The early and accurate detection of breast lesions through mammography is crucial for improving survival rates. However, the existing deep learning-based methods often rely on costly pixel-level annotations, limiting their scalability in real-world applications. To address this issue, a novel local extremum mapping (LEM) mechanism is proposed for mammogram classification and weakly supervised lesion localization. The proposed method first divides the input mammogram into multiple regions and generates score maps through convolutional neural networks. Then, it identifies the most informative regions by filtering local extrema in the score maps and aggregating their scores for final classification. This strategy enables lesion localization with only image-level labels, significantly reducing annotation costs. Experiments on two public mammography datasets, CBIS-DDSM and INbreast, demonstrate that the proposed method achieves competitive performance. On the INbreast dataset, LEM improves classification accuracy to 96.3% with an AUC of 0.976. Furthermore, the proposed method effectively localizes lesions with a dice similarity coefficient of 0.37, outperforming Grad-CAM and other baseline approaches. These results highlight the practical significance and potential clinical applications of our approach, making automated mammogram analysis more accessible and efficient.