Gonzalez-Diaz, Rocio , Gutierrez-Naranjo, Miguel A. , PALUZO HIDALGO, EDUARDO
Si
Neural Comput. Appl.
Article
Científica
6
1.169
01/09/2022
000791074200004
2-s2.0-85129430863
One of the main drawbacks of the practical use of neural networks is the long time required in the training process. Such a training process consists of 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 a representative dataset which is a dataset smaller than the original one, satisfying a nearness condition independent of isometric transformations. Representativeness is measured using persistence diagrams (a computational topology tool) due to its computational efficiency. We theoretically prove that the accuracy of a perceptron evaluated on the original dataset coincides with the accuracy of the neural network evaluated on the representative dataset when the neural network architecture is a perceptron, the loss function is the mean squared error, and certain conditions on the representativeness of the dataset are imposed. These theoretical results accompanied by experimentation open a door to reducing the size of the dataset to gain time in the training process of any neural network.
Data reduction; Neural networks; Representative datasets; Computational topology