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<div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" title="Посети главна страница [z]" accesskey="z"><span>Главна страница</span></a></li><li id="n-Што-е-Википедија?" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%92%D0%BE%D0%B2%D0%B5%D0%B4"><span>Што е Википедија?</span></a></li><li id="n-featuredcontent" class="mw-list-item"><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%98%D0%B7%D0%B1%D1%80%D0%B0%D0%BD%D0%B8_%D1%81%D1%82%D0%B0%D1%82%D0%B8%D0%B8"><span>Избрана содржина</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BB%D1%83%D1%87%D0%B0%D1%98%D0%BD%D0%B0" title="Вчитај случајна страница [x]" accesskey="x"><span>Случајна 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[r]" accesskey="r"><span>Скорешни промени</span></a></li><li id="n-pump" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A1%D0%B5%D0%BB%D1%81%D0%BA%D0%B0_%D1%87%D0%B5%D1%88%D0%BC%D0%B0"><span>Селска чешма</span></a></li><li id="n-Викисредби" class="mw-list-item"><a href="/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%92%D0%B8%D0%BA%D0%B8%D1%81%D1%80%D0%B5%D0%B4%D0%B1%D0%B0"><span>Викисредби</span></a></li><li id="n-help" class="mw-list-item"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents" title="Место каде што може да се информирате."><span>Помош</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Википедија" src="/static/images/mobile/copyright/wikipedia-wordmark-sr.svg" style="width: 7.8125em; height: 1.4375em;"> <img class="mw-logo-tagline" alt="Слободна енциклопедија" src="/static/images/mobile/copyright/wikipedia-tagline-mk.svg" width="114" height="11" style="width: 7.125em; height: 0.6875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%91%D0%B0%D1%80%D0%B0%D1%98" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Пребарај низ Википедија [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Пребарај</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Пребарајте по Википедија" aria-label="Пребарајте по Википедија" autocapitalize="sentences" title="Пребарај низ Википедија [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Специјална:Барај"> </div> <button class="cdx-button cdx-search-input__end-button">Пребарај</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Лични алатки"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Изглед"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Сменете ги големината на фонтот, ширината и бојата" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Изглед" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Изглед</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=mk.wikipedia.org&uselang=mk" class=""><span>Дарување</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BE%D0%B7%D0%B4%D0%B0%D1%98%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0%D0%A1%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0+%D1%81%D0%BE+%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8+%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8" title="Ви препорачуваме да направите сметка и да се најавите, иако тоа не е задолжително" class=""><span>Направи сметка</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9D%D0%B0%D1%98%D0%B0%D0%B2%D1%83%D0%B2%D0%B0%D1%9A%D0%B5&returnto=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0+%D1%81%D0%BE+%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8+%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8" title="Ви препорачуваме да се најавите, иако тоа не е задолжително. [o]" accesskey="o" class=""><span>Најава</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Повеќе можности" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Лични алатки" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Лични алатки</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal" title="Корисничко мени" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=mk.wikipedia.org&uselang=mk"><span>Дарување</span></a></li><li id="pt-contribute" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:Contribute"><span class="vector-icon mw-ui-icon-edit