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help > ICC Technical Question RE: Step Function?
May 27, 2016 07:05 PM | Alfonso Nieto-Castanon - Boston University
ICC Technical Question RE: Step Function?
Hi Jeff,
Just to clarify, yes, the reviewer seems to be suggesting that Martuzzi et al. used positive-only correlation values, but that is just not true: note in Equations 1 and 3 in their manuscript that the step function u(|r(i,j)|-thr) will be 1 both for positive above-threshold correlations r(i,j)>thr as well as for negative above-threshold correlations r(i,j)<-thr). Unfortunately I do not know of any studies comparing absolute and positive-only weighted degree centrality measures. My take from the literature is that the interest on positive-only correlations stems from the time when negative correlations were seen skeptically (e.g. Cohen et al. arguments about potential artifactual anticorrelations), but further studies and particularly improvements in denoising procedures (e.g. aCompCor) have mostly put these concerns to rest. From the perspective of information transfer most commonly used when interpreting graph theoretical measures both positive- and negative-correlations would lead to the same degree of mutual information between the nodes so it makes sense to include both in the network-forming definitions.
Hope this helps, and congrats on your paper!
Best
Alfonso
Originally posted by Jeff Browndyke:
Just to clarify, yes, the reviewer seems to be suggesting that Martuzzi et al. used positive-only correlation values, but that is just not true: note in Equations 1 and 3 in their manuscript that the step function u(|r(i,j)|-thr) will be 1 both for positive above-threshold correlations r(i,j)>thr as well as for negative above-threshold correlations r(i,j)<-thr). Unfortunately I do not know of any studies comparing absolute and positive-only weighted degree centrality measures. My take from the literature is that the interest on positive-only correlations stems from the time when negative correlations were seen skeptically (e.g. Cohen et al. arguments about potential artifactual anticorrelations), but further studies and particularly improvements in denoising procedures (e.g. aCompCor) have mostly put these concerns to rest. From the perspective of information transfer most commonly used when interpreting graph theoretical measures both positive- and negative-correlations would lead to the same degree of mutual information between the nodes so it makes sense to include both in the network-forming definitions.
Hope this helps, and congrats on your paper!
Best
Alfonso
Originally posted by Jeff Browndyke:
Thanks, Alfonso! Hopefully this
explanation will assuage the concerns of the reviewer. You
refer to "other degree centrality measures have been used for
unweighted networks define by above-threshold 'raw' -positive only
- correlation values," which I guess is what the reviewer is
suggesting that Martuzzi et al used in their 2011 manuscript.
Do you know of any studies making a direct comparison between absolute and positive only values for degree centrality estimation?
BTW - our group just got a manuscript accepted on a different project altogether using CONN. I'll send you the reference once it is available online.
Warm regards,
Jeff
Originally posted by Alfonso Nieto-Castanon:
Do you know of any studies making a direct comparison between absolute and positive only values for degree centrality estimation?
BTW - our group just got a manuscript accepted on a different project altogether using CONN. I'll send you the reference once it is available online.
Warm regards,
Jeff
Originally posted by Alfonso Nieto-Castanon:
Hi Jeff,
The version of ICC implemented in CONN is Martuzzi's ICC-power measure (also referred to as ICC-p0 in the original Martuzzi's 2011 manuscript). The main advantage of this measure (compared for example to ICC-d or other ICC-p measures) is that it does not require the specification of any a priori arbitrary threshold (of course another conceptual and practical advantage of ICC-power is that it can be easily computed from and related to the eigenvalues/eigenvectors of the voxel-to-voxel correlation matrix, which makes it fit right in with all of the voxel-to-voxel measures implemented in CONN). The original Martuzzi's manuscript explores several of these alternatives and shows that in practice all of these lead to very similar results. Regarding the use of both positive and negative connectivity measures in ICC's computation, that is common to all ICC measures (i.e. even when specifying a threshold value, like ICC-d and other ICC-p measures, that threshold is defined in terms of the absolute correlation values, so all ICC measures include both positive- and negative- connectivity effects in their computation). Of course, this choice could be seen as somewhat arbirary, and similar measures could potentially be defined that only look at positive-only conectivity values (but this was not simply how ICC measures were defined). Unfortunately I do not know of any paper that has explored the practical differences between these different definitions. Yet, keep in mind that typically anticorrelations are considerably weaker than positive correlations, so the differences between using positive-only or both positive-and-negative connections might be in practice very small. Last, in case this helps, in terms of interpreation ICC-power measures can be interpreted as a measure of degree centrality for a weighted network where the link strength between each pair of voxels/nodes is characterized by the r2 functional connectivity values between the same voxels (squared r values). Other choices, such as ICC-d, can also be interpreted as similar measures of degree centrality but using different network-forming criteria (e.g. ICC-d uses unweighted networks defined by above-threshold absolute-correlation values, and other degree centrality measures have been used for unweighted networks define by above-threshold "raw" -positive only- correlation values), so it basically boils down to which definition of brain networks might be most informative (for which, as far as I can tell, there is no consensual answer).
