Computational topology on neural networks: from the data to the model

Machine learning is drawn from a dataset that needs to be explained. Following this aim, a model is described to make predictions. These datasets can be of very different nature, as well as the problems they pose: supervised or unsupervised classification, regression... In this work, we have studied, from a computational topology point of view, two machine learning’s pillars: the datasets considered as sets of =-dimensional points, and a specific model, artificial neural networks. we have applied topological data analysis techniques to classify literary trends from a literature dataset and to reduce the size of datasets controlling the loss of information, and, finally, we have developed a new neural network architecture based on simplicial complexes and the maps defined between them, and we have also proved certain properties such as that the new family of neural networks are universal approximators and robust to "adversarial examples".

Author dc:creator

• Paluzo Hidalgo, Eduardo

Advisors dc:contributor.advisor

• González Díaz, Rocío
• Gutiérrez Naranjo, Miguel Ángel

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 Internacional

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/11441/116665

OAI identifier oai:identifier

oai:idus.us.es:11441/116665