mw-ui-icon-wikimedia-edit"></span> <span>Придонесувајте</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%A1%D0%BE%D0%B7%D0%B4%D0%B0%D1%98%D0%9A%D0%BE%D1%80%D0%B8%D1%81%D0%BD%D0%B8%D1%87%D0%BA%D0%B0%D0%A1%D0%BC%D0%B5%D1%82%D0%BA%D0%B0&returnto=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0+%D1%81%D0%BE+%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8+%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8" title="Ви препорачуваме да направите сметка и да се најавите, иако тоа не е задолжително"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Направи сметка</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9D%D0%B0%D1%98%D0%B0%D0%B2%D1%83%D0%B2%D0%B0%D1%9A%D0%B5&returnto=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0+%D1%81%D0%BE+%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8+%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8" title="Ви препорачуваме да се најавите, иако тоа не е задолжително. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Најава</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Страници за одјавени уредници <a href="/wiki/%D0%9F%D0%BE%D0%BC%D0%BE%D1%88:%D0%92%D0%BE%D0%B2%D0%B5%D0%B4" aria-label="Дознајте повеќе за уредувањето"><span>дознајте повеќе</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9C%D0%BE%D1%98%D0%A0%D0%B0%D0%B7%D0%B3%D0%BE%D0%B2%D0%BE%D1%80" title="Разговор за уредувањата од оваа IP-адреса [n]" accesskey="n"><span>Разговор</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div 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src=\"//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Handcuffs_icon.svg/35px-Handcuffs_icon.svg.png\" decoding=\"async\" width=\"35\" height=\"27\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Handcuffs_icon.svg/53px-Handcuffs_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Handcuffs_icon.svg/70px-Handcuffs_icon.svg.png 2x\" data-file-width=\"512\" data-file-height=\"399\" /\u003E\u003C/a\u003E\u003Cfigcaption\u003EУредувачки ден „Злосторнички организации“\u003C/figcaption\u003E\u003C/figure\u003E\n\u003Cp\u003EСе известуваат сите заинтересирани уредници на Википедија на македонски јазик дека на 18 февруари 2025 година ќе се одржи \u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B4%D0%B5%D0%BD%D0%BE%D0%B2%D0%B8\" title=\"Википедија:Уредувачки денови\"\u003Eуредувачки ден\u003C/a\u003E на тема „\u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B4%D0%B5%D0%BD%D0%BE%D0%B2%D0%B8_2025#Злосторнички_организации\" title=\"Википедија:Уредувачки денови 2025\"\u003EЗлосторнички организации\u003C/a\u003E\u003C/b\u003E“.\n\u003Cbr style=\"clear:both;\" /\u003E\n\u003C/p\u003E\n\u003Cfigure class=\"mw-halign-left\" typeof=\"mw:File\"\u003E\u003Ca href=\"/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Isotop_C-12.svg\" class=\"mw-file-description\"\u003E\u003Cimg src=\"//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Isotop_C-12.svg/30px-Isotop_C-12.svg.png\" decoding=\"async\" width=\"30\" height=\"30\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Isotop_C-12.svg/45px-Isotop_C-12.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Isotop_C-12.svg/60px-Isotop_C-12.svg.png 2x\" data-file-width=\"200\" data-file-height=\"200\" /\u003E\u003C/a\u003E\u003Cfigcaption\u003E\u003C/figcaption\u003E\u003C/figure\u003E\n\u003Cp\u003EСе известуваат сите заинтересирани уредници на Википедија на македонски јазик дека во периодот 10 февруари до 9 март 2025 година ќе се одржи \u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BD%D0%B0%D1%82%D0%BF%D1%80%D0%B5%D0%B2%D0%B0%D1%80%D0%B8\" title=\"Википедија:Уредувачки натпревари\"\u003Eуредувачки натпревар\u003C/a\u003E на тема „\u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A3%D1%80%D0%B5%D0%B4%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%BD%D0%B0%D1%82%D0%BF%D1%80%D0%B5%D0%B2%D0%B0%D1%80%D0%B8/%D0%A5%D0%B5%D0%BC%D0%B8%D1%81%D0%BA%D0%B8_%D0%B5%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B8_%D0%B8_%D0%B8%D0%B7%D0%BE%D1%82%D0%BE%D0%BF%D0%B8\" title=\"Википедија:Уредувачки натпревари/Хемиски елементи и изотопи\"\u003EХемиски елементи и изотопи\u003C/a\u003E\u003C/b\u003E“. Прочитајте ги правилата и вклучете се!