Improving neural networks using topological data analysis

Generalisation measures are metrics that indicate how well a neural network will perform in presence of unknown data. Differentiable generalisation measures with respect to the parameters of a neural network that use only the training set are candidates to be used as loss regularisation terms to imp...

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Detalles Bibliográficos
Autor: Ballester Bautista, Rubén
Tipo de recurso: tesis de maestría
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/373847
Acceso en línea:https://hdl.handle.net/2117/373847
Access Level:acceso abierto
Palabra clave:Algebra, Homological
Categories (Mathematics)
Machine learning
TDA
Topological data analysis
Topology
Metric
Distances
Differential calculus
Persistent homology
Persistence diagrams
Correlation
Deep learning
Neural networks
Regularisation
Loss functions
Training algorithms
Àlgebra homològica
Categories (Matemàtica)
Aprenentatge automàtic
Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
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spelling Improving neural networks using topological data analysisBallester Bautista, RubénAlgebra, HomologicalCategories (Mathematics)Machine learningTDATopological data analysisTopologyMetricDistancesDifferential calculusPersistent homologyPersistence diagramsCorrelationMachine learningDeep learningNeural networksRegularisationLoss functionsTraining algorithmsÀlgebra homològicaCategories (Matemàtica)Aprenentatge automàticClassificació AMS::55 Algebraic topology::55U Applied homological algebra and category theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::GeometriaGeneralisation measures are metrics that indicate how well a neural network will perform in presence of unknown data. Differentiable generalisation measures with respect to the parameters of a neural network that use only the training set are candidates to be used as loss regularisation terms to improve neural network training processes. Recently, persistent homology has been used to build robust generalisation measures of this kind by means of persistence diagrams. However, some of these measures involve non-standard distances, and thus the usual stability and differentiability results are not valid. In this thesis, we prove more general stability and differentiability results that fit the conditions required by the previous topological measures. Also, we define a new measure called topological redundancy that we use together with one of the previous topological terms to improve accuracies of networks with respect to usual training without topological regularisation terms.Universitat Politècnica de CatalunyaPfeifle, Julián20222022-09-0120222022-10-03master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2117/373847reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3738472026-05-27T15:37:01Z
dc.title.none.fl_str_mv Improving neural networks using topological data analysis
title Improving neural networks using topological data analysis
spellingShingle Improving neural networks using topological data analysis
Ballester Bautista, Rubén
Algebra, Homological
Categories (Mathematics)
Machine learning
TDA
Topological data analysis
Topology
Metric
Distances
Differential calculus
Persistent homology
Persistence diagrams
Correlation
Machine learning
Deep learning
Neural networks
Regularisation
Loss functions
Training algorithms
Àlgebra homològica
Categories (Matemàtica)
Aprenentatge automàtic
Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
title_short Improving neural networks using topological data analysis
title_full Improving neural networks using topological data analysis
title_fullStr Improving neural networks using topological data analysis
title_full_unstemmed Improving neural networks using topological data analysis
title_sort Improving neural networks using topological data analysis
dc.creator.none.fl_str_mv Ballester Bautista, Rubén
author Ballester Bautista, Rubén
author_facet Ballester Bautista, Rubén
author_role author
dc.contributor.none.fl_str_mv Pfeifle, Julián
dc.subject.none.fl_str_mv Algebra, Homological
Categories (Mathematics)
Machine learning
TDA
Topological data analysis
Topology
Metric
Distances
Differential calculus
Persistent homology
Persistence diagrams
Correlation
Machine learning
Deep learning
Neural networks
Regularisation
Loss functions
Training algorithms
Àlgebra homològica
Categories (Matemàtica)
Aprenentatge automàtic
Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
topic Algebra, Homological
Categories (Mathematics)
Machine learning
TDA
Topological data analysis
Topology
Metric
Distances
Differential calculus
Persistent homology
Persistence diagrams
Correlation
Machine learning
Deep learning
Neural networks
Regularisation
Loss functions
Training algorithms
Àlgebra homològica
Categories (Matemàtica)
Aprenentatge automàtic
Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
description Generalisation measures are metrics that indicate how well a neural network will perform in presence of unknown data. Differentiable generalisation measures with respect to the parameters of a neural network that use only the training set are candidates to be used as loss regularisation terms to improve neural network training processes. Recently, persistent homology has been used to build robust generalisation measures of this kind by means of persistence diagrams. However, some of these measures involve non-standard distances, and thus the usual stability and differentiability results are not valid. In this thesis, we prove more general stability and differentiability results that fit the conditions required by the previous topological measures. Also, we define a new measure called topological redundancy that we use together with one of the previous topological terms to improve accuracies of networks with respect to usual training without topological regularisation terms.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-09-01
2022
2022-10-03
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/373847
url https://hdl.handle.net/2117/373847
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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