{"id":180193,"date":"2024-06-06T23:56:09","date_gmt":"2024-06-06T22:56:09","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=180193"},"modified":"2024-02-26T00:14:28","modified_gmt":"2024-02-25T23:14:28","slug":"sigmoid-function-what-is-it-whats-it-for","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/sigmoid-function-what-is-it-whats-it-for","title":{"rendered":"Sigmoid function: What is it? What&#8217;s it for?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"180193\" class=\"elementor elementor-180193\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bb911a6 e-flex e-con-boxed e-con\" data-id=\"bb911a6\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7b250c9 elementor-widget elementor-widget-heading\" data-id=\"7b250c9\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">An essential concept in mathematics, the Sigmoid function applies perfectly to neural networks. Find out more about this function, its different phases and applications. <\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4065c6f e-flex e-con-boxed e-con\" data-id=\"4065c6f\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-9982e8b elementor-widget elementor-widget-heading\" data-id=\"9982e8b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What is the Sigmoid function?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7aa842f elementor-widget elementor-widget-text-editor\" data-id=\"7aa842f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>Also known as the S-curve, the <strong>Sigmoid function is expressed as follows:<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a8efe49 elementor-widget__width-initial elementor-widget elementor-widget-shortcode\" data-id=\"a8efe49\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><math xmlns='http:\/\/www.w3.org\/1998\/Math\/MathML'>\n  <mi> f <\/mi>\n  <mrow>\n    <mo> ( <\/mo>\n      <mi> x <\/mi>\n    <mo> ) <\/mo>\n  <\/mrow>\n  <mo> = <\/mo>\n  <mfrac>\n    <mrow>\n      <mn> 1 <\/mn>\n    <\/mrow>\n    <mrow>\n      <mn> 1 <\/mn>\n      <mo> + <\/mo>\n      <msup>\n        <mrow>\n          <mi> e <\/mi>\n        <\/mrow>\n        <mrow>\n          <mo> - <\/mo>\n          <mi> &#x03BB; <!-- greek small letter lambda --> <\/mi>\n          <mi> x <\/mi>\n        <\/mrow>\n      <\/msup>\n    <\/mrow>\n  <\/mfrac>\n<\/math><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-954dbe8 elementor-widget elementor-widget-text-editor\" data-id=\"954dbe8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The visual representation of the curve is characterized by an exponential increase in one variable, which then becomes linear, then asymptotic. The whole thing then<strong> forms a kind of S. Hence the name of the sigmoid function.<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-807b8b1 e-flex e-con-boxed e-con\" data-id=\"807b8b1\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-68e74fa elementor-widget elementor-widget-heading\" data-id=\"68e74fa\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What are the phases of the Sigmoid curve?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-705149a elementor-widget elementor-widget-text-editor\" data-id=\"705149a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The S-curve is visually characterized by 4 very distinct phases. These are shown below.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7fcf14c elementor-widget elementor-widget-heading\" data-id=\"7fcf14c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The offset phase<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49a8e48 elementor-widget elementor-widget-text-editor\" data-id=\"49a8e48\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Initially, the curve grows relatively slowly. This is the latency period.<\/p><p>This can be seen, for example, in market research for the launch of a new product. At first, few buyers dare to take the plunge and acquire a product that is still unknown.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f0cd0f8 elementor-widget elementor-widget-heading\" data-id=\"f0cd0f8\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The exponential phase<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-12632f5 elementor-widget elementor-widget-text-editor\" data-id=\"12632f5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Gradually, the<strong> curve begins to increase until it reaches exponential growth.<\/strong><\/p><p>Again, this type of curve can be found in market research. It&#8217;s only when the first buyers have tested the product or service that the majority of consumers are ready to take the plunge. The snowball effect is set in motion. Customer satisfaction and word-of-mouth help organizations acquire more and more new customers. The result is <a href=\"https:\/\/datascientest.com\/en\/growth-marketing-definition-and-differences-from-growth-hacking\">exponential growth.<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d5602a6 elementor-widget elementor-widget-heading\" data-id=\"d5602a6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The transitional phase<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-174223a elementor-widget elementor-widget-text-editor\" data-id=\"174223a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>After exponential growth, the Sigmoid function is characterized by a transitional phase in which the curve slows down, rises or falls slightly. Small variations are then observed.