{"id":555,"date":"2016-07-17T19:22:21","date_gmt":"2016-07-17T22:22:21","guid":{"rendered":"https:\/\/sbia.org.br\/lnlm\/?page_id=555"},"modified":"2016-07-17T19:22:21","modified_gmt":"2016-07-17T22:22:21","slug":"vol9-no4-art2","status":"publish","type":"page","link":"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol9-no4\/vol9-no4-art2\/","title":{"rendered":"Par\u00e2metro de Exatid\u00e3o para Aproximac\u00e3o de Func\u00f5es Utilizando Multilayer Perceptrons nos Dom\u00ednios Real, Complexo e de Clifford"},"content":{"rendered":"<p><strong>T\u00edtulo:<\/strong> Par\u00e2metro de Exatid\u00e3o para Aproximac\u00e3o de Func\u00f5es Utilizando Multilayer Perceptrons nos Dom\u00ednios Real, Complexo e de Clifford<\/p>\n<p><strong>Autores:<\/strong> Torchi, Thalles S.; Romero, Milton R.; Martins, Evandro M.<\/p>\n<p align=\"justify\"><strong>Resumo:<\/strong> Na fase de utiliza\u00e7\u00e3o, as Redes Neurais Artificiais (RNA) Multilayer Perceptrons, treinadas com o algoritmo de Backpropagation, n\u00e3o conseguem aproximar a fun\u00e7\u00e3o de interesse para 100% dos dados de entrada. Este trabalho prop\u00f5e uma metodologia para abordagem de dois pontos de interesse: 1\u00ba) estimar um par\u00e2metro de exatid\u00e3o para as sa\u00eddas de RNA na fase de utiliza\u00e7\u00e3o, com o objetivo de definir quais sa\u00eddas podem ser consideradas confi\u00e1veis e quais n\u00e3o, definindo como confi\u00e1veis as sa\u00eddas que se aproximam do comportamento da fun\u00e7\u00e3o de interesse; e 2\u00ba) estabelecer o n\u00famero de padr\u00f5es a serem utilizados na fase de treinamento, que permitam a converg\u00eancia e a generaliza\u00e7\u00e3o da rede na metodologia proposta. A metodologia baseia-se no treino e utiliza\u00e7\u00e3o de duas redes: a RNA Direta (RNAD), utilizada para aproximar a fun\u00e7\u00e3o de interesse, e a RNA Inversa (RNAI), utilizada para aproximar a inversa (FI) da fun\u00e7\u00e3o de interesse. Caso a fun\u00e7\u00e3o a ser aproximada n\u00e3o tenha FI definida, o dom\u00ednio \u00e9 restringido para onde exista. Na utiliza\u00e7\u00e3o destas redes ser\u00e1 computada a diferen\u00e7a entre a entrada da RNAD e a sa\u00edda da RNAI. Quando a entrada da RNAD e a sa\u00edda da RNAI forem computacionalmente iguais, ou seja, sua diferencia muito pr\u00f3xima de zero, tanto quanto \u00e0 aplica\u00e7\u00e3o exigir, ser\u00e1 considerado que a sa\u00edda da rede direta (RNAD), isto \u00e9, a aproxima\u00e7\u00e3o da fun\u00e7\u00e3o de interesse, \u00e9 confi\u00e1vel. O m\u00e9todo \u00e9 comprovado experimentalmente a partir de dados sint\u00e9ticos, utilizando a fun\u00e7\u00e3o , a fim de permitir o controle entre as entradas e sa\u00eddas das redes com o intuito de valida\u00e7\u00e3o do m\u00e9todo nos dom\u00ednios Real, Complexo e de Clifford.  Os dados sint\u00e9ticos e n\u00e3o dados de aplica\u00e7\u00f5es reais, se utilizam para demonstrar a viabilidade do algoritmo permitindo comparar os tr\u00eas dom\u00ednios, pois poss\u00edveis erros contidos nos dados reais se mesclariam com poss\u00edveis erros no algoritmo dificultando a valida\u00e7\u00e3o do m\u00e9todo proposto. Os resultados mostram que o m\u00e9todo \u00e9 robusto e permite determinar o par\u00e2metro de exatid\u00e3o para as sa\u00eddas da RNA, o crit\u00e9rio de converg\u00eancia e a qualidade da generaliza\u00e7\u00e3o das mesmas, permitindo a compara\u00e7\u00e3o gr\u00e1fica dos tr\u00eas dom\u00ednios.<\/p>\n<p><strong>Palavras-chave:<\/strong> RNA; par\u00e2metro de exatid\u00e3o; Multilayer Perceptrons; Dom\u00ednio Complexo; Dom\u00ednio Clifford<\/p>\n<p><strong>P\u00e1ginas:<\/strong> 15<\/p>\n<p><strong>C\u00f3digo DOI:<\/strong> <a href=\"http:\/\/dx.doi.org\/10.21528\/lnlm-vol9-no4-art2\">10.21528\/lmln-vol9-no4-art2<\/a><\/p>\n<p><strong>Artigo em PDF:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2016\/07\/vol9-no4-art2.pdf\" rel=\"\">vol9-no4-art2.pdf<\/a><\/p>\n<p><strong>Arquivo BibTex:<\/strong> <a href=\"https:\/\/sbia.org.br\/lnlm\/wp-content\/uploads\/sites\/4\/2016\/07\/vol9-no4-art2.bib\" rel=\"\">vol9-no4-art2.bib<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>T\u00edtulo: Par\u00e2metro de Exatid\u00e3o para Aproximac\u00e3o de Func\u00f5es Utilizando Multilayer Perceptrons nos Dom\u00ednios Real, Complexo e de Clifford Autores: Torchi, Thalles S.; Romero, Milton R.; Martins, Evandro M. Resumo: Na fase de utiliza\u00e7\u00e3o, as Redes Neurais Artificiais (RNA) Multilayer Perceptrons, <a href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol9-no4\/vol9-no4-art2\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":551,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-555","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Par\u00e2metro de Exatid\u00e3o para Aproximac\u00e3o de Func\u00f5es Utilizando Multilayer Perceptrons nos Dom\u00ednios Real, Complexo e de Clifford - Learning and NonLinear Models<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/sbia.org.br\/lnlm\/publicacoes\/vol9-no4\/vol9-no4-art2\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Par\u00e2metro de Exatid\u00e3o para Aproximac\u00e3o de Func\u00f5es Utilizando Multilayer Perceptrons nos Dom\u00ednios Real, Complexo e de Clifford - Learning and NonLinear Models\" \/>\n<meta property=\"og:description\" content=\"T\u00edtulo: Par\u00e2metro de Exatid\u00e3o para Aproximac\u00e3o de Func\u00f5es Utilizando Multilayer Perceptrons nos Dom\u00ednios Real, Complexo e de Clifford Autores: Torchi, Thalles S.; Romero, Milton R.; Martins, Evandro M. 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