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Microscopic analysis of breast cancer images is the primary task in diagnosing cancer malignancy. Recent attempts to automate this task have employed deep learning models whose success has depended on large volumes of data, while acquiring annotated data in biomedical domains is time-consuming and may not always be feasible. A typical strategy to address this is to apply transfer learning using pre-trained models on a large natural image database (e.g., ImageNet) instead of training a model from scratch. This approach, however, has not been effective in several previous studies due to fundamental differences between natural and medical images. In this study, for the first time we proposed the idea of using a compatible data set of histopathological images to classify breast cancer cytological biopsy specimens. Despite intrinsic differences between histopathological and cytological images, we demonstrate that the features learned by deep networks during the pre-training procedure are compatible with those obtained throughout fine-tuning process. To thoroughly investigate this assertion, we explore three different strategies for training as well as two different approaches for fine-tuning deep learning models. By comparing the obtained results with those of previous state-of-the-art research conducted on the same data set, we demonstrate that the proposed method boasts of improved classification accuracy by 6% to 17% compared to the studies which were based on traditional machine learning techniques, and also enhanced accuracy by roughly 7% compared to those who utilized deep learning methods, eventually achieving 98.73% validation accuracy and 94.55% test accuracy. Exploring different training scenarios also revealed that using a compatible dataset has helped to elevate the classification accuracy by 3.0% compared to the typical approach of using ImageNet. Experimental results show that our approach, despite using a very small number of training images, has achieved performance comparable to that of experienced pathologists and has the potential to be applied in clinical settings.