## 1 Introduction
Deep learning has been used in mammography not only for the detection and classification of microcalcifications and masses [17; 18], but also for mammography-based risk prediction and stratification [19], the detection and classification of abnormal findings [20], breast density classification [21], and many other applications. However, CNNs (Convolution Neural Networks), used in deep learning, have a limit to the input matrix size. Therefore, when mammography images with a large matrix size are compressed to the CNN input size, information on small lesions such as small masses and microcalcifications may be lost. By segmenting the mammography image into patches, it is possible to input the image with the original resolution, and each patch generated by the segmentation can be classified according to the presence or absence of calcification, enabling the detection of calcification [22]. However, training with deep learning requires a large amount of data, and labeling the large number of patches generated by patch segmentation is time-consuming and labor-intensive. Therefore, we thought that semi-supervised learning would make it possible to learn efficiently from a small amount of labeled data. Machine learning is generally divided into supervised learning, unsupervised learning, and semi-supervised learning, with the main difference being the presence or absence of labels on the training data [23]. Semi-supervised learning is a method that falls between supervised learning, which uses only labeled data, and unsupervised learning, which does not use labeled data [24]. Most research using deep learning in medical imaging focuses on supervised learning, which requires the large-scale labeling of data by experts. However, labeled data are difficult to obtain, whereas unlabeled data are increasing every day and can be prepared in large quantities and easily [25]. Semi-supervised learning combines unlabeled data with a limited amount of labeled data to reduce the effort of labeling, which is a time-consuming task, and to improve model performance by making use of unlabeled data [24]. This technique is often used, especially when limited labeled data and large unlabeled data are available [26]. The utility of semi-supervised learning has been tested in a variety of medical imaging applications [25; 27]. Due to the limitations of the input size of the CNN, compressing mammographic images may result in the loss of small lesions. However, by dividing the images into patches, they can be input at their original resolution, allowing for the detection of calcifications by classifying each patch for the presence or absence of calcifications. Labeling a large number of generated patches is time-consuming and labor-intensive, so we considered that semi-supervised learning, which leverages a small amount of labeled data, would be effective. There have been several studies using semi-supervised learning for mammography [28; 29]. Additionally, this study examined the differences in accuracy due to varying classification probabilities (threshold differences) in semi-supervised learning. No previous studies have been found that investigated the differences in classification accuracy for the presence or absence of calcifications in mammograms based on varying classification probabilities in semi-supervised learning. In this study, we investigate the effect of semi-supervised learning on mammographic calcification detection.