Say I have a classifier that assigns a score to an image based on whether it has a cat in it. The higher the score, the more likely there's a cat in it. But for this classifier, the value of the score is unbounded, and could be any positive number, in principle. Is there a well-defined way to create a ROC curve for this classifier, if all the images have yes/no labels? Just as a traditional ROC curve involves all thresholds between 0 and 1, could a modified ROC curve involve all decision thresholds between 0 and the highest score?
I could normalize the scores to [0,1] by dividing them by the highest score in the set, but I want to avoid that if possible.