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href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=zh.wikipedia.org&uselang=zh"><span>资助维基百科</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95" title="我们推荐您创建账号并登录，但这不是强制性的"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</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"> 未登录编辑者的页面 <a 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</div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" 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">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</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">序言</div> </a> </li> <li id="toc-算法" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#算法"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>算法</span> </div> </a> <ul id="toc-算法-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参数选择" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参数选择"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>参数选择</span> </div> </a> <ul id="toc-参数选择-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-加权最近邻分类器" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#加权最近邻分类器"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>加权最近邻分类器</span> </div> </a> <ul id="toc-加权最近邻分类器-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-属性" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#属性"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>属性</span> </div> </a> <ul id="toc-属性-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-决策边界" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#决策边界"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>决策边界</span> </div> </a> <ul id="toc-决策边界-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-连续变量估计" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#连续变量估计"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>连续变量估计</span> </div> </a> <ul id="toc-连续变量估计-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-發展" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#發展"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>發展</span> </div> </a> <ul id="toc-發展-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参见" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参见"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>参见</span> </div> </a> <ul id="toc-参见-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-注释" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#注释"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>注释</span> </div> </a> <ul id="toc-注释-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考文獻" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考文獻"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>參考文獻</span> </div> </a> <button aria-controls="toc-參考文獻-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关參考文獻子章节</span> </button> <ul id="toc-參考文獻-sublist" class="vector-toc-list"> <li id="toc-引用" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#引用"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>引用</span> </div> </a> <ul id="toc-引用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-来源" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#来源"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.2</span> <span>来源</span> </div> </a> <ul id="toc-来源-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-拓展阅读" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#拓展阅读"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>拓展阅读</span> </div> </a> <ul id="toc-拓展阅读-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="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <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="开关目录" > <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">开关目录</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">K-近邻算法</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="前往另一种语言写成的文章。23种语言可用" > <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-23" 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">23种语言</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/%D9%83%D9%8A_%D8%A3%D9%82%D8%B1%D8%A8_%D8%AC%D8%A7%D8%B1" title="كي أقرب جار – 阿拉伯语" lang="ar" hreflang="ar" data-title="كي أقرب جار" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Knn" title="Knn – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Knn" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%A9%DB%95%DB%8C_%D9%86%D8%B2%DB%8C%DA%A9%D8%AA%D8%B1%DB%8C%D9%86_%DA%BE%D8%A7%D9%88%D8%B3%DB%8E%DA%A9%D8%A7%D9%86" title="کەی نزیکترین ھاوسێکان – 中库尔德语" lang="ckb" hreflang="ckb" data-title="کەی نزیکترین ھاوسێکان" data-language-autonym="کوردی" data-language-local-name="中库尔德语" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Algoritmus_k-nejbli%C5%BE%C5%A1%C3%ADch_soused%C5%AF" title="Algoritmus k-nejbližších sousedů – 捷克语" lang="cs" hreflang="cs" data-title="Algoritmus k-nejbližších sousedů" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/K-n%C3%A6rmeste_naboer" title="K-nærmeste naboer – 丹麦语" lang="da" hreflang="da" data-title="K-nærmeste naboer" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/N%C3%A4chste-Nachbarn-Klassifikation" title="Nächste-Nachbarn-Klassifikation – 德语" lang="de" hreflang="de" data-title="Nächste-Nachbarn-Klassifikation" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm" title="K-nearest neighbors algorithm – 英语" lang="en" hreflang="en" data-title="K-nearest neighbors algorithm" data-language-autonym="English" data-language-local-name="英语" 