Political network

[youjin1207]

• [x] draw node contribution bar graph as a decreasing order within the group.
• [x] draw a grouped adjacency matrix and see what lead to negative contribution (especially science group.)

[youjin1207]

@jovo @cshen6 What do you think about these two figures? I think the significantly negative contribution might be attributed to (a) concentrating edges between particular X (types) or (b) having lots of relationship across groups. You can see the latter case in the second period, the last Party (green). outline_polipart.pdf

[cshen6]

yes the adjacency matrix is very informative.

The strong negativity comes from the fact that SC does not contact much with other groups at all in the first period, so their contribution is (very negative cross group distance by network * positive cross group distance by label)= very negative contribution.

Say, if you manually fill up some links between SC and other groups, the SC contribution should be a lot closer to 0.

Although this example is saying that strong negativity is also useful for identifying some dependency signal, I guess? This can be true, depending on how we have ranked & centered.

On Mon, Dec 5, 2016 at 9:47 PM, Youjin Lee notifications@github.com wrote:

@jovo https://github.com/jovo @cshen6 https://github.com/cshen6 What do you think about these two figures? I think the significantly negative contribution might be attributed to (a) concentrating edges between particular X (types) or (b) having lots of relationship across groups. You can see the latter case in the second period, the last Party (green). outline_polipart.pdf https://github.com/neurodata/Multiscale-Network-Test/files/632863/outline_polipart.pdf

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[cshen6]

I recall that if we do absolute contribution, the simulation is also consistent for node contribution, right?

On Tue, Dec 6, 2016 at 8:20 AM, Cencheng Shen cshen6@jhu.edu wrote:

yes the adjacency matrix is very informative.

The strong negativity comes from the fact that SC does not contact much with other groups at all in the first period, so their contribution is (very negative cross group distance by network * positive cross group distance by label)= very negative contribution.

Say, if you manually fill up some links between SC and other groups, the SC contribution should be a lot closer to 0.

Although this example is saying that strong negativity is also useful for identifying some dependency signal, I guess? This can be true, depending on how we have ranked & centered.

On Mon, Dec 5, 2016 at 9:47 PM, Youjin Lee notifications@github.com wrote:

@jovo https://github.com/jovo @cshen6 https://github.com/cshen6 What do you think about these two figures? I think the significantly negative contribution might be attributed to (a) concentrating edges between particular X (types) or (b) having lots of relationship across groups. You can see the latter case in the second period, the last Party (green). outline_polipart.pdf https://github.com/neurodata/Multiscale-Network-Test/files/632863/outline_polipart.pdf

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[jovo]

Can we simulate to obtain this effect? A synthetic data analysis type result?

On Tue, Dec 6, 2016 at 8:21 AM cshen6 notifications@github.com wrote:

I recall that if we do absolute contribution, the simulation is also

consistent for node contribution, right?

On Tue, Dec 6, 2016 at 8:20 AM, Cencheng Shen cshen6@jhu.edu wrote:

yes the adjacency matrix is very informative.

The strong negativity comes from the fact that SC does not contact much

with other groups at all in the first period, so their contribution is

(very negative cross group distance by network * positive cross group

distance by label)= very negative contribution.

Say, if you manually fill up some links between SC and other groups, the

SC contribution should be a lot closer to 0.

Although this example is saying that strong negativity is also useful for

identifying some dependency signal, I guess? This can be true, depending on

how we have ranked & centered.

On Mon, Dec 5, 2016 at 9:47 PM, Youjin Lee notifications@github.com

wrote:

@jovo https://github.com/jovo @cshen6 https://github.com/cshen6 What

do you think about these two figures? I think the significantly negative

contribution might be attributed to (a) concentrating edges between

particular X (types) or (b) having lots of relationship across groups. You

can see the latter case in the second period, the last Party (green).

outline_polipart.pdf

< https://github.com/neurodata/Multiscale-Network-Test/files/632863/outline_polipart.pdf

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[youjin1207]

Yes I will try such simulation - I think it is also very related to "nonlinear" dependency in terms of categorical variables.
I took an absolute value to sum of row + column, not to the column sum. But I will try column sum as well. These are very interesting observations.

[cshen6]

The simplest simulation is to just fill up the SC connectivity a bit, and see what happens.

A model based simulation will be a 3 block model, from B= [0.5,0.2,0.05;0.2,0.5,0.05;0.05,0.05,0.1]. The labels are 1,2,3. Namely the first two blocks are kind of dense, but the last block is rarely connected with the other two blocks.

If it fits our conjecture, nodes from the first two blocks should be positive contributed, while nodes from the last block should be way negative.

On Tue, Dec 6, 2016 at 2:29 PM, Youjin Lee notifications@github.com wrote:

Yes I will try such simulation - I think it is also very related to "nonlinear" dependency in terms of categorical variables. I took an absolute value to sum of row + column, not to the column sum. But I will try column sum as well. These are very interesting observations.

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[youjin1207]

I did simulation (a) using real data by adding edges one by one for Science group to any others and also (b) 3 block model. In the first case, significant negativity seems to disappear as I added one-two edges but negativity of pink group becomes evident. In the latter case, if you see Figure 16, block 3 having sparse edge distribution has negative contribution, but not monotonic to the power.

My conjecture on this is : (a) contribution measure is relative measure, only valid within each example; (b) (Relatively) Sparse edge distribution usually leads to negative contribution.

[cshen6]

very cool! I think your conjecture is right.

On Wed, Dec 7, 2016 at 10:03 PM, Youjin Lee notifications@github.com wrote:

I did simulation https://github.com/neurodata/Multiscale-Network-Test/blob/master/Draft/outline.pdf (a) using real data by adding edges one by one for Science group to any others and also (b) 3 block model. In the first case, significant negativity seems to disappear as I added one-two edges but negativity of pink group becomes evident. In the latter case, if you see Figure 16, block 3 having sparse edge distribution has negative contribution, but not monotonic to the power.

My conjecture on this is : (a) contribution measure is relative measure, only valid within each example; (b) (Relatively) Sparse edge distribution usually leads to negative contribution.

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