I'm trying to evaluate some classification algorithms' results in my imbalanced dataset. With imabalnced, I mean that there are much more negative labels than positive ones. Accuracy and precision are always good, but recall and Area Under the Precision-Recall curve (PR_AUC) are not so good. I'm seeking the classifier that maximizes the PR_AUC.
1.- Do you think this is a good criteria to select a classification algorithm in this case?
2.- Are recall and PR_AUC proportional? I mean, if a classifier gives better recall results than another one, but worse PR_AUC results... Am I doing something wrong? Or it has a logical explanation? Which one is the best criteria for imbalanced datasets?
Thank you for your help!