Sorry Jody, sorry everyone,
V is of course mxm.
Jesper
Jesper Andersson wrote:
> Dear Jody,
>
> "eigenvariates" and "eigenimages" refer to a factorisation of functional
> imaging data of the following form. Say you have your data stored in an nxm
>
> matrix Y where n is the number of voxels in each image volume, and m the
> number of scans in the time series. We may now factor Y in the following
> form
>
> Y = U*S*V'
>
> where U is an orthogonal nxm matrix, S is a diagonal mxm matrix and V an
> orthogonal nxn matrix. This is a bit like trying to factorise a number into
>
> the product of three other numbers, i.e. there are a lot of ways of doing
> it. To make the factorisation unique the first column of U multiplied with
> the first number in S multiplied with the first column of V has to be the
> combination which explains the maximum possible amount of the variance in
> Y. The second combination has to be that which explains the most variance
> in Y after the first one has been removed etc. This is called singular
> value decomposition.
>
> In neuroimaging the columns of U are typically/often denoted eigenimages,
> and the columns of V may be called "eigenvariates", "eigentimecourses" or
> something like that.
>
> Its usefulness in neuroimaging comes from the similarity between the
> factorisation above and the multivariate version of the general linear
> model
>
> Y = P*X' + E
>
> where Y is still the data, X is the good old design matrix, the columns of
> P contains the parametric images (one for each column of X) and E is the
> error matrix.
>
> For well behaved data (e.g. PET) the SVD factorisation can sometimes be
> useful in that the "automatic generation" of the "design matrix" V can give
>
> new insights to the experiment. It can also be used as a data reduction
> method or as a preconditioning of data prior to e.g. ICA.
>
> As a general reference I quite like the explanation given in "Numerical
> Recipies in C" by Press et al. For Neuroimaging purposes you might refer to
>
> Friston et al 1993 in JCBFM, or you could look for papers by S. Strother.
>
> Good luck
> Jesper
> Jody Tanabe wrote:
>
> > Hello,
> >
> > Could someone please provide a reference or explain to me what the first
> > eigenvariate is?
> >
> > Thank you kindly,
> > Jody
>
> Jody Tanabe wrote:
>
> > Hello,
> >
> > Could someone please provide a reference or explain to me what the first
> > eigenvariate is?
> >
> > Thank you kindly,
> > Jody
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