{"id":172137,"date":"2023-10-16T08:20:01","date_gmt":"2023-10-16T07:20:01","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=172137"},"modified":"2023-10-16T08:24:44","modified_gmt":"2023-10-16T07:24:44","slug":"svm-support-vector-machines-unveiled-understanding-implementation-significance-part-2","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/svm-support-vector-machines-unveiled-understanding-implementation-significance-part-2","title":{"rendered":"SVM (Support Vector Machines) Unveiled: Understanding, Implementation, Significance &#8211; Part 2"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"172137\" class=\"elementor elementor-172137\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dccdccc e-flex e-con-boxed e-con\" data-id=\"dccdccc\" 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-4d4c4b28 elementor-widget elementor-widget-heading\" data-id=\"4d4c4b28\" 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\">Welcome to the second part of this dossier dedicated to Vector Machine Support. <\/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-6e877c20 e-flex e-con-boxed e-con\" data-id=\"6e877c20\" 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-efa8311 elementor-widget elementor-widget-text-editor\" data-id=\"efa8311\" 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><a href=\"https:\/\/datascientest.com\/en\/svm-support-vector-machines-unveiled-understanding-implementation-significance\">In the previous article<\/a>, we detailed the operation and main<strong> shortcomings of Maximal Margin Classifiers.<\/strong><\/p><p>Our aim now is to<a href=\"https:\/\/datascientest.com\/en\/knn-what-is-the-knn-algorithm\"> allow our algorithm to make a certain number of errors<\/a> when selecting the separation line. This is known as the &#8220;soft margin&#8221;. We will now describe in detail how the Soft Margin Classifiers algorithm works, halfway between the <strong>Support Vector Machine<\/strong> and the Maximal Margin Classifier.<\/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-3d866c83 e-flex e-con-boxed e-con\" data-id=\"3d866c83\" 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-5b4e6ba3 elementor-widget elementor-widget-heading\" data-id=\"5b4e6ba3\" 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\">Soft Margin Classifiers<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-452e0f02 elementor-widget elementor-widget-text-editor\" data-id=\"452e0f02\" 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>In the previous article, we defined the margin as the distance separating a line from the nearest observation.<\/p><p>In this second part, we&#8217;ll also use the term margin, but this time it will refer to the set of points closer to the line than the nearest observation<\/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-28c7e8fc elementor-widget elementor-widget-image\" data-id=\"28c7e8fc\" data-element_type=\"widget\" data-widget_type=\"image.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-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/pasted-image-0.png\" class=\"attachment-full size-full wp-image-172140\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/pasted-image-0.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/pasted-image-0-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4d35c8e8 elementor-widget elementor-widget-text-editor\" data-id=\"4d35c8e8\" 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>Here, for example, the margin is the area shown in pink on the graph. In fact, it&#8217;s the space between the 2 outer lines.<\/p><p>To make our<strong> algorithm<\/strong> more flexible, we&#8217;ll use a threshold, which corresponds to the number of observations we&#8217;ll tolerate within the margin.<\/p><p>Then, as before, we&#8217;ll try to determine the dividing line that maximizes the margin.<\/p><p>However, we are no longer concerned with the observations inside the margin. This allows us to achieve a certain insensitivity to extreme values.<\/p><p>Here&#8217;s what we get in the previous example with different threshold values:<\/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-15c7659d e-flex e-con-boxed e-con\" data-id=\"15c7659d\" 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<div class=\"elementor-element elementor-element-17803e3b e-con-full e-flex e-con\" data-id=\"17803e3b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-47499a81 elementor-widget elementor-widget-image\" data-id=\"47499a81\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/1.png\" class=\"attachment-large size-large wp-image-172141\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/1.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/1-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">No observation in the margin\t<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-39620538 e-con-full e-flex e-con\" data-id=\"39620538\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7252e252 elementor-widget elementor-widget-image\" data-id=\"7252e252\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/2.png\" class=\"attachment-large size-large wp-image-172142\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/2.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/2-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">1 observation in the margin<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2df9d6af e-con-full e-flex e-con\" data-id=\"2df9d6af\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-499bf232 elementor-widget elementor-widget-image\" data-id=\"499bf232\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/3.png\" class=\"attachment-large size-large wp-image-172143\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/3.