On Sat, Feb 9, 2013 at 11:43 AM, Uwe Ligges <lig...@statistik.tu-dortmund.de > wrote:
> > > On 08.02.2013 20:14, David Romano wrote: > >> Hi everyone, >> >> I'm not exactly sure how to ask this question most clearly, but I hope >> that >> giving the context in which it occurs for me will help: I'm trying to >> compare the brain images of two patient populations; each image is >> composed >> of voxels (the 3D analogue of pixels), and I have two images per patient, >> one reflecting grey matter concentration at each voxel, and the other >> reflecting white matter concentration at each voxel. >> >> I determined the groups by means of an analysis that involved information >> from both types of images, and what I set out to do was to get a rough >> idea >> of where in the brain the two groups showed the most striking differences. >> >> My first attempt was to replace -- on a voxel by voxel basis -- the >> bivariate grey/white data by a combined univariate measure, namely the >> first principal component score. From these principal component scores I >> calculated Cohen's d to obtain a rough estimate of the effect size at each >> voxel, and the resulting brain images show very nice separation into >> meaningful brain regions, some corresponding to negative effect sizes and >> some to positive ones. >> >> What puzzles me about how nice the separation into brain regions is, is >> that the meaning of positive and negative is determined by the choice of >> the first principal component direction at each voxel, but this choice is >> -- in principle (no pun intended -- sorry!) -- arbitrary. (Meaning >> whether >> an eigenvector or its negative is chosen as the direction is in principle >> arbitrary.) >> >> So here are my questions: Does the algorithm used in R produce the same >> principal component directions if applied to the same data repeatedly? >> > > Yes, but it may change if you execute it on another machine (depends on > compiler hence also 32-bit vs 64-bit and OS). > > > > And if so, should the directions chosen by the algorithm change >> continuously with the data? For example, if one data set were obtained by >> applying a small amount of noise to another, should the resulting >> directions be close to each other (as opposed to close negative of each >> other)? (Assuming the data is far from being "singular" in some vague >> sense I'm not sure how to make precise.) >> > > Noise means the sign can change again. > > Of course, you can define yourself e.g. the direction of the very first > value and change signs otherwise. > > > > My second attempt was to do the same, but with the first lda scores, so I >> have the same questions about lda directions, too. >> > > > Same for lda. > > Best, > Uwe Ligges > Thanks, Uwe; all good to know. Best, David > > Any light you could shed on these questions would be very welcome! >> >> Thanks in advance, >> David Romano >> >> [[alternative HTML version deleted]] >> >> ______________________________**________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/**listinfo/r-help<https://stat.ethz.ch/mailman/listinfo/r-help> >> PLEASE do read the posting guide http://www.R-project.org/** >> posting-guide.html <http://www.R-project.org/posting-guide.html> >> and provide commented, minimal, self-contained, reproducible code. >> >> [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
