Next steps for distinguishability measure

Post date: Oct 7, 2012 10:14:57 PM

According to the draft for INFORMS 2012, the followings are what we should pursue further (beyond the scope of INFORMS presentation though).

Improve robustness of pair-wise t-test in distinguishability measure

Since we use only 10 examples for pair-wise t-test, the estimation is arguably not very stable. (Practically it requires >30 examples) So, we might consider including the 1-degree neighbors n(A) of the voxel of interest, A, to increase the robustness. However, the beta coefficients from n(A) are known to correlate with ones from A, that violate the t-test assumption that examples for each distribution are iid. Nevertheless, this approach is worth trying, and the issue can be addressed as a drawback.

Informative brain regions outside VTC found by distinguishability measure

In figure 7 of the draft, there are informative brain regions outside VTC found by distinguishability measure. What regions are they? [Sonya has a plan for this. Thanks! ]

Consistency of atlas and functional brain clustering

Mapping the anatomical brain map (atlas) to the clusters found by spectral clustering+CD.

[Sonya will provide the masks of the subregions in the VTC, thanks a million!]

After that, we can use Jaccard index to calculate the consistency numerically.

A problem, though, is visualizing the clusters on the 3D brain is hard to understand. So, we might need to unfold from 3D to 2D.

Find functional boundaries invariant to the stimuli (and the subjects too?)

Since we have only 8 stimulus categories, I don't think that this 8 categories would provide sufficient information to cluster all major subregions in the VTC. On the contrary, the question we should ask would be:

"what regions can we discover from using 8 stimuli categories?" or

"is there any consistent boundaries across the different number of segments (5, 8, 12, ...)?"

Another good question would be: "Is there any boundary invariant to the stimuli?"

And if we start on multiple-subject test, it will be interesting to ask: "Is there any consistent boundary across subjects?"

Plot pair-wise distinguishability values pair by pair

For each pair of classes (i,j), we plot the pair-wise distinguishability values on the slice of the brain. So, we will have 7x7 triangle image matrix. For example, if we have 4 classes, we will have

     2     3     4    

1: (1,2) (1,3) (1,4)

2:       (2,3) (2,4)

3:             (3,4) 

We expect to see some trends for each class pair.

Plot the "class-maximally-separated" region on the bain

The CD for each voxel indicates how well the voxel can separate a particular class from the rest. In the figures on page 7, we have the biclustering result, and therefore we know which voxels tends to maximally separate which class(es). So, it is a very interesting idea to plot which regions in the brain perform best on separating which classes by plotting the peak of biclustering on the 3D brain so that we know what regions they are.

Individual class-pair separation on biclustering

Based on the same figure on the page7, we would like to show more details of the class-pair separation. To do so we will "zoom in" for each class (column) by insert the pair-wise distinguishability rather than the class-specific (which is the averaged class-pairwise). At the end, we will have the similar biclustering matrix of the size 577x56(=8x7). Note that we fix the same order of the voxels (row) and the class merged (column) This visualization would give a good idea on how individual class-pair is separated.