Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification

<!DOCTYPE html> <html lang="es-MX"> <head id="Head"><meta content="text/html; charset=UTF-8" http-equiv="Content-Type" /> <meta property="og:title" content="Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional"> <meta property="og:site_name" content="Cinvestav"> <meta property="og:url" content="https://www.cinvestav.mx"> <meta property="og:description" content="El Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional es una institución pública mexicana dedicada al desarrollo de ciencia, tecnología y a la educación a nivel de posgrado. 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Inició sus actividades en 1961 bajo la dirección del científico mexicano Arturo Rosenblueth Stearns."><title> Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification </title><meta id="MetaDescription" name="description" content="Abstract This article presents a learning algorithm for dendrite morphological neurons (DMN) based on stochastic gradient descent (SGD). In..." /><meta id="MetaRobots" name="robots" content="INDEX, FOLLOW" /><link href="/Resources/Shared/stylesheets/dnndefault/7.0.0/default.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/Portals/_default/ie.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/DesktopModules/EasyDNNNews/Templates/_default/Advantage/Advantage.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/DesktopModules/EasyDNNnews/Templates/_default/Cinvestav2020v2/Cinvestav2020v2.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/DesktopModules/EasyDNNNews/Templates/_default/Advantage/StylesCSS/atlantic.css?cdv=114" type="text/css" rel="stylesheet"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/Portals/_default/skins/cinvestav2020v2/menus/pure-css-justified/pure-css-nav-jus.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/Portals/_default/skins/cinvestav2020v2/menus/mobile/mobmenu.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/DesktopModules/EasyDNNNews/static/rateit/css/rateit.css?cdv=114" type="text/css" rel="stylesheet"/><link href="/DesktopModules/EasyDNNNews/static/common/common.css?cdv=114" type="text/css" rel="stylesheet"/><script src="/DesktopModules/EasyDNNNews/static/eds_jquery/eds_jq.js?cdv=114" type="text/javascript"></script><script src="/Resources/libraries/jQuery/03_05_01/jquery.js?cdv=114" type="text/javascript"></script><script src="/Resources/libraries/jQuery-Migrate/03_02_00/jquery-migrate.js?cdv=114" type="text/javascript"></script><script src="/Resources/libraries/jQuery-UI/01_12_01/jquery-ui.js?cdv=114" type="text/javascript"></script><meta name="eds__GmapsInitData" content="{"instanceGlobal":"EasyDnnSolutions1_1_instance","google":{"maps":{"api":{"key":"AIzaSyAkmOUFL1XjI2_jiIAA0X366s_nfQ8tPpk","libraries":["geometry","places"]}}}}" /><meta property="og:site_name" content="Centro de investigación y de Estudios Avanzados del Instituto Politécnico Nacional" /> <meta property="og:title" content="Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification" /> <meta property="og:description" content="Abstract This article presents a learning algorithm for dendrite morphological neurons (DMN) based on stochastic gradient descent (SGD). In particular, we focus on a DMN topology that comprises spherical dendrites, smooth maximum activation function nodes, and a softmax output layer, whose original learning algorithm is performed in two independent stages: (1) dendrites’ centroids are learned by k-means, and (2) softmax layer weights are adjusted by gradient descent. A drawback of this..." /> <meta property="og:url" content="https://www.cinvestav.mx/investigacion/publicaciones/learning-smooth-dendrite-morphological-neurons-by-stochastic-gradient-descent-for-pattern-classification" /> <meta property="og:type" content="article" /> <meta property="og:image" content="https://www.cinvestav.mx/Portals/0/EasyDNNnews/13786/1-s2.0-S0893608023005294-gr3_lrg.jpg" /> <meta name="twitter:card" content="summary_large_image" /> <meta name="twitter:title" content="Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification" /> <meta name="twitter:description" content="Abstract This article presents a learning algorithm for dendrite morphological neurons (DMN) based on stochastic gradient descent (SGD). In particular, we focus