<\/p><p>In the context of our market research, this refers to the period when the majority of potential customers have already been targeted. Here, there aren&#8217;t many new leads\/prospects left. At the same time, the first signs of customer dissatisfaction can appear. This can lead to a slowdown or even a drop in sales. But this doesn&#8217;t happen automatically.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8fc2249 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"8fc2249\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Mastering the Sigmoid function<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d970108 elementor-widget elementor-widget-heading\" data-id=\"d970108\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The plateau stadium<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c6e1172 elementor-widget elementor-widget-text-editor\" data-id=\"c6e1172\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>And finally, the Sigmoid curve stabilizes until it resembles a plateau. All values remain more or less identical.<\/p><p>In the commercial world, this applies to well-established companies that have acquired a stable customer base.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c9aeefa elementor-widget elementor-widget-text-editor\" data-id=\"c9aeefa\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Good to know:<\/strong> beyond <strong>market research<\/strong>, the Sigmoid function can be observed in a wide variety of cases, such as contagions that turn into epidemics (covid crisis), an individual&#8217;s height or weight over the course of a lifetime, not to <a href=\"https:\/\/datascientest.com\/en\/convolutional-neural-network-everything-you-need-to-know\">mention neural networks.<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5547ce2 e-flex e-con-boxed e-con\" data-id=\"5547ce2\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-29dd283 elementor-widget elementor-widget-heading\" data-id=\"29dd283\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What's the link between the Sigmoid function and machine learning?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6e088fb elementor-widget elementor-widget-text-editor\" data-id=\"6e088fb\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The<strong> Sigmoid function<\/strong> is often used in neural networks. It acts as an activation function. More precisely, it enables the network to produce a result based on the available data.<\/p><p>So, when input data<a href=\"https:\/\/datascientest.com\/en\/deep-neural-network-what-is-it-and-how-is-it-working\"> enters the neural network,<\/a> each neuron applies a transformation to it. This enables them to produce a new result.<\/p><p>But with the<strong> Sigmoid function<\/strong>, the result is non-linear. The spatial representation of the data is therefore modified. In other words, the neural network is able to explore the data from different angles. These different perspectives enable us to better understand the data, its meaning and to arrive at the most relevant result.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-cc39006 e-flex e-con-boxed e-con\" data-id=\"cc39006\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7ab50b9 elementor-widget elementor-widget-heading\" data-id=\"7ab50b9\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Join DataScientest<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6cbbf73 elementor-widget elementor-widget-text-editor\" data-id=\"6cbbf73\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Like <a href=\"https:\/\/datascientest.com\/en\/expected-goals-understand-the-math-behind-it\">many mathematical and statistical formulas,<\/a> the <strong>Sigmoid function<\/strong> is indispensable for creating machine learning models. But mastering mathematics is not enough to design and use neural networks. You also need to know p<a href=\"https:\/\/datascientest.com\/en\/python-the-most-popular-language\">rogramming languages<\/a>, machine learning, deep learning, data engineering and more. Datascientest offers training in all these disciplines.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-948e5f0 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"948e5f0\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Find out more about our training courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-52d9f95 e-flex e-con-boxed e-con\" data-id=\"52d9f95\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5467121 elementor-widget elementor-widget-html\" data-id=\"5467121\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"The shift phase\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Initially, the curve grows relatively slowly. 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Also known as the S-curve, the Sigmoid function is expressed as follows: f ( x ) = 1 1 + e &#8211; &#x03BB; x The visual [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":180195,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Sigmoid function: What is it? What&#039;s it for?<\/title>\n<meta name=\"description\" content=\"The sigmoid function, also known as the logistic function, is a mathematical function that maps input values to a range between 0 and 1. 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