Given that Deep Learning has been widely used to create models capable of performing medical image classification, there is the challenge of collecting a large amount of data to train these models. With the aim of investigating the impact of training data reduction on the performance of neural network models in medical data contexts, this work presents the approach TraiRANN . This new approach allows the application of data reduction techniques, with experiments being carried out using the Relative Neighborhood Graph (RNG) techniques and also a random selection of elements from the set, followed by an evaluation of the performance of the trained models. The method was tested on two image datasets: COVID-19 and Leukemia, and it has proven capable of creating models that achieve performance similar to models trained with the complete training set. For the experiments, we evaluated the performance of three neural network models: VGG16, ResNet50V2, and DenseNet201. It was observed that the ResNet50V2 and DenseNet201 networks achieved the best performance, reaching an accuracy of 97.4% when the COVID-19 dataset is reduced and 86.1% when the reduction is applied to the Leukemia dataset – performance comparable to models trained with the complete dataset. It is noteworthy that the TraiRANN can be straightforwardly adapted to use other training set reduction techniques.