Yes, that is the idea. It is useful to know how many zero eigenvalues to expect so that one can better judge how close to zero one should set the threshold.
========================= F. James Rohlf Distinguished Professor, Stony Brook University http://life.bio.sunysb.edu/ee/rohlf > -----Original Message----- > From: morphmet [mailto:[EMAIL PROTECTED] > Sent: Thursday, February 15, 2007 2:22 PM > To: morphmet > Subject: RE: Advice on IMP > > Yes it does seem that putting a generalized inverse into CVAGen is > the > best solution, I'll try to get to it. > > In the interim, what if you use a number of PC axes equal to the > degrees > of freedom remaining in the data (2k-4-n+1), where n is the number > of > groups? The percent variance remaining along the remainder of the > axes > should be zero (or close to it, given rounding errors in software). > So > this first set of variables (those with non-zero eigenvalues) would > contain the same information as the whole set of PC axes, wouldn't > it? > It's just a simple transformation of basis set. > > If the above is correct, then could one just examine the variance > explained along the first N PC axes, and chose N such that the > remaining > axes have eigenvalues essentially equal to zero, and then proceed > with > the CVA on those N axes, without substantial loss of variance? > > This is a short term solution, obviously, the ideal approach is to > replace the calculation in CVAGen with a generalized inverse (and > add a > warning message) > > -Dave > > H. David Sheets, PhD > Chair,Dept of Physics, Canisius College > 2001 Main St > Buffalo NY 14208 > > ---- Original message ---- > >Date: Wed, 14 Feb 2007 15:27:29 -0500 > >From: morphmet <[EMAIL PROTECTED]> > >Subject: RE: Advice on IMP > >To: morphmet <[email protected]> > > > >That approach will allow you to perform a CVA but it does have a > >logical problem. CVA will work best if it can find large > differences > >between groups that correspond to directions that have little > >variation within groups. If you use just the first few PCs based on > >within-group variation then you are also eliminating potential > >directions of small within-group variation in the multivariate > space > >that could yield the most effective separation of groups. May not > be a > >problem for your data but it seems a shame to eliminate the > >possibility of finding such differences. > > > >The inclusion of semilandmarks is a different problem. For each > >semilandmark there will be one more or less singular direction and > >hence one within-group eigenvalue for each semilandmark that should > be > >close to zero. Those dimensions (PCs) should be eliminated or else > one > >should use a CVA program that uses a generalized inverse. The CVA > >module in NTSYSpc allows one to specify a cut-off value. All > >eigenvalues below that threshold (perhaps set at something like > 10^-8) > >will be ignored. > > > >========================= > >F. James Rohlf > >Distinguished Professor, Stony Brook University > >http://life.bio.sunysb.edu/ee/rohlf > > > > > >> -----Original Message----- > >> From: morphmet [mailto:[EMAIL PROTECTED] > >> Sent: Wednesday, February 14, 2007 11:49 AM > >> To: morphmet > >> Subject: Re: Advice on IMP > >> > >> Hi All- > >> > >> Jim Rohlf has already stated the reason for the problem here, CVA > >> requires a division by a pooled covariance matrix estimated from > >> your > >> data. To avoid have a singularity in this matrix, you need a > sample > >> size larger than the degrees of freedom remaining in your > variables. > >> > >> The ideal approach to this is to get more data, but that may be > >> difficult. > >> > >> I have a version of CVAGen that will first perform a PCA on the > >> partial > >> warp scrores and uniform components, and then perform a CVA on a > >> limited > >> number of the PCA scores. So if you have 20 variables in the > data > >> and > >> only 20 specimens, you might find that the first 5 or 6 PCA axes > >> have > >> 90% or more of the variance, so that a CVA using only 5 or 6 PCA > >> axes > >> might might produce reasonable results. This approach may be > >> particularly useful if you are using a lot of semi-landmarks. > >> > >> This version of CVAGen is on the page at > >> > >> http://www.canisius.edu/~sheets/moremorph.html > >> > >> under the New Two-D Software section, called PCA_CVA. It might > >> prove > >> helpful. > >> > >> I should put a test routine for this degrees of freedom issue and > >> put a > >> more informative error message into the program. > >> > >> In the second question below, I'm not sure what is happening. I > >> assume > >> the two data sets have the same numbers of landmarks? > >> If you can send me a copy of the files, I can have a look and > chase > >> this > >> down. > >> > >> -Dave > >> > >> > >> H. David Sheets, PhD > >> Chair,Dept of Physics, Canisius College > >> 2001 Main St > >> Buffalo NY 14208 > >> > >> ---- Original message ---- > >> >Date: Tue, 13 Feb 2007 14:35:55 -0500 > >> >From: morphmet <[EMAIL PROTECTED]> > >> >Subject: Advice on IMP > >> >To: morphmet <[email protected]> > >> > > >> >Hi everybody! > >> >I am using geometric morphometrics in a study on mandibles of > mice. > >> I > >> >have encountered problems using programs in the IMP series, and > I > >> would > >> >be very grateful if somebody more experienced with these could > give > >> me a > >> >hint on what to do here: > >> > > >> >1)I load an output file from CoordGen and a GroupList file into > >> CVAGen. > >> >The program displays the landmarks but does not finish the > >> analysis, > >> >instead posting an error message: ?The within-group sum of > squares > >> and > >> >cross products matrix is singular?. I have inspected both input > >> files > >> >several times; I cannot find any error; they do also perform > well > >> in > >> >PCAGen. What does the message tell me about my data? > >> > > >> >2) I load two X1Y1CS format files into TwoGroup. The landmarks > are > >> >displayed and I can calculate Goodalls F. Anyway, when I click > on > >> ?F > >> >test, Procrustes? I am getting an error message saying that > ?matrix > >> >dimensions must agree?. Why is this? What do I have to change? > >> > > >> >If anyone wishes to reply to me directly, my email address is: > >> >[EMAIL PROTECTED] > >> >Thank you very much and let me know if I can return you a favor. > >> > > >> >Louis > >> > > >> > >_________________________________________________________________ > >> >Haben Spinnen Ohren? Finden Sie es heraus ? mit dem MSN Suche > >> Superquiz > >> >via > >> >http://www.msn-superquiz.de Jetzt mitmachen und gewinnen! > >> > > >> > > >> > > >> >-- > >> >Replies will be sent to the list. > >> >For more information visit http://www.morphometrics.org > >> > > >> > >> > >> > >> -- > >> Replies will be sent to the list. > >> For more information visit http://www.morphometrics.org > > > > > > > > > >-- > >Replies will be sent to the list. > >For more information visit http://www.morphometrics.org > > > > > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
