In my understanding to PCA, its main goal is to reduce the dimensionality of a problem without the loss of too much information. In other words, according to Prof. Rohlf, the purpose of PCA is to give you a low dimensional space that accounts for as much variation as possible. However, I agree with Oyvind that many scientists use PCA as a visualization device, projecting a multivariate data set onto a sheet of paper.
On the other hand, testing the multivariate normality before applying any multivariate data analysis technique is one of the most serious problems because in most cases none do that and if any tried to do he may choose the wrong way. Actually, we (biologists and paleontologists) need a definite guide to follow when we face such problem. Best regards ---------------------------------------------------------------------------- --- Dr. Ashraf M. T. Elewa Associate Professor Geology Department Faculty of Science Minia University Egypt [EMAIL PROTECTED] http://myprofile.cos.com/aelewa ----- Original Message ----- From: <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Wednesday, May 19, 2004 04:29 ? Subject: Re: size correction & discriminant functions analyses > Just a comment on this one, from a pragmatic point of view. > > It is of course true that PCA is only *guaranteed* to > produce components maximizing variance if you have > multivariate normality. The theory of PCA is based on this > assumption. But in many cases, PCA is used purely as a > visualization device, projecting a multivariate data set > onto a sheet of paper so we can see it. For visualization > of non-normal data, one could play around with different > techniques, such as PCA, PCO, NMDS, projection pursuit etc., > and then find that PCA does (or does not) perform well > for the given data set. There is no law against making > any linear combination you want of your variates, if it > reveals information. For example, PCA may be perfectly > adequate for resolving two well-separated groups, if > the within-group variance is relatively small. > > Of course, when using PCA for non-normal data one must > be a little careful and not over-interpret the results > (especially not the component loadings), but I think > it's too harsh to dismiss its use totally. > > I'm sure the hard-liners will flame me to pieces for > this email, but I hope they will at least give me > credit for my courage :-) > > > Dr. Oyvind Hammer > Geological Museum > University of Oslo > > > > > PCA Analysis assumes multivariate normality. > > > > Kathleen M. Robinette, Ph.D. > > Principal Research Anthropologist > > Air Force Research Laboratory > > > > == > Replies will be sent to list. > For more information see http://life.bio.sunysb.edu/morph/morphmet.html. == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
