Hi
On 22 Jul 2011, at 21:00, Dianne Patterson wrote:
> Hi All,
> I am having trouble understanding what exactly is contained in each of the matrices that ICA works with....the spatial map x component matrix is especially confusing.
>
> Suppose I have several original voxels, like this, we'll posit 2 slices so it is a 3d volume and 5 timepoints so it is a 4d volume
>
> slice A:
> voxel a1 timecoure: 1 2 3 4 5
> voxel a2 timecourse: 5 3 7 6 2
>
> slice B:
> voxel b1 timecoure: 3 5 7 9 4
> voxel b2 timecourse: 8 6 4 2 1
>
> My first 2d matrix is time by component, so, what will be in it?
> My impression from the illustration on the Melodic page is that it will contain the time courses in columns:
> 1 5 3 8
> 2 3 5 6
> 3 7 7 4
> 4 6 9 2
> 5 2 4 1
Nope, this is just the raw data in 2D matrix form, no decomposition has happened at this stage. After removing each time course mean value this data is the LHS of the main ICA equation
X=A*S+E
There is a small technical issue in your example in that you have more time points then voxels - not allowed in the melodic case, so let's simplify to the first 3 time points and let's also de-mean. Your LHS then is
-1 0 -2 2
0 -2 0 0
1 2 2 -2
This now is X. You see that there is a strong trend for a linear increase in 3 of your 4 voxels, so a reasonable first component would be to model this as
-1 0 -2 2 1
0 -2 0 0 = 0 x -1 0 -2 2 + E
1 2 2 -2 -1
The middle matrix then is the ICA time course matrix and it describes a linear increase across your 3 time points, the second matrix is the ICA component matrix which shows you where in the brain there is the linear increase and also tells you directionality. E is the error term.
Does this make more sense? If not, I recommend reading some of the fine ICA papers out there…
hth
Christian
> but then I have no idea how the components can be in the rows (do the components have their own row? can we split the timelines into different components? [my impression is that we could, in theory, but that we don't because there are not as many timepoints as voxels]),
> are the timelines in this matrix some sort of generated set of independent timelines, and not the originals?
>
> So what is in the spatial matrix...a transposition of the time matrix?
>
> Sorry to be so dense...but I'm really struggling here.
>
> Thankyou,
>
> Dianne
> --
> Dianne Patterson, Ph.D.
> Research Scientist
> [log in to unmask]
> University of Arizona
> Speech and Hearing Science 314
> 1131 E 2nd Street, Building #71
> (Just East of Harvill)
> 621-9877
>
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