This study presents a novel deep learning architecture for multi-class classification and localization of abnormalities in medical imaging illustrated through experiments on mammograms. The proposed network combines two learning branches. One branch is for region classification with a newly added normal-region class. Second branch is region detection branch for ranking regions relative to one another. Our method enables detection of abnormalities at full mammogram resolution for both weakly and semi-supervised settings. A novel objective function allows for the incorporation of local annotations into the model. We present the impact of our schemes on several performance measures for classification and localization, to evaluate the cost effectiveness of the lesion annotation effort. Our evaluation was primarily conducted over a large multi-center mammography dataset of ~3,000 mammograms with various findings. The results for weakly supervised learning showed significant improvement compared to previous approaches. We show that the time consuming local annotations involved in supervised learning can be addressed by a weakly supervised method that can leverage a subset of locally annotated data. Weakly and semi-supervised methods coupled with detection can produce a cost effective and explainable model to be adopted by radiologists in the field.