\n\u003Cbr style=\"clear:both;\" /\u003E\n\u003C/p\u003E\n\u003Cfigure class=\"mw-halign-left\" typeof=\"mw:File\"\u003E\u003Ca href=\"/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Flag_of_Slovenia.svg\" class=\"mw-file-description\"\u003E\u003Cimg src=\"//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Flag_of_Slovenia.svg/30px-Flag_of_Slovenia.svg.png\" decoding=\"async\" width=\"30\" height=\"15\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Flag_of_Slovenia.svg/45px-Flag_of_Slovenia.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Flag_of_Slovenia.svg/60px-Flag_of_Slovenia.svg.png 2x\" data-file-width=\"1200\" data-file-height=\"600\" /\u003E\u003C/a\u003E\u003Cfigcaption\u003E\u003C/figcaption\u003E\u003C/figure\u003E\n\u003Cp\u003EСе известуваат членовите на \u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%92%D0%B8%D0%BA%D0%B8_%D0%9A%D0%BB%D1%83%D0%B1\" title=\"Википедија:Вики Клуб\"\u003EВики Клубовите\u003C/a\u003E дека во периодот од 1 до 28 февруари 2025 година се одржува уредувачки натпревар „\u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%97%D0%B0%D0%BF%D0%BE%D0%B7%D0%BD%D0%B0%D1%98%D1%82%D0%B5_%D1%98%D0%B0_%D0%A1%D0%BB%D0%BE%D0%B2%D0%B5%D0%BD%D0%B8%D1%98%D0%B0\" title=\"Википедија:Запознајте ја Словенија\"\u003EЗапознајте ја Словенија\u003C/a\u003E\u003C/b\u003E“. Приклучете се и освојте една од наградите!\n\u003Cbr style=\"clear:both;\" /\u003E\n\u003C/p\u003E\u003Cp\u003EВо тек е \u003Cb\u003E\u003Ca href=\"/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%98%D0%B0:%D0%A1%D0%B5%D0%BB%D1%81%D0%BA%D0%B0_%D1%87%D0%B5%D1%88%D0%BC%D0%B0#Можни_решенија\" title=\"Википедија:Селска чешма\"\u003Eгласање\u003C/a\u003E\u003C/b\u003E по предлозите за користењето извори од отоманскиот период.\n\u003C/p\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Мрежно место"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Содржина" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Содржина</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">скриј</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Почеток</div> </a> </li> <li id="toc-Опис" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Опис"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Опис</span> </div> </a> <ul id="toc-Опис-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Алгоритамот_на_машините_со_поддржувачки_вектори" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Алгоритамот_на_машините_со_поддржувачки_вектори"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Алгоритамот на машините со поддржувачки вектори</span> </div> </a> <ul id="toc-Алгоритамот_на_машините_со_поддржувачки_вектори-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Наводи" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Наводи"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Наводи</span> </div> </a> <ul id="toc-Наводи-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Содржина" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Содржина" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Прик./скр. содржина" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Прик./скр. содржина</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Машина со поддржувачки вектори</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Појдете на статија на друг јазик. Достапно на 33 јазици" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-33" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">33 јазици</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B4%D8%B9%D8%A7%D8%B9_%D8%A7%D9%84%D8%AF%D8%B9%D9%85_%D8%A7%D9%84%D8%A2%D9%84%D9%8A" title="شعاع الدعم الآلي — арапски" lang="ar" hreflang="ar" data-title="شعاع الدعم الآلي" data-language-autonym="العربية" data-language-local-name="арапски" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%BE%E0%A6%AA%E0%A7%8B%E0%A6%B0%E0%A7%8D%E0%A6%9F-%E0%A6%AD%E0%A7%87%E0%A6%95%E0%A7%8D%E0%A6%9F%E0%A6%B0_%E0%A6%AE%E0%A7%87%E0%A6%B6%E0%A6%BF%E0%A6%A8" title="সাপোর্ট-ভেক্টর মেশিন — бенгалски" lang="bn" hreflang="bn" data-title="সাপোর্ট-ভেক্টর মেশিন" data-language-autonym="বাংলা" data-language-local-name="бенгалски" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81_%D0%BF%D0%BE%D0%B4%D0%B4%D1%8A%D1%80%D0%B6%D0%B0%D1%89%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8" title="Машина