This solution is an example of the use of one type of generalized inverse. There are a number of different generalizations that retain some of the properties of an actual inverse.
As indicated, a 95% rule will lose information. However, one can cutoff at 100% If one has n specimens in a p-dimensional space, then when n-1 < p there will be eigenvectors with effectively zero eigenvalues that can be eliminated with no loss of information about variation among the specimens. ----------------------- F. James Rohlf, Distinguished Professor State University of New York, Stony Brook, NY 11794-5245 www: http://life.bio.sunysb.edu/ee/rohlf > -----Original Message----- > From: morphmet [mailto:[EMAIL PROTECTED] > Sent: Monday, March 21, 2005 6:02 PM > To: morphmet > Subject: Re: generalised inverse matrices > > Brett- > > I'm not sure just what analysis you are carrying out, but one > alternative approach is to use a PCA to reduce the > dimensionality of your data prior to further analysis. One > might discard some number of the PCA axes, retaining enough > to explain 95% of the variance in your data. > > This is a loss of information of course, which may not be > acceptable in your analysis. > > -Dave > > > ---- Original message ---- > >Date: Wed, 16 Mar 2005 09:27:19 -0500 > >From: morphmet <[EMAIL PROTECTED]> > >Subject: generalised inverse matrices > >To: morphmet <[email protected]> > > > >Hello All, > > > >I am having issues with singular matrices because the number > of variables > >(linear morphometric measures) I have far exceeds the number > of samples. I > >don't wish to introduce a bias into my analyses by selecting > variables to > >include/exclude from my data matrix, hence I am wondering > about the validity > >of using generalised inverse matrices. > > > >Is the use of generalised inverse matrices a valid/ accepted one? > >Are generalised inverse matrices statistically robust and > will people > >believe my results? > >Has anyone published using generalised inverse matrices? > >How would I defend the use of generalised inverse matrices? > > > >Thanks in advance, > > > >Brett Human > > > >************************ > >Brett Human, PhD > >Shark Researcher > >27 Southern Ave > >West Beach SA 5024 > >Australia > >Ph: +61 8 8356 6891 > >email: [EMAIL PROTECTED] > >************************ > >-- > >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
