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These days deep learning is the fastest-growing field in the field of Machine Learning (ML) and Deep Neural Networks (DNN). Among many of DNN structures, the Convolutional Neural Networks (CNN) are currently the main tool used for the image analysis and classification purposes. Although great achievements and perspectives, deep neural networks and accompanying learning algorithms have some relevant challenges to tackle. In this paper, we have focused on the most frequently mentioned problem in the field of machine learning, that is the lack of sufficient amount of the training data or uneven class balance within the datasets. One of the ways of dealing with this problem is so called data augmentation. In the paper we have compared and analyzed multiple methods of data augmentation in the task of image classification, starting from classical image transformations like rotating, cropping, zooming, histogram based methods and finishing at Style Transfer and Generative Adversarial Networks, along with the representative examples. Next, we presented our own method of data augmentation based on image style transfer. The method allows to generate the new images of high perceptual quality that combine the content of a base image with the appearance of another ones. The newly created images can be used to pre-train the given neural network in order to improve the training process efficiency. Proposed method is validated on the three medical case studies: skin melanomas diagnosis, histopathological images and breast magnetic resonance imaging (MRI) scans analysis, utilizing the image classification in order to provide a diagnose. In such kind of problems the data deficiency is one of the most relevant issues. Finally, we discuss the advantages and disadvantages of the methods being analyzed.