Univ. of Illinois Urbana-Champaign<br> <a href=3D"mailto:jwbeauch@xxxxxxxx">jwbeauch@xxxxxxxx</a><br> <br> </blockquote> </div> <br> <br clear=3D"all"> <br> -- <br> Dr Jan Schnupp <br> University of Oxford<br> Dept. of Physiology, Anatomy and Genetics<br> Sherrington Building - Parks Road<br> Oxford OX1 3PT - UK<br> +44-1865-272513<br> <a href=3D"http://www.oxfordhearing.com">www.oxfordhearing.com</a> </blockquote> <br> <br> <pre class=3D"moz-signature" cols=3D"72">--=20 Olivier Tache Associate Researcher - Doctorate Applicant Laboratoire Informatique et Cr=C3=A9ation Artistique INPG, 46, av. F=C3=A9lix Viallet 38031 Grenoble Cedex, France Tel. +33 (0) 476574660 Fax +33 (0) 476574889</pre> </body> </html> --------------080609080105050401020205--