I have built a classification model to recognise a class and I have evaluated it on several datasets. The problem is that some of these datasets do not have any true instance of the class in question, and so, the model should ideally recognise zero instances.
If the model has 0 false positives on such a dataset, I may claim that the precision of this model on this dataset is 100%. Conceptually, a classification model that recognises 0 instances out of 0 with no FP is a precise model. If, however, the model has only one false positive, the precision will drop down to 0 although a model with only one FP may generally be assumed to have a good precision.
With regards to the recall, since the TP and FN will always be 0, may I claim that the recall on such datasets should always be 100%?
If not, what is the appropriate way to calculate precision/recall in such cases? I am, by the way, aware of the existence of other accuracy evaluation measures but I need to calculate these two (i.e. precision and recall).