## 2 Related Work  
The development and application of deep learning techniques for breast cancer diagnosis, especially in the field of mammography, have seen significant advancements in recent years. Initially, traditional machine learning techniques were widely employed, utilizing algorithms such as Multi-class Support Vector Machines (SVMs) and K-Means clustering. These methods focused on the statistical analysis of features extracted manually from images, providing a foundational approach for early classification efforts [30]. As the field progressed, the advent of convolutional neural networks (CNNs) marked a significant shift, with architectures such as MobileNetv2 and ResNet offering more sophisticated image analysis capabilities through deep learning, enabling automatic feature extraction directly from raw images [31; 32].  
Further advancements led to the integration of segmentation techniques alongside CNNs, enhancing the precision of classifications. Methods such as U-Net began to be employed for isolating lesions from surrounding tissue before classification, improving the accuracy by focusing the CNNs on relevant image segments only [33]. The culmination of these developments has been the adoption of multi-input CNN models that integrate segmented image data with patient metadata, using diverse architectures to capture a broad spectrum of mammographic features effectively. Researchers have explored various strategies to optimize the accuracy and efficiency of these models, particularly through the use of multi-input systems that combine different data types and processing techniques [34].  
The incorporation of multi-input CNN models marks a pivotal advancement in mammographic imaging. These models integrate multiple data streams, such as high-resolution images, extracted regions of interest, and additional contextual information, to enhance diagnostic precision [35]. Some studies propose end-to-end models that maximize the use of high-resolution images through a multi-input strategy, including cropping, original image downsampling, and region-of-interest extraction using CAM, supplemented by attention mechanisms to enhance classification accuracy [36].  
The adoption of semi-supervised learning techniques in mammographic imaging represents another significant advancement. Semi-supervised learning combines a small amount of labeled data with a large amount of unlabeled data, which helps to improve model performance while reducing the effort of data labeling. This approach is particularly useful in medical imaging, where obtaining labeled data is often expensive and time-consuming [37; 38]. In recent years, semi-supervised learning has been increasingly applied to mammographic image analysis, further enhancing the effectiveness and efficiency of deep learning models in this domain [39].  
Therefore, in addition to the related work mentioned above and the studies on mammography discussed in the Introduction, the novelty of this study, compared to previous research, can be demonstrated (Table 1) by the following aspects: the utilization of semi-supervised learning for mammography, the reduction of labeling effort, the improvement in classification accuracy, the investigation of classification probability thresholds, a new approach to classification accuracy, and the combination of patch division and semi-supervised learning.