CONN : functional connectivity toolbox

help > RE: MVPA analysis questions
Sep 18, 2012  06:09 PM
RE: MVPA analysis questions

Dear Darren,

Thank you for your reply. Possible the coming
manuscript will highlight some questions that i have after Alfonso's answers:

1. Why conditions are dependent on each other in some
way? i.e., why one condition forces others to be negative? If I do understand
correctly, computing SVD (=PCA when M voxel separately assumes that the SVD is performed on a matrix MxN where M - a
number of scans and N - correlation values between this one particular voxel
and the rest of the brain. After all standard procedures (mean normalisation,
defining eigenvectors in space and time and eigenvalues) normally we will get a
Principal Component (say, we are interested in only first one) that consists of
different values and can be positive and negative (please, see any papers on
SVD).  After an arbitrary thresholding highly correlated voxels (! highly
correlated with our particular voxel) with positive and negative values will
compose our first Principal component. Right? In previous studies (e.g.,
Worsley et al., 2005) the positive and negative signs were interpreted as:
(citing:
In non-mathematical terms, SVD seeks to express the
correlation structure by a small number of “principal components” multiplied by
random weights that vary randomly over time or subject. Voxels with high
principal component values clearly co- vary together and are therefore
positively correlated; voxels with high opposite signed components co-vary in
opposite senses and are therefore negatively correlated. In practice we extract
the first few principal components, then threshold these components at an arbitrary
level (since there is as yet no P-value results for local maxima of principal
or independent components). These regions are then our estimate of the
connected voxels).

My question is: how the negative and positive signs
are treated in conn? Does conn takes only the absolute value (if so - why?
Rotation-invariant explanation is does not solve the problem with
interpretation and mathematical meaning of the components of SVD).

2. How the principal components for each voxel are
mapped in the brain? Say, we have got that principal component for voxel 1
included some highly correlated voxels, e.g. voxels 10, 11, 12. For voxel 2 we
have got highly correlated voxels 10, 11, 15, 17. So how the overlapped
components are mapped? Logically, in some cumulative manner.

I have some questions more, but these two above are
crucial for understanding conn.

Darren and Alfonso, may I ask your opinion? Thank you