Hope this helps
Alfonso
Originally posted by Jeff Browndyke:
The version of ICC implemented in CONN is Martuzzi's ICC-power measure (also referred to as ICC-p0 in the original Martuzzi's 2011 manuscript). The main advantage of this measure (compared for example to ICC-d or other ICC-p measures) is that it does not require the specification of any a priori arbitrary threshold (of course another conceptual and practical advantage of ICC-power is that it can be easily computed from and related to the eigenvalues/eigenvectors of the voxel-to-voxel correlation matrix, which makes it fit right in with all of the voxel-to-voxel measures implemented in CONN). The original Martuzzi's manuscript explores several of these alternatives and shows that in practice all of these lead to very similar results. Regarding the use of both positive and negative connectivity measures in ICC's computation, that is common to all ICC measures (i.e. even when specifying a threshold value, like ICC-d and other ICC-p measures, that threshold is defined in terms of the absolute correlation values, so all ICC measures include both positive- and negative- connectivity effects in their computation). Of course, this choice could be seen as somewhat arbirary, and similar measures could potentially be defined that only look at positive-only conectivity values (but this was not simply how ICC measures were defined). Unfortunately I do not know of any paper that has explored the practical differences between these different definitions. Yet, keep in mind that typically anticorrelations are considerably weaker than positive correlations, so the differences between using positive-only or both positive-and-negative connections might be in practice very small. Last, in case this helps, in terms of interpreation ICC-power measures can be interpreted as a measure of degree centrality for a weighted network where the link strength between each pair of voxels/nodes is characterized by the r2 functional connectivity values between the same voxels (squared r values). Other choices, such as ICC-d, can also be interpreted as similar measures of degree centrality but using different network-forming criteria (e.g. ICC-d uses unweighted networks defined by above-threshold absolute-correlation values, and other degree centrality measures have been used for unweighted networks define by above-threshold "raw" -positive only- correlation values), so it basically boils down to which definition of brain networks might be most informative (for which, as far as I can tell, there is no consensual answer).
Hope this helps
Alfonso
Originally posted by Jeff Browndyke:
Our group submitted a manuscript examining the
relationship between ICC change pre/post and cognitive change
pre/post. We provided information about the ICC technique as
noted in the original CONN manuscript, but received the following
reviewer query about whether CONN ICC uses a threshold / step
function:
"The authors described ICC in the supplementary material. However, a threshold (or step function u(x)) did not specify in the evaluation of ICC. Without a threshold, both positive and negative connectivity were included in the computation of ICC. However, according to R. Martuzzi et al. (2011), which developed a measure of ICC for the first time, the connectivity strength was binarized by a step function. In general, researchers compute degree (including ICC) by using the positive connectivity only."
So, does CONN ICC use a step function (positive connectivity only)? If not, are there other papers/references for ICC being used without one? Justification for not including it?
Any recommendations on how best to address this would be most appreciated.
Warm regards to all,
Jeff
"The authors described ICC in the supplementary material. However, a threshold (or step function u(x)) did not specify in the evaluation of ICC. Without a threshold, both positive and negative connectivity were included in the computation of ICC. However, according to R. Martuzzi et al. (2011), which developed a measure of ICC for the first time, the connectivity strength was binarized by a step function. In general, researchers compute degree (including ICC) by using the positive connectivity only."
So, does CONN ICC use a step function (positive connectivity only)? If not, are there other papers/references for ICC being used without one? Justification for not including it?
Any recommendations on how best to address this would be most appreciated.
Warm regards to all,
Jeff
Threaded View
| Title | Author | Date |
|---|---|---|
| Jeff Browndyke | May 24, 2016 | |
| Jeff Browndyke | Jul 18, 2016 | |
| Alfonso Nieto-Castanon | May 26, 2016 | |
| Jeff Browndyke | May 27, 2016 | |
| Alfonso Nieto-Castanon | May 27, 2016 | |
| Jeff Browndyke | Jul 16, 2016 | |
| Alfonso Nieto-Castanon | Jul 18, 2016 | |
| Jeff Browndyke | Jul 18, 2016 | |