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I have read both on SO and on CValidated and still feel I do not completely understand the following matter.

If I have a binary segmentation (consider a medical problem, where you have healthy and damaged tissue), which loss is better to use, BCE or CCE?

Some have stated that(and I perfectly understand) that CCE is more computationally expensive than BCE for binary classification and that there is no reason for using CCE. While I understand the justification, I have not found a study which clearly compares the final output/results compared side by side (Acc/Dice/Jaccard metrics on validation/test datasets with BCE vs CCE).

Are there clear cases in which BCE outperforms CCE or vice-versa for binary segmentation?

Timbus Calin
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    Categorical cross-entropy for two classes is same to binary cross-entropy. – f4f Nov 20 '19 at 12:45
  • After some digging, I found the answer here: https://stackoverflow.com/questions/57726064/binary-cross-entropy-vs-categorical-cross-entropy-with-2-classes – Timbus Calin Nov 20 '19 at 12:59

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The answer is provided at the following link Binary cross entropy Vs categorical cross entropy with 2 classes.

It is stated that from a mathematical viewpoint(result, not computational overhead), softmax on two classes is exactly the same like in case of BCE, the same answer as @f4f.

Timbus Calin
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    To measure if there is any computational overhead you shall test your setup, obviously its dependent on used framework. But I think that state of the art frameworks will perform with same efficiency for both cases. – f4f Nov 20 '19 at 13:18
  • Thank you for the response, sensible observation. – Timbus Calin Nov 20 '19 at 13:19
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    You are welcome. – f4f Nov 20 '19 at 13:33