с поддържащи вектори — бугарски" lang="bg" hreflang="bg" data-title="Машина с поддържащи вектори" data-language-autonym="Български" data-language-local-name="бугарски" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/M%C3%A0quina_de_vector_de_suport" title="Màquina de vector de suport — каталонски" lang="ca" hreflang="ca" data-title="Màquina de vector de suport" data-language-autonym="Català" data-language-local-name="каталонски" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Support_vector_machines" title="Support vector machines — чешки" lang="cs" hreflang="cs" data-title="Support vector machines" data-language-autonym="Čeština" data-language-local-name="чешки" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Support_Vector_Machine" title="Support Vector Machine — германски" lang="de" hreflang="de" data-title="Support Vector Machine" data-language-autonym="Deutsch" data-language-local-name="германски" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Tugivektor-masin" title="Tugivektor-masin — естонски" lang="et" hreflang="et" data-title="Tugivektor-masin" data-language-autonym="Eesti" data-language-local-name="естонски" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Support_vector_machine" title="Support vector machine — англиски" lang="en" hreflang="en" data-title="Support vector machine" data-language-autonym="English" data-language-local-name="англиски" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/M%C3%A1quina_de_vectores_de_soporte" title="Máquina de vectores de soporte — шпански" lang="es" hreflang="es" data-title="Máquina de vectores de soporte" data-language-autonym="Español" data-language-local-name="шпански" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Euskarri_bektoredun_makina" title="Euskarri bektoredun makina — баскиски" lang="eu" hreflang="eu" data-title="Euskarri bektoredun makina" data-language-autonym="Euskara" data-language-local-name="баскиски" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%A7%D8%B4%DB%8C%D9%86_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1_%D9%BE%D8%B4%D8%AA%DB%8C%D8%A8%D8%A7%D9%86%DB%8C" title="ماشین بردار پشتیبانی — персиски" lang="fa" hreflang="fa" data-title="ماشین بردار پشتیبانی" data-language-autonym="فارسی" data-language-local-name="персиски" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Machine_%C3%A0_vecteurs_de_support" title="Machine à vecteurs de support — француски" lang="fr" hreflang="fr" data-title="Machine à vecteurs de support" data-language-autonym="Français" data-language-local-name="француски" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%84%9C%ED%8F%AC%ED%8A%B8_%EB%B2%A1%ED%84%B0_%EB%A8%B8%EC%8B%A0" title="서포트 벡터 머신 — корејски" lang="ko" hreflang="ko" data-title="서포트 벡터 머신" data-language-autonym="한국어" data-language-local-name="корејски" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Mesin_vektor_pendukung" title="Mesin vektor pendukung — индонезиски" lang="id" hreflang="id" data-title="Mesin vektor pendukung" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезиски" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Macchine_a_vettori_di_supporto" title="Macchine a vettori di supporto — италијански" lang="it" hreflang="it" data-title="Macchine a vettori di supporto" data-language-autonym="Italiano" data-language-local-name="италијански" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%9B%D7%95%D7%A0%D7%AA_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%9D_%D7%AA%D7%95%D7%9E%D7%9B%D7%99%D7%9D" title="מכונת וקטורים תומכים — хебрејски" lang="he" hreflang="he" data-title="מכונת וקטורים תומכים" data-language-autonym="עברית" data-language-local-name="хебрејски" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Atramini%C5%B3_vektori%C5%B3_klasifikatorius" title="Atraminių vektorių klasifikatorius — литвански" lang="lt" hreflang="lt" data-title="Atraminių vektorių klasifikatorius" data-language-autonym="Lietuvių" data-language-local-name="литвански" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Support_vector_machine" title="Support vector machine — холандски" lang="nl" hreflang="nl" data-title="Support vector