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/3-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">2 comments in the margin<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-bfddd23 e-con-full e-flex e-con\" data-id=\"bfddd23\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2adf585d elementor-widget elementor-widget-image\" data-id=\"2adf585d\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/4.png\" class=\"attachment-large size-large wp-image-172144\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/4.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/4-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">3 comments in the margin<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\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-7cd91b34 e-flex e-con-boxed e-con\" data-id=\"7cd91b34\" 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-28f93a6c elementor-widget elementor-widget-text-editor\" data-id=\"28f93a6c\" 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>3 observations in the margin<\/p><p>However, <a href=\"https:\/\/datascientest.com\/en\/management-of-unbalanced-classification-problems-ii\">this does not mean that the classification is any better.<\/a> We then use cross-validation to choose the best possible threshold.<\/p><p>If you&#8217;ve never <a href=\"https:\/\/datascientest.com\/en\/the-importance-of-cross-validation\">heard of cross validation<\/a>, here&#8217;s a quick definition.<\/p><p>In reality, when you increase the threshold, you decrease the variance but increase the bias. In jargon, the higher the threshold, the lower the risk of overfitting.<\/p><p><strong>\u26a0\ufe0fNote:<\/strong> Observations within and at the boundaries of the margin are called Support Vectors, and the Soft Margin Classifiers algorithm is also called Support Vectors Classifier.<\/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-5e95400f e-flex e-con-boxed e-con\" data-id=\"5e95400f\" 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-5e0371c6 elementor-widget elementor-widget-heading\" data-id=\"5e0371c6\" 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\">Support Vector Machine<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-59691a06 elementor-widget elementor-widget-text-editor\" data-id=\"59691a06\" 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><span style=\"font-weight: 400; color: #000000;\">We have found a solution to the first problem, but not to the second. The Support Vector Classifier algorithm still doesn&#8217;t work in the following case:<\/span><\/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-9dc5641 elementor-widget elementor-widget-image\" data-id=\"9dc5641\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/pasted-image-0-1.png\" class=\"attachment-full size-full wp-image-172145\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/pasted-image-0-1.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/pasted-image-0-1-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6b3d2d67 elementor-widget elementor-widget-text-editor\" data-id=\"6b3d2d67\" 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>In fact, when the algorithm doesn&#8217;t work, the data is said to be non-linearly separable, and there are mathematical tools for determining whether a <a href=\"https:\/\/datascientest.com\/en\/what-is-a-dataset-how-do-i-work-with-it\">dataset is, or is not, linearly separable.<\/a><\/p><p>When faced with a dataset, we use these tools. If the dataset is linearly separable, you don&#8217;t need to look very far &#8211; just apply the Soft Margin Classifier. Things get trickier, however, when the dataset is not linearly separable.<\/p><p>To simplify visualization, we&#8217;re going to change the dataset, and this time take observations of dimension 1, i.e. on a straight line (and not a plane).<\/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-14ffe9fe elementor-widget elementor-widget-image\" data-id=\"14ffe9fe\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/aaaaa.png\" class=\"attachment-full size-full wp-image-172146\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/aaaaa.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/aaaaa-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4aeb9528 elementor-widget elementor-widget-text-editor\" data-id=\"4aeb9528\" 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>There&#8217;s no need to explain why no straight line can separate the &#8220;+&#8221; and &#8220;-&#8221; in this particular configuration.<\/p><p>The idea of the <strong>Support Vector Machine<\/strong> is to project the data into a higher-dimensional space, to make it separable.<\/p><p>Returning to our 1-dimensional example, we&#8217;re going to project the data into a 2-dimensional space. To do this, we&#8217;ll need what we call a kernel function. The kernel function acts as an intermediary between the two spaces.<\/p><p>Let&#8217;s take the cube function (f(x) = x^3) as an example. Here&#8217;s how to apply the kernel function to the dataset to project it into a 2-dimensional space:<\/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-6fdbe245 e-flex e-con-boxed e-con\" data-id=\"6fdbe245\" 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<div class=\"elementor-element elementor-element-2421039c e-con-full e-flex e-con\" data-id=\"2421039c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-798c1d3e elementor-widget elementor-widget-image\" data-id=\"798c1d3e\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/bbbbb.png\" class=\"attachment-large size-large wp-image-172147\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/bbbbb.