on a DMN topology that comprises..." /> <meta name="twitter:image" content="https://www.cinvestav.mx/Portals/0/EasyDNNnews/13786/1-s2.0-S0893608023005294-gr3_lrg.jpg" /> <script type="application/ld+json">{ "@context": "http://schema.org", "@type": "NewsArticle", "mainEntityOfPage": { "@type": "WebPage", "@id": "https://cinvestav.mx/Inicio-old/ArtMID/380/ArticleID/13786/Learning-smooth-dendrite-morphological-neurons-by-stochastic-gradient-descent-for-pattern-classification" }, "headline": "Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification", "image": { "@type": "ImageObject", "url": "https://www.cinvestav.mx/Portals/0/EasyDNNnews/13786/1-s2.0-S0893608023005294-gr3_lrg.jpg" }, "datePublished": "2024-11-27T11:32:00.0000000", "dateModified": "2024-11-27T11:35:48.6070000", "author": { "@type": "Person", "name": "Leobardo Pérez Martínez" }, "publisher": { "@type": "Organization", "name": "Centro de investigación y de Estudios Avanzados del Instituto Politécnico Nacional", "logo": { "@type": "ImageObject", "url": "" } }, "description": "" } </script><meta name="viewport" content="width=device-width,initial-scale=1" /></head> <body id="Body"> <form method="post" action="/investigacion/publicaciones/learning-smooth-dendrite-morphological-neurons-by-stochastic-gradient-descent-for-pattern-classification" onsubmit="javascript:return WebForm_OnSubmit();" id="Form" enctype="multipart/form-data"> <div class="aspNetHidden"> <input type="hidden" name="__EVENTTARGET" id="__EVENTTARGET" value="" /> <input type="hidden" name="__EVENTARGUMENT" id="__EVENTARGUMENT" value="" /> <input type="hidden" name="__VIEWSTATE" id="__VIEWSTATE" value="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" /> </div> <script type="text/javascript"> //<![CDATA[ var theForm = document.forms['Form']; 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</div> </li> </ul> </div> </div> </div></div></div></div> <div id="dnn_g4x8_B" class="col-md-8"><div class="DnnModule DnnModule-EasyDNNnews DnnModule-3856"><a name="3856"></a><div id="dnn_ctr3856_ContentPane"><div id="dnn_ctr3856_ModuleContent" class="DNNModuleContent ModEasyDNNnewsC"> <script type="text/javascript"> /*<![CDATA[*/ eds3_5_jq(function ($) { $('#dnn_ctr3856_ViewEasyDNNNewsMain_ctl00_pnlViewArticle_edn_printButton').on('click', function (){ var prtContent = document.getElementById('dnn_ctr3856_ViewEasyDNNNewsMain_ctl00_pnlViewArticle'), spacelessTitle = 'Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification'.replace(/\s/g, '_'), WinPrint = window.open(this.href, spacelessTitle, 'toolbar=no,location=no,status=no,menubar=no,scrollbars=yes,resizable=yes,width=450,height=250'); WinPrint.document.write("<!DOCTYPE html PUBLIC \"-//W3C//DTD XHTML 1.0 Strict//EN\" \"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd\">"); WinPrint.document.write("<html><head><title>Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification</title><link rel=\"stylesheet\" type=\"text/css\" href=\"https://www.cinvestav.mx/DesktopModules/EasyDNNnews/Templates/_default/Cinvestav2020v2/Cinvestav2020v2.css\"/></head><body>"); WinPrint.document.write("<div class=\"eds_news_module_3856 news eds_subCollection_news eds_news_Cinvestav2020v2 eds_template_Details_Article_Eventos eds_templateGroup_detailsArticleEventos eds_styleSwitchCriteria_module-3856 eds_print\">") WinPrint.document.write(prtContent.innerHTML); WinPrint.document.write("</div></body></html>"); WinPrint.document.close(); WinPrint.focus(); setTimeout(function () { WinPrint.print(); setTimeout(function () { WinPrint.close(); }, 100); WinPrint.onafterprint = function(){ WinPrint.close()}; }, 500); return false; }); }); eds3_5_jq(function ($) { if (typeof edn_fluidvids != 'undefined') edn_fluidvids.init({ selector: ['.edn_fluidVideo iframe'], players: ['www.youtube.com', 'player.vimeo.com'] }); }); /*]]>*/ </script> <div class="eds_news_module_3856 news eds_subCollection_news eds_news_Cinvestav2020v2 eds_template_Details_Article_Eventos eds_templateGroup_detailsArticleEventos eds_styleSwitchCriteria_module-3856"> <div id="dnn_ctr3856_ViewEasyDNNNewsMain_ctl00_pnlViewArticle"> <article class="edNews_article edNews_articleDetails cuadro" data-article-meta="{"url":"https://www.cinvestav.mx/Default.aspx?tabid=167\u0026artmid=3856\u0026articleid=13786\u0026language=es-MX","id":13786,"comments":{"numberOf":0},"pageArticleTitle":"Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification"}"> <div