machine" data-language-autonym="Nederlands" data-language-local-name="холандски" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B5%E3%83%9D%E3%83%BC%E3%83%88%E3%83%99%E3%82%AF%E3%82%BF%E3%83%BC%E3%83%9E%E3%82%B7%E3%83%B3" title="サポートベクターマシン — јапонски" lang="ja" hreflang="ja" data-title="サポートベクターマシン" data-language-autonym="日本語" data-language-local-name="јапонски" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A8%AA%E0%A9%8B%E0%A8%B0%E0%A8%9F_%E0%A8%B5%E0%A9%88%E0%A8%95%E0%A8%9F%E0%A8%B0_%E0%A8%AE%E0%A8%B8%E0%A8%BC%E0%A9%80%E0%A8%A8" title="ਸਪੋਰਟ ਵੈਕਟਰ ਮਸ਼ੀਨ — пенџапски" lang="pa" hreflang="pa" data-title="ਸਪੋਰਟ ਵੈਕਟਰ ਮਸ਼ੀਨ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="пенџапски" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Maszyna_wektor%C3%B3w_no%C5%9Bnych" title="Maszyna wektorów nośnych — полски" lang="pl" hreflang="pl" data-title="Maszyna wektorów nośnych" data-language-autonym="Polski" data-language-local-name="полски" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/M%C3%A1quina_de_vetores_de_suporte" title="Máquina de vetores de suporte — португалски" lang="pt" hreflang="pt" data-title="Máquina de vetores de suporte" data-language-autonym="Português" data-language-local-name="португалски" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%BE%D0%BF%D0%BE%D1%80%D0%BD%D1%8B%D1%85_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%BE%D0%B2" title="Метод опорных векторов — руски" lang="ru" hreflang="ru" data-title="Метод опорных векторов" data-language-autonym="Русский" data-language-local-name="руски" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Metoda_podpornih_vektorjev" title="Metoda podpornih vektorjev — словенечки" lang="sl" hreflang="sl" data-title="Metoda podpornih vektorjev" data-language-autonym="Slovenščina" data-language-local-name="словенечки" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4%D0%B0_%D0%BF%D0%BE%D1%82%D0%BF%D0%BE%D1%80%D0%BD%D0%B8%D1%85_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B0" title="Метода потпорних вектора — српски" lang="sr" hreflang="sr" data-title="Метода потпорних вектора" data-language-autonym="Српски / srpski" data-language-local-name="српски" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Tukivektorikone" title="Tukivektorikone — фински" lang="fi" hreflang="fi" data-title="Tukivektorikone" data-language-autonym="Suomi" data-language-local-name="фински" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/St%C3%B6dvektormaskin" title="Stödvektormaskin — шведски" lang="sv" hreflang="sv" data-title="Stödvektormaskin" data-language-autonym="Svenska" data-language-local-name="шведски" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AE%BF%E0%AE%95%E0%AF%88%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%B3%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%BE%E0%AE%99%E0%AF%8D%E0%AE%95%E0%AF%81_%E0%AE%87%E0%AE%AF%E0%AE%A8%E0%AF%8D%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AE%AE%E0%AF%8D" title="மிகைத்தளத்தாங்கு இயந்திரம் — тамилски" lang="ta" hreflang="ta" data-title="மிகைத்தளத்தாங்கு இயந்திரம்" data-language-autonym="தமிழ்" data-language-local-name="тамилски" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Destek_vekt%C3%B6r_makinesi" title="Destek vektör makinesi — турски" lang="tr" hreflang="tr" data-title="Destek vektör makinesi" data-language-autonym="Türkçe" data-language-local-name="турски" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%BE%D0%BF%D0%BE%D1%80%D0%BD%D0%B8%D1%85_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D1%96%D0%B2" title="Метод опорних векторів — украински" lang="uk" hreflang="uk" data-title="Метод опорних векторів" data-language-autonym="Українська" data-language-local-name="украински" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%C3%A1y_vect%C6%A1_h%E1%BB%97_tr%E1%BB%A3" title="Máy vectơ hỗ trợ — виетнамски" lang="vi" hreflang="vi" data-title="Máy vectơ hỗ trợ" data-language-autonym="Tiếng Việt" data-language-local-name="виетнамски" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%94%AF%E6%8F%B4%E5%90%91%E9%87%8F%E6%A9%9F" title="支援向量機 — кантонски" lang="yue" hreflang="yue" data-title="支援向量機" data-language-autonym="粵語" data-language-local-name="кантонски" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%94%AF%E6%8C%81%E5%90%91%E9%87%8F%E6%9C%BA" title="支持向量机 — кинески" lang="zh" hreflang="zh" data-title="支持向量机" data-language-autonym="中文" data-language-local-name="кинески" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q282453#sitelinks-wikipedia" title="Уредување на меѓујазични врски" class="wbc-editpage">Уреди врски</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Именски простори"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8" title="Преглед на содржинската страница [c]" accesskey="c"><span>Страница</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%A0%D0%B0%D0%B7%D0%B3%D0%BE%D0%B2%D0%BE%D1%80:%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&action=edit&redlink=1" rel="discussion" class="new" title="Разговор за содржинската страница (страницата не постои) [t]" accesskey="t"><span>Разговор</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Менување на јазичната варијанта" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span 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href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&veaction=edit" title="Уредете ја страницава [v]" accesskey="v"><span>Уреди</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&action=edit" title="Уредување на изворниот код на страницава [e]" accesskey="e"><span>Уреди извор</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&action=history" title="Претходни верзии на оваа страница. 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vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Алатки</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">премести во страничникот</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">скриј</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Повеќе можности" > <div class="vector-menu-heading"> Дејства </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8"><span>Читај</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&veaction=edit" title="Уредете ја страницава [v]" accesskey="v"><span>Уреди</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&action=edit" title="Уредување на изворниот код на страницава [e]" accesskey="e"><span>Уреди 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id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="mk" dir="ltr"><p><b>Машина со поддржувачки вектори</b> (<a href="/wiki/%D0%90%D0%BD%D0%B3%D0%BB%D0%B8%D1%81%D0%BA%D0%B8" class="mw-redirect" title="Англиски">англиски</a>: <i>support-vector machine</i>, <i>SVM</i>) претставува метод на <a href="/wiki/%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D1%81%D0%BA%D0%BE_%D1%83%D1%87%D0%B5%D1%9A%D0%B5" title="Машинско учење">машинско учење</a>, со соодветен <a href="/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%B0%D0%BC" title="Алгоритам">алгоритам</a> за учење, кој се употребува за анализа на податоци, за класификација и за <a href="/w/index.php?title=%D0%A0%D0%B5%D0%B3%D1%80%D0%B5%D1%81%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Регресија (страницата не постои)">регресија</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Опис"><span id=".D0.9E.D0.BF.D0.B8.D1.81"></span>Опис</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&veaction=edit&section=1" title="Уреди го одделот „Опис“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&action=edit&section=1" title="Уреди изворен код на одделот: Опис"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Машината со поддржувачки вектори (<i>SVM</i>) врши класификација така што ја пронаоѓа онаа <a href="/wiki/%D0%9F%D1%80%D0%B0%D0%B2%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Права (геометрија)">права</a>, <a href="/wiki/%D0%A0%D0%B0%D0%BC%D0%BD%D0%B8%D0%BD%D0%B0" class="mw-redirect mw-disambig" title="Рамнина">рамнина</a> или <a href="/w/index.php?title=%D0%A5%D0%B8%D0%BF%D0%B5%D1%80%D1%80%D0%B0%D0%BC%D0%BD%D0%B8%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Хиперрамнина (страницата не постои)">хиперрамнина</a> што ја максимизира маргината помеѓу двете класи. Тоа се постигнува преку опишување на најширокиот канал помеѓу две класи.