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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