Distributed information in the brain

This page is devoted to the proof that the information in the brain is distributive. This experiment is inspired by distinguishability measure.

Characteristic curve for VTC voxels: average accuracy vs number of voxels with a specific V_thres

1. Pick a distinguishability threshold V_thres (e.g., 0.1, 0.2, 0.3, 0.4, 0.5)
2. populate voxels with V<V_thres
3. Rearrange the voxels in shuffled order
4. Perform classification by adding one voxel at a time using the order determined in 3).
5. Repeat 3) and 4) for 100 times to have the characteristic curve of accuracy vs the number of voxels for the threshold V_thres

Now we plot the average accuracy for each choice of V_thres:

The matlab codes are made available:

Characteristic curve VTC voxels: average accuracy vs number of voxels within a searchlight volume

1. Pick a distinguishability threshold V_thres (e.g., 0.1, 0.2, 0.3, 0.4, 0.5)
2. populate S, a set of voxel i with Vi<V_thres
3. Pick 100 landmarks in S, uniform distributed is prefered
4. For each landmark m_i, find nki = n_k(m_i), the set of k nearest neighborin xyz coordinate
5. Calculate the accuracy acc_ki, centroid xyz_ki for each nki group.
6. We can plot (x,y) = (k, average_k(acc_ki))
7. We also can plot xyz_ki, acc_ki in the brain space, just to see which region in the brain tends to jointly operate well.
8. Repeat 4-7 by varying the number of nearest neightbor k.

Experimental results

When increasing the number of k (in k-nn), the accuracy tends to increase and decrease after over-inclusive.

Perhaps k can be an indicator to say what is the boundary of each supervoxel

Comments:

• In this case, the neighbors are selected based on k-nn, so sometimes the neighbor might be pretty far away from the seed. IN the next experiment, we should try to fixed the radius from the seed and populate all the voxels with V < V_thr and compare.
• It's interesting to see if the accuracy obtained from neighbors with closer distance to the seed is greater than ones further? If yes, then we conclude the voxels in the close affinity is more cooperative than the ones further.

The code is made available here.

The on-going experiment:

Test if the cooperative behavior is clearer with nearest voxels than further voxel

1. pick some seed voxels set S
2. Include some neighbors around each voxel in S using k-nn or r-radius, let's call set S+near
3. Include some neighbors with further distance say r, let's call set S+far
4. Compare the accuracy of both S+near and S+far
5. If S+near is significantly better than S+far, then we can conclude the cooperative has near range.

The maximum accuracy occurs at the ring 6-10 because the voxels closer to that is similar and does not provide an additional information to the classifier. Therefore, the ones further provide better additional information.

Art's idea to prove that the VTC is not at the optimal combination

We want to show that by including more voxels, we gain better (training) accuracy.

1. Calculate the accuracy for the VTC-mask voxels
2. For each voxel in the VTC mask, include neighbors in the radius r, call this augmented set VTC+
3. Calculate the accuracy for VTC+
4. If accuracy in 3) is greater than 1), we then conclude the given VTC mask is not optimal

We can also get better accuracy by removing some (non-informative) voxels from the VTC. And we can get even better by including some more versatile voxels outside the VTC mask.