Bicomplex neural networks with hypergeometric activation functions
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/36748 |
Resumo: | Bicomplex convolutional neural networks (BCCNN) are a natural extension of the quaternion convolutional neural networks for the bicomplex case. As it happens with the quaternionic case, BCCNN has the capability of learning and modelling external dependencies that exist between neighbour features of an input vector and internal latent dependencies within the feature. This property arises from the fact that, under certain circumstances, it is possible to deal with the bicomplex number in a component-wise way. In this paper, we present a BCCNN, and we apply it to a classification task involving the colorized version of the well-known dataset MNIST. Besides the novelty of considering bicomplex numbers, our CNN considers an activation function a Bessel-type function. As we see, our results present better results compared with the one where the classical ReLU activation function is considered. |
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Bicomplex neural networks with hypergeometric activation functionsArtificial neural networks and deep learningActivation functionsBicomplex convolutional neural networksHypergeometric functionsBessel functionsBicomplex convolutional neural networks (BCCNN) are a natural extension of the quaternion convolutional neural networks for the bicomplex case. As it happens with the quaternionic case, BCCNN has the capability of learning and modelling external dependencies that exist between neighbour features of an input vector and internal latent dependencies within the feature. This property arises from the fact that, under certain circumstances, it is possible to deal with the bicomplex number in a component-wise way. In this paper, we present a BCCNN, and we apply it to a classification task involving the colorized version of the well-known dataset MNIST. Besides the novelty of considering bicomplex numbers, our CNN considers an activation function a Bessel-type function. As we see, our results present better results compared with the one where the classical ReLU activation function is considered.Springer2023-03-30T14:57:34Z2023-04-01T00:00:00Z2023-04info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/36748eng0188-700910.1007/s00006-023-01268-wVieira, N.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:10:32Zoai:ria.ua.pt:10773/36748Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:07:20.569589Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Bicomplex neural networks with hypergeometric activation functions |
title |
Bicomplex neural networks with hypergeometric activation functions |
spellingShingle |
Bicomplex neural networks with hypergeometric activation functions Vieira, N. Artificial neural networks and deep learning Activation functions Bicomplex convolutional neural networks Hypergeometric functions Bessel functions |
title_short |
Bicomplex neural networks with hypergeometric activation functions |
title_full |
Bicomplex neural networks with hypergeometric activation functions |
title_fullStr |
Bicomplex neural networks with hypergeometric activation functions |
title_full_unstemmed |
Bicomplex neural networks with hypergeometric activation functions |
title_sort |
Bicomplex neural networks with hypergeometric activation functions |
author |
Vieira, N. |
author_facet |
Vieira, N. |
author_role |
author |
dc.contributor.author.fl_str_mv |
Vieira, N. |
dc.subject.por.fl_str_mv |
Artificial neural networks and deep learning Activation functions Bicomplex convolutional neural networks Hypergeometric functions Bessel functions |
topic |
Artificial neural networks and deep learning Activation functions Bicomplex convolutional neural networks Hypergeometric functions Bessel functions |
description |
Bicomplex convolutional neural networks (BCCNN) are a natural extension of the quaternion convolutional neural networks for the bicomplex case. As it happens with the quaternionic case, BCCNN has the capability of learning and modelling external dependencies that exist between neighbour features of an input vector and internal latent dependencies within the feature. This property arises from the fact that, under certain circumstances, it is possible to deal with the bicomplex number in a component-wise way. In this paper, we present a BCCNN, and we apply it to a classification task involving the colorized version of the well-known dataset MNIST. Besides the novelty of considering bicomplex numbers, our CNN considers an activation function a Bessel-type function. As we see, our results present better results compared with the one where the classical ReLU activation function is considered. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-03-30T14:57:34Z 2023-04-01T00:00:00Z 2023-04 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/36748 |
url |
http://hdl.handle.net/10773/36748 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0188-7009 10.1007/s00006-023-01268-w |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137728705593344 |