{"id":13045,"date":"2021-12-05T20:22:21","date_gmt":"2021-12-06T01:22:21","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=13045"},"modified":"2026-06-02T14:59:24","modified_gmt":"2026-06-02T18:59:24","slug":"tr-01-03-on-opitmal-pairwise-linear-classifiers-for-normal-distributions-the-d-dimensional-case","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-2001\/tr-01-03-on-opitmal-pairwise-linear-classifiers-for-normal-distributions-the-d-dimensional-case\/","title":{"rendered":"TR-01-03: On Opitmal Pairwise Linear Classifiers for Normal Distributions: The d-Dimensional Case"},"content":{"rendered":"\n
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\n TR-01-03: On Opitmal Pairwise Linear Classifiers for Normal Distributions: The d-Dimensional Case\n <\/h1>\n \n \n <\/header>\n\n <\/div>\n\n <\/div>\n\n <\/div>\n<\/section>\n\n

Carleton University
\nTechnical Report<\/a> TR-01-03
\nJanuary 2001<\/p>\n\n\n\n

On Opitmal Pairwise Linear Classifiers for Normal Distributions: The d-Dimensional Case<\/h2>\n\n\n\n
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Luis Rueda & B. John Oommen<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Abstract<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

We consider the well-studied Pattern Recognition (PR) problem of designing linear classifi\fers. When dealing with normally distributed classes, it is well known that the optimal Bayes classifi\fer is linear only when the covariance matrices are equal. This was the only known condition for classifi\fer linearity. In a previous work, we presented the theoretical framework for optimal pairwise linear classifi\fers for two- dimensional normally distributed random vectors. We derived the necessary and sufficient conditions that the distributions have to satisfy so as to yield the optimal linear classifi\fer as a pair of straight lines.<\/p>\n\n\n\n

TR-01-03.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Carleton University Technical Report TR-01-03 January 2001 On Opitmal Pairwise Linear Classifiers for Normal Distributions: The d-Dimensional Case Luis Rueda & B. John Oommen Abstract We consider the well-studied Pattern Recognition (PR) problem of designing linear classifi\fers. When dealing with normally distributed classes, it is well known that the optimal Bayes classifi\fer is linear only […]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":12272,"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-13045","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":false},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13045","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=13045"}],"version-history":[{"count":1,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13045\/revisions"}],"predecessor-version":[{"id":13046,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/13045\/revisions\/13046"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/12272"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=13045"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=13045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}