{"id":13022,"date":"2021-12-02T20:57:31","date_gmt":"2021-12-03T01:57:31","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13022"},"modified":"2026-06-02T14:59:24","modified_gmt":"2026-06-02T18:59:24","slug":"tr-00-03-on-optimal-pairwaise-linear-classifiers-for-normal-distributions-the-two-dimensional-case","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2000\/tr-00-03-on-optimal-pairwaise-linear-classifiers-for-normal-distributions-the-two-dimensional-case\/","title":{"rendered":"TR-00-03: On Optimal Pairwaise Linear Classifiers for Normal Distributions: The Two-Dimensional case"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-00-03: On Optimal Pairwaise Linear Classifiers for Normal Distributions: The Two-Dimensional case\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n<p>Carleton University<br>\n<a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2000\/\">Technical Report<\/a> TR-00-03<br>\nMay 2000<\/p>\n\n\n\n<h2 id=\"on-optimal-pairwaise-linear-classifiers-for-normal-distributions-the-two-dimensional-case\" class=\"wp-block-heading\">On Optimal Pairwaise Linear Classifiers for Normal Distributions: The Two-Dimensional case<\/h2>\n\n\n\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">\n<div class=\"tr_t3\">Luis Rueda &amp; B. John Oommen<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<h3>Abstract<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p>Computing linear classi\u001cfiers is a very important problem in statistical Pattern Recognition (PR). These classifi\u001cers have been investigated by the PR community extensively since they are the ones which are both easy to implement and comprehend. It is well known that when dealing with normally distributed classes, the optimal discriminant function for two-classes is linear only when the covariance matrices are equal. Other approaches, such as the Fisher&#8217;s discriminant, the perceptron algorithm, minimum square distance classi\u001cfiers, etc., have solved this problem by generating a linear classifi\u001cer in normal and non-normal distributions, but these classi\u001cfiers are typically suboptimal.<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-00-03.pdf\">TR-00-03.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton University Technical Report TR-00-03 May 2000 On Optimal Pairwaise Linear Classifiers for Normal Distributions: The Two-Dimensional case Luis Rueda &amp; B. John Oommen Abstract Computing linear classi\u001cfiers is a very important problem in statistical Pattern Recognition (PR). These classifi\u001cers have been investigated by the PR community extensively since they are the ones which are [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":12258,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-13022","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=13022"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13022\/revisions"}],"predecessor-version":[{"id":13023,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13022\/revisions\/13023"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12258"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=13022"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=13022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}