<sup id="cite_ref-Bishop,_C._M._2006_1-0" class="reference"><a href="#cite_note-Bishop,_C._M._2006-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> На пример, доколку имаме <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B5%D1%81%D1%82%D0%B2%D0%BE" title="Множество">множество</a> на податоци чии ентитети може да припаѓаат на две класи и притоа станува збор за линеарно-сепарабилно множество, оние ентитети (<a href="/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80" title="Вектор">вектори</a>) од множеството кои ја дефинираат таа правата (рамнината или хипер-рамнината) се нарекуваат „поддржувачки вектори“ (<i>support vectors</i>).<sup id="cite_ref-Witten,_I._H._2005_2-0" class="reference"><a href="#cite_note-Witten,_I._H._2005-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> SVM функционираат така што ги пронаоѓаат двете најблиски точки кои припаѓаат на двете различни класи и ја дефинираат (поддржуваат) најдобрата права (рамнина, т.е. хипер-рамнина) која ги разделува класите. Дополнително, SVM цртаат линија која ги поврзува овие две точки. Понатаму, SVM одлучуваат дека најдобрата права која ги разделува класите е онаа која е нормална на <a href="/wiki/%D0%9E%D1%82%D1%81%D0%B5%D1%87%D0%BA%D0%B0" title="Отсечка">отсечката</a> која ги поврзува двете точки и ја дели на два еднакви дела.<sup id="cite_ref-Bishop,_C._M._2006_1-1" class="reference"><a href="#cite_note-Bishop,_C._M._2006-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Han,_J._2011_3-0" class="reference"><a href="#cite_note-Han,_J._2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Алгоритамот_на_машините_со_поддржувачки_вектори"><span id=".D0.90.D0.BB.D0.B3.D0.BE.D1.80.D0.B8.D1.82.D0.B0.D0.BC.D0.BE.D1.82_.D0.BD.D0.B0_.D0.BC.D0.B0.D1.88.D0.B8.D0.BD.D0.B8.D1.82.D0.B5_.D1.81.D0.BE_.D0.BF.D0.BE.D0.B4.D0.B4.D1.80.D0.B6.D1.83.D0.B2.D0.B0.D1.87.D0.BA.D0.B8_.D0.B2.D0.B5.D0.BA.D1.82.D0.BE.D1.80.D0.B8"></span>Алгоритамот на машините со поддржувачки вектори</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&veaction=edit&section=2" title="Уреди го одделот „Алгоритамот на машините со поддржувачки вектори“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&action=edit&section=2" title="Уреди изворен код на одделот: Алгоритамот на машините со поддржувачки вектори"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%D0%9F%D0%BE%D0%B4%D0%B0%D1%82%D0%BE%D1%82%D0%B5%D0%BA%D0%B0:Svm_intro.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Svm_intro.svg/220px-Svm_intro.svg.png" decoding="async" width="220" height="157" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Svm_intro.svg/330px-Svm_intro.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Svm_intro.svg/440px-Svm_intro.svg.png 2x" data-file-width="232" data-file-height="166" /></a><figcaption>Две можни одвојувачки линии со различни големини на рабовите</figcaption></figure> <p>Алгоритамот на SVM работи на следниов начин:<sup id="cite_ref-Witten,_I._H._2005_2-1" class="reference"><a href="#cite_note-Witten,_I._H._2005-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Дефинира оптимална хипер-рамнина која ги разделува инстанциите во однос на класите на кои им припаѓаат, според нивните атрибути (својства). Оптималната хипер-рамнина се наоѓа на тој начин што се максимизира маргината помеѓу поддржувачките вектори.</li> <li>Проширување на претходниот чекор со цел да се решат проблемите каде податоците не се линеарно сепарабилни – на тој начин што се даваат „пенали“, односно казни при погрешно класифицирање.</li> <li>Доколку станува збор за податоци кои не се линеарно сепарабилни, можно е тие имплицитно да се мапираат во повеќедимензионален простор во кој би биле линеарно сепарабилни и полесно би се направила класификацијата.</li></ol> <p>Доколку податоците се линеарно сепарабилни, докажано е дека решението сигурно ќе биде најдено, односно идеалната хипер-рамнина со максимална маргина ќе биде пронајдена. Идеалната SVM треба да создаде хипер-рамнина која целосно ги одвојува векторите во групи (класи) во кои нема преклопување на елементите.<sup id="cite_ref-Han,_J._2011_3-1" class="reference"><a href="#cite_note-Han,_J._2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Сепак, идеално одвојување најчесто не е можно и тогаш SVM ја пронаоѓа онаа хипер-рамнина која ја максимизира маргината помеѓу инстанциите од групите на различните класи и ги минимизира погрешните класифицирања. Минимизирањето на погрешните класифицирања се прави со воведување на т.