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I am working through this course. It seems that the professor is not dividing the dataset into true positive, false positive, true negative, and false negative.

In the context of image binary classification, is it necessary to divide the dataset into true positive, false positive, true negative, and false negative?

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No it's not. The numbers of true positives, false positives, true negatives, false negatives, are something you can check from a confusion matrix when you evaluate the performance of your trained model on a test set. It's useful to know where your model is making more mistakes.

It's not something you can do before training.

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