The sparse Brain network is achieved via two ways, thresholding of connectivity matrix or imposing the sparseness constraint in the connectivity matrix estimation. (This seems very similar to k-sparse auto encoders and imposing sparsity via KL Divergence.). But it is not yet known what threshold or sparseness level is best in determining the hidden connectivity structure of the brain. So the authors of this paper show the equivalence between sparseness and threshold, additionally they observe topological changes when varying the threshold/sparseness from ADHD children.
When we have matrix X, that is composed of n dimensional vector, we can create a connectivity matrix C (correlation matrix/partial correlation) by either thresholding or imposing the sparseness by minimizing the L1 norm of C.
And to show that thresholding is equivalent to imposing sparseness, the authors introduce the penalized linear regression to estimate the correlation and partial correlation. Two functions are solve via gradient descent method. The visualization tool Barcode was used.
They found that brain networks of ASD and ADHD groups might be more difficult to be merged into a component due to common under-connectivity and local over-connectivity. ( I guess this is related to the brain symptoms, hence I have no idea what the above statement means.)
The authors were able to show equivalence between sparsity level and threshold of the network. ( I really have no idea what they are talking about. But from the diagram alone, it seems like as the hyper parameter lambda changes the brain regions can be either be more connected or less. )
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- (2018). Citeseerx.ist.psu.edu. Retrieved 19 September 2018, from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.233.5406&rep=rep1&type=pdf