н. „slack“ променлива, на тој начин што се дозволува некои случаи да ја преминат маргината, но таквите случаи се казнуваат. </p><p>Наједноставен начин да се разделат две групи на податоци е со помош на права линија, рамнина или N-димензионална хипер-рамнина. Сепак, постојат ситуации каде некој нелинеарен регион може да ги оддели групите поефикасно. SVM се справува со ваквите случаи со користење на т.н. „кернел функција“ (<i>kernel function</i>), т.е. <a href="/w/index.php?title=%D0%9D%D0%B5%D0%BB%D0%B8%D0%BD%D0%B5%D0%B0%D1%80%D0%BD%D0%B0_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0&action=edit&redlink=1" class="new" title="Нелинеарна функција (страницата не постои)">нелинеарна функција</a> која ги мапира податоците во друг, различен простор (димензија). Ваквата постапка претпоставува постоење на кернел <a href="/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%98%D0%B0" class="mw-disambig" title="Функција">функција</a> која ги трансформира податоците кои не се линеарно сепарабилни во простор со повеќе димензии (својства), каде е можно да се изврши линеарно раздвојување.<sup id="cite_ref-Witten,_I._H._2005_2-2" class="reference"><a href="#cite_note-Witten,_I._H._2005-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Наводи"><span id=".D0.9D.D0.B0.D0.B2.D0.BE.D0.B4.D0.B8"></span>Наводи</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&veaction=edit&section=3" title="Уреди го одделот „Наводи“" class="mw-editsection-visualeditor"><span>уреди</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D0%B0_%D1%81%D0%BE_%D0%BF%D0%BE%D0%B4%D0%B4%D1%80%D0%B6%D1%83%D0%B2%D0%B0%D1%87%D0%BA%D0%B8_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8&action=edit&section=3" title="Уреди изворен код на одделот: Наводи"><span>уреди извор</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Bishop,_C._M._2006-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Bishop,_C._M._2006_1-0">1,0</a></sup> <sup><a href="#cite_ref-Bishop,_C._M._2006_1-1">1,1</a></sup></span> <span class="reference-text">Bishop, C. M. (2006), <i>Pattern recognition and machine learning</i>, Springer.</span> </li> <li id="cite_note-Witten,_I._H._2005-2"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Witten,_I._H._2005_2-0">2,0</a></sup> <sup><a href="#cite_ref-Witten,_I._H._2005_2-1">2,1</a></sup> <sup><a href="#cite_ref-Witten,_I._H._2005_2-2">2,2</a></sup></span> <span class="reference-text">Witten, I. H., and Frank, E. (2005), <i>Data Mining: Practical machine learning tools and techniques</i>, Morgan Kaufmann.</span> </li> <li id="cite_note-Han,_J._2011-3"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Han,_J._2011_3-0">3,0</a></sup> <sup><a href="#cite_ref-Han,_J._2011_3-1">3,1</a></sup></span> <span class="reference-text">Han, J., Kamber, M., and Pei, J. (2011), <i>Data mining: concepts and techniques: concepts and techniques</i>, Elsevier.</span> </li> </ol></div></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Преземено од „<a dir="ltr" href="https://mk.wikipedia.org/w/index.php?title=Машина_со_поддржувачки_вектори&oldid=5251497">https://mk.wikipedia.org/w/index.php?title=Машина_со_поддржувачки_вектори&oldid=5251497</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%A1%D0%BF%D0%B5%D1%86%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0:%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D0%B8" title="Специјална:Категории">Категорија</a>: <ul><li><a href="/wiki/%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D1%98%D0%B0:%D0%9C%D0%B0%D1%88%D0%B8%D0%BD%D1%81%D0%BA%D0%BE_%D1%83%D1%87%D0%B5%D1%9A%D0%B5" title="Категорија:Машинско учење">Машинско учење</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Последната промена на страницава е извршена на 20 август 2024 г. во 10:26 ч.</li> <li id="footer-info-copyright">Текстот е достапен под условите на лиценцата <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Криејтив комонс Наведи извор-Сподели под исти услови</a>. 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