question about PLS data matrix
mkim
Posted on 07/31/08 13:50:31
Number of posts: 34
A question came up about what else PLS might do when setting up the data matrix prior to the singular value decomposition. According to all the papers, once the data matrix is set up with each voxel or voxel-timepoint combination being a column and all the subjects and conditions etc. in rows, the column-wise mean value is subtracted off, and then the SVD is run.
The question is, how does that affect our later understanding of the voxel “intensities”? i.e., we can show a voxel’s intensity values after the analysis, in our case it’s one value per subject per condition (since we’re doing a block analysis), that vary around zero. The question was, is a value of .4 larger than a value of .2? I figured that for a given voxel, since the mean being subtracted off is voxel-wise, the answer is yes, .4 means that voxel’s values were .4 units greater than the mean in that condition, and .2 means the voxel’s values were .2 greater than its mean. So whatever the mean was, it doesn’t affect the interpretation.
But when we compare across voxels, we don’t know if one voxel’s mean was 1 unit and the other voxel’s mean was 10 units. If the mean is 1 and the voxel intensity is .2, that’s 20% off the mean. If the mean is 10 and the voxel intensity is .4, that’s only 4% off the mean. It may still be quite reliable according to the brain score ratios, but it’s simply not as large a response.
Is there any chance of recouping the voxel-wise means that are subtracted off?
Does it not matter, since the usual SPM pre-processing scales the subject average intensity to be the same value, and the individual voxel differences around that value are only on the order of 2% and thus not relevant, in practice??
Did we misunderstand, and PLS actually subtracts off the mean and then scales by the variance on a voxel-wise basis, so a change of .2 is in standard units across all voxels?
Thanks!
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nlobaugh
Posted on 07/31/08 14:23:14
Number of posts: 229
A question came up about what else PLS might do when setting up the
data matrix prior to the singular value decomposition. According to all
the papers, once the data matrix is set up with each voxel or
voxel-timepoint combination being a column and all the subjects and
conditions etc. in rows, the column-wise mean value is subtracted off,
and then the SVD is run.
small point of clarification: SVD is run on the matrix of deviation task/condition means
The question is, how does that affect our later understanding of the
voxel “intensities”?
It doesn't really... when you go into 'voxel intensity response' modules, or extract voxel values using 'multiple voxels extraction', you are seeing the actual data that you have put into your datamat. So the values reflect any scaling/intensity normalization that you have applied either outside of the GUI or as you created the datamat(s)
It may still be quite reliable according
to the brain score ratios, but it’s simply not as large a response.
this is one of the 'better' features of the PLS approach as implemented here - you have the possibility of finding small, stable differences/correlations :-)