One of the main drawbacks of the practical use of neural networks is the long time needed in
the training process. Such training process consists in an iterative change of parameters trying to
minimize a loss function. These changes are driven by a dataset, which can be seen as a set of
labeled points in an n-dimensional space. In this paper, we explore the concept of representative
dataset which is smaller than the original dataset and satisfies a nearness condition independent of
isometric transformations. The representativeness is measured using persistence diagrams due to its
computational efficiency. We also prove that the accuracy of the learning process of a neural network
on a representative dataset is comparable with the accuracy on the original dataset when the neural
network architecture is a perceptron and the loss function is the mean squared error. These theoretical
results accompanied with experimentation open a door to the size reduction of the dataset in order to
gain time in the training process of any neural network