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/bbbbb-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-275890b1 e-con-full e-flex e-con\" data-id=\"275890b1\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5e37dbe elementor-view-default elementor-position-top elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"5e37dbe\" data-element_type=\"widget\" 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sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-218086ac e-con-full e-flex e-con\" data-id=\"218086ac\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-101bcc3 elementor-view-default elementor-position-top elementor-mobile-position-top elementor-widget elementor-widget-icon-box\" data-id=\"101bcc3\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-icon\">\n\t\t\t\t<span class=\"elementor-icon elementor-animation-\" >\n\t\t\t\t<svg aria-hidden=\"true\" class=\"e-font-icon-svg e-fas-grip-lines\" viewBox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M496 288H16c-8.8 0-16 7.2-16 16v32c0 8.8 7.2 16 16 16h480c8.8 0 16-7.2 16-16v-32c0-8.8-7.2-16-16-16zm0-128H16c-8.8 0-16 7.2-16 16v32c0 8.8 7.2 16 16 16h480c8.8 0 16-7.2 16-16v-32c0-8.8-7.2-16-16-16z\"><\/path><\/svg>\t\t\t\t<\/span>\n\t\t\t<\/div>\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h3 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<span  >\n\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t<\/h3>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-61e1b788 e-con-full e-flex e-con\" data-id=\"61e1b788\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4601907 elementor-widget elementor-widget-image\" data-id=\"4601907\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/dddd.png\" class=\"attachment-large size-large wp-image-172149\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/dddd.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/dddd-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\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-734f60e0 e-flex e-con-boxed e-con\" data-id=\"734f60e0\" 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-1ebad97f elementor-widget elementor-widget-text-editor\" data-id=\"1ebad97f\" 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>In other words, if we denote f the kernel function, for each observation x, we place a point with coordinates (x, f(x)) in the plane.<\/p><p>The projected dataset is now separable, as shown in the following image. The Soft Margin Classifiers algorithm described above can be used to calculate the best separation line, and that&#8217;s all there is to it.<\/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-b0b85f0 elementor-widget elementor-widget-image\" data-id=\"b0b85f0\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"349\" height=\"231\" src=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/e.png\" class=\"attachment-full size-full wp-image-172150\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2023\/10\/e.png 349w, https:\/\/datascientest.com\/en\/files\/2023\/10\/e-300x199.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3857ae06 elementor-widget elementor-widget-text-editor\" data-id=\"3857ae06\" 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>We&#8217;ve just described in <strong>detail how Support Vector Machines work.<\/strong> And even though we&#8217;ve deliberately left out some of the details (such as the choice of kernel function), you now have an overview of the subject.<\/p><p>SVM algorithms can be adapted to classification problems involving more than 2 classes, and to regression problems. They are therefore quick and easy to implement on any type of dataset, which certainly explains their success.<\/p><p>Where a <a href=\"https:\/\/datascientest.com\/en\/recurrent-neural-network-what-is-it\">neural network<\/a> requires upstream work to determine the right structure and parameters to use, SVMs achieve good results even without preparation. If you&#8217;d like to <a href=\"https:\/\/datascientest.com\/en\/data-poisoning-a-threat-to-machine-learning-models\">learn more about Machine Learning,<\/a> take a look at our Machine Learning Course.<\/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-3bbbed12 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"3bbbed12\" 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\/machine-learning-engineer-course\">\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\">Discover our Machine Learning Training<\/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\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Welcome to the second part of this dossier dedicated to Vector Machine Support. In the previous article, we detailed the operation and main shortcomings of Maximal Margin Classifiers. Our aim now is to allow our algorithm to make a certain number of errors when selecting the separation line. This is known as the &#8220;soft margin&#8221;. [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":172139,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2409],"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>SVM (Support Vector Machines) Unveiled: Understanding, Implementation, Significance - Part 2<\/title>\n<meta name=\"description\" content=\"SVM, or Support Vector Machines, demystified: Understand what they are, how they work, and why they&#039;re essential in machine learning, Part 2\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/svm-support-vector-machines-unveiled-understanding-implementation-significance-part-2\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"SVM (Support Vector Machines) Unveiled: Understanding, Implementation, Significance - Part 2\" \/>\n<meta property=\"og:description\" content=\"Welcome to the second part of this dossier dedicated to Vector Machine Support. 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