Thresholding Connectivity Matrices Query

Dear Mike,

I have a question regarding thresholding of connectivity matrices prior to using graph theoretical approaches to explore network topology.

In a recent analysis I used the approach you mentioned in your book of first pooling together connectivity values across all conditions and then determined the value 1 SD above the median connectivity value and subsequently applied this to each of my seperate conditions to threshold the matrices (note as I was looking at connectivity [wPLI] across several different frequencies, I ran this separately for each frequency). After thresholding, I then binarized the matrices before running my topological analyses.

Anyway, a colleague recently queried whether using this approach might potentially be problematic, the reason being that because the median value was obtained from the pooled matrices across all subjects, could this mean that subjects who have lower connectivity, relative to other subjects, could potentially be underrepresented in the final result (i.e., the pairwise connectivity values for these subjects might not surpass the threshold obtained using the full sample)? Just wondering what you think about this? Is it indeed possible that this could be the case? I realise thresholding is very arbitrary which is why I quite liked the more data driven approach you suggested in your book. Any thoughts would be greatly appreciated. Thanks.

Hi Brian. Indeed, there is no ideal threshold. I think I discuss this a bit in the book.

Anyway, I would recommend giving each subject their own threshold. There could also be inter-subject differences in overall connectivity strength because of electrode preparation or skull thickness, and you don’t want those kinds of non-brain-related differences to introduce any biases.

I know this thresholding can be annoying because of the uncertainty. Another possibility is to re-run your analyses using a range of threshold values, and then plot the final results as a function of the threshold. That will allow you to determine whether the overall pattern of results is independent of the threshold.

Thanks very much for your reply Mike.