Some problems about topology loss

[linxcan]

Hello, when we looked at the baseline model, we found that the model will use 1-gt, and 0 as positive when calculating the topology loss. Why do you do this, shouldn’t 1 be positive?

[faikit]

Hi, in the adjacency matrix, 1 represents the positive edge. But for calculating the loss, the prediction loss regards 0 as positive.

[linxcan]

Thank you for your reply, but if the network uses 0 as the positive class to calculate the loss, shouldn’t the topological network predict that 0 is the positive edge? Isn’t this the opposite of GT?

[faikit]

In (1 - GT), the 0 means that the 0-th channel of the predicted adjacency matrix is positive, and we just have one channel on the predicted result. You can think about a multiclass classification problem that the number means that the instance belongs to the n-th class.

[linxcan]

Can I understand it this way, in the results predicted by the topology network, does 0 mean that there is a connection?

[faikit]

No. In the predicted results, we got one channel, which's value is 0.8 for example, meaning the predicted edge is positive. Just take it another way, for a classification problem with 3 classes, the predicted confidence of an instance is [0.8, 0.1, 0.1], which means the instance is predicted as the 0-th, and the corresponding GT for calculating the loss is 0 (assuming the GT is 0-th class).

[linxcan]

But when calculating the loss, the value predicted by the network is compared with 0th. Doesn’t the 0 predicted by the network correspond to the 0th of GT? Doesn’t the value of 0 predicted by the network correspond to the connection of GT?

[faikit]

I think 0 is not a value but a class in the (1 - GT). It is a loss for classification instead of regression.

[linxcan]

Thanks for your reply, I still have some questions. In (1-GT), class 0 is meaningful, which represents connected edges. Doesn’t the class 0 predicted by the topology network correspond to the class 0 of (1-GT)?

[faikit]

For a positive edge in GT, the network should predict it as class 0, that's correct. And predicting the 0-th class means that the 0-th channel of the adjacency matrix should have greater values, then we use a threshold of > 0.5 to determine a predicted positive edge.

[linxcan]

Thank you! Your patience and clear explanation were incredibly helpful.