class="edNews_mediaContainer"> <picture> <source media="(max-width: 480px)" srcset="/Portals/0/EasyDNNNews/13786/images/1-s2.0-S0893608023005294-gr3_lrg-400-400-p-L-97.jpg"> <source media="(max-width: 640px)" srcset="/Portals/0/EasyDNNNews/13786/images/1-s2.0-S0893608023005294-gr3_lrg-600-600-p-L-97.jpg"> <center><img class="img-responsive" src="/Portals/0/EasyDNNNews/13786/images/1-s2.0-S0893608023005294-gr3_lrg-600-600-p-L-97.jpg" /></center> <p>  </p> </picture> </div> <h1 class="title ">Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification</h1> <h4>Wilfrido Gómez-Flores and Humberto Sossa. </h4> <p>  </p> <h2>Abstract</h2> <p>This article presents a learning algorithm for dendrite morphological neurons (DMN) based on <a href="https://www.sciencedirect.com/topics/earth-and-planetary-sciences/stochastic-gradient-descent" title="Learn more about stochastic gradient descent from ScienceDirect's AI-generated Topic Pages">stochastic gradient descent</a> (SGD). In particular, we focus on a DMN topology that comprises spherical dendrites, smooth maximum activation function nodes, and a softmax output layer, whose original learning algorithm is performed in two independent stages: (1) dendrites’ <a href="https://www.sciencedirect.com/topics/earth-and-planetary-sciences/centroid" title="Learn more about centroids from ScienceDirect's AI-generated Topic Pages">centroids</a> are learned by k-means, and (2) softmax layer weights are adjusted by gradient descent. A drawback of this learning method is that both stages are unplugged; once dendrites’ centroids are defined, they keep static during weights learning, so no feedback is performed to correct the dendrites’ positions to improve classification performance. To overcome this issue, we derive the delta rules for adjusting the dendrites’ centroids and the output layer weights by minimizing the cross-entropy loss function under an SGD scheme. This gradient descent-based learning is feasible because the smooth maximum activation function that interfaces the dendrite units with the output layer is differentiable. The proposed DMN is compared against eight morphological neuron models with distinct topologies and learning methods and four well-established classifiers: <a href="https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/support-vector-machine" title="Learn more about support vector machine from ScienceDirect's AI-generated Topic Pages">support vector machine</a> (SVM), multilayer <a href="https://www.sciencedirect.com/topics/earth-and-planetary-sciences/self-organizing-systems" title="Learn more about perceptron from ScienceDirect's AI-generated Topic Pages">perceptron</a> (MLP), and random forest (RF), and k-nearest neighbors (k-NN). Besides, the classification performance is evaluated on 81 datasets. The experimental results show that the proposed method tends to outperform the DMN methods and is competitive or even better than SVM, MLP, RF, and k-NN. Thus, it is an alternative approach that can effectively be used for pattern classification. Moreover, SGD for DMN learning standardizes this neural model, like current artificial <a href="https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/neural-network" title="Learn more about neural networks from ScienceDirect's AI-generated Topic Pages">neural networks</a>.</p> <p> </p> <p><a aria-label="Persistent link using digital object identifier" href="https://doi.org/10.1016/j.neunet.2023.09.033" rel="noreferrer noopener" target="_blank" title="Persistent link using digital object identifier">https://doi.org/10.1016/j.neunet.2023.09.033</a></p> <div class="edNews_clearFix"></div> <div class="edNews_socialPrintWrapper"> <iframe src="https://www.facebook.com/plugins/like.php?locale=en_US&href=https%3a%2f%2fwww.cinvestav.mx%2finvestigacion%2fpublicaciones%2flearning-smooth-dendrite-morphological-neurons-by-stochastic-gradient-descent-for-pattern-classification&width=96&layout=button_count&action=like&size=large&show_faces=true&share=false&height=21" width="96" 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Learning smooth dendrite morphological neurons by stochastic gradient descent for pattern classification