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/K_vecinos_m%C3%A1s_pr%C3%B3ximos" title="K vecinos más próximos – 西班牙语" lang="es" hreflang="es" data-title="K vecinos más próximos" data-language-autonym="Español" data-language-local-name="西班牙语" 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/K_auzokide_hurbilenak" title="K auzokide hurbilenak – 巴斯克语" lang="eu" hreflang="eu" data-title="K auzokide hurbilenak" data-language-autonym="Euskara" data-language-local-name="巴斯克语" 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/%D8%A7%D9%84%DA%AF%D9%88%D8%B1%DB%8C%D8%AA%D9%85_%DA%A9%DB%8C-%D9%86%D8%B2%D8%AF%DB%8C%DA%A9%E2%80%8C%D8%AA%D8%B1%DB%8C%D9%86_%D9%87%D9%85%D8%B3%D8%A7%DB%8C%D9%87" title="الگوریتم کی-نزدیک‌ترین همسایه – 波斯语" lang="fa" hreflang="fa" data-title="الگوریتم کی-نزدیک‌ترین همسایه" data-language-autonym="فارسی" data-language-local-name="波斯语" 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/M%C3%A9thode_des_k_plus_proches_voisins" title="Méthode des k plus proches voisins – 法语" lang="fr" hreflang="fr" data-title="Méthode des k plus proches voisins" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%95%D7%A8%D7%99%D7%AA%D7%9D_%D7%A9%D7%9B%D7%9F_%D7%A7%D7%A8%D7%95%D7%91" title="אלגוריתם שכן קרוב – 希伯来语" lang="he" hreflang="he" data-title="אלגוריתם שכן קרוב" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Algoritma_k_tetangga_terdekat" title="Algoritma k tetangga terdekat – 印度尼西亚语" lang="id" hreflang="id" data-title="Algoritma k tetangga terdekat" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" 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/K-nearest_neighbors" title="K-nearest neighbors – 意大利语" lang="it" hreflang="it" data-title="K-nearest neighbors" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/K%E8%BF%91%E5%82%8D%E6%B3%95" title="K近傍法 – 日语" lang="ja" hreflang="ja" data-title="K近傍法" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/K-%EC%B5%9C%EA%B7%BC%EC%A0%91_%EC%9D%B4%EC%9B%83_%EC%95%8C%EA%B3%A0%EB%A6%AC%EC%A6%98" title="K-최근접 이웃 알고리즘 – 韩语" lang="ko" hreflang="ko" data-title="K-최근접 이웃 알고리즘" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/K-NN" title="K-NN – 书面挪威语" lang="nb" hreflang="nb" data-title="K-NN" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/K_najbli%C5%BCszych_s%C4%85siad%C3%B3w" title="K najbliższych sąsiadów – 波兰语" lang="pl" hreflang="pl" data-title="K najbliższych sąsiadów" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</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_k_%D0%B1%D0%BB%D0%B8%D0%B6%D0%B0%D0%B9%D1%88%D0%B8%D1%85_%D1%81%D0%BE%D1%81%D0%B5%D0%B4%D0%B5%D0%B9" title="Метод k ближайших соседей – 俄语" lang="ru" hreflang="ru" data-title="Метод k ближайших соседей" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%B0%D0%BC_%D0%BA_%D0%BD%D0%B0%D1%98%D0%B1%D0%BB%D0%B8%D0%B6%D0%B8%D1%85_%D1%81%D1%83%D1%81%D0%B5%D0%B4%D0%B0" title="Алгоритам к најближих суседа – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Алгоритам к најближих суседа" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%82%E0%B8%B1%E0%B9%89%E0%B8%99%E0%B8%95%E0%B8%AD%E0%B8%99%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%84%E0%B9%89%E0%B8%99%E0%B8%AB%E0%B8%B2%E0%B9%80%E0%B8%9E%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%99%E0%B8%9A%E0%B9%89%E0%B8%B2%E0%B8%99%E0%B9%83%E0%B8%81%E0%B8%A5%E0%B9%89%E0%B8%AA%E0%B8%B8%E0%B8%94_k_%E0%B8%95%E0%B8%B1%E0%B8%A7" title="ขั้นตอนวิธีการค้นหาเพื่อนบ้านใกล้สุด k ตัว – 泰语" lang="th" hreflang="th" data-title="ขั้นตอนวิธีการค้นหาเพื่อนบ้านใกล้สุด k ตัว" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</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_k-%D0%BD%D0%B0%D0%B9%D0%B1%D0%BB%D0%B8%D0%B6%D1%87%D0%B8%D1%85_%D1%81%D1%83%D1%81%D1%96%D0%B4%D1%96%D0%B2" title="Метод k-найближчих сусідів – 乌克兰语" lang="uk" hreflang="uk" data-title="Метод k-найближчих сусідів" data-language-autonym="Українська" data-language-local-name="乌克兰语" 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/Gi%E1%BA%A3i_thu%E1%BA%ADt_k_h%C3%A0ng_x%C3%B3m_g%E1%BA%A7n_nh%E1%BA%A5t" title="Giải thuật k hàng xóm gần nhất – 越南语" lang="vi" hreflang="vi" data-title="Giải thuật k hàng xóm gần nhất" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</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/Q1071612#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</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="命名空间"> <div id="p-associated-pages" 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.ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-Expert_needed plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">此條目需要<b>精通或熟悉<a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%A7%91%E5%AD%A6" title="计算机科学">计算机科学</a>的编者</b>参与及协助编辑。<span 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3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-subgroup,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-pretitle,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-heading,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-above,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) 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.sidebar-below{background:inherit!important;color:inherit!important;border-color:#54595d!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar a:not(.new):not(.mw-selflink):link{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks"><tbody><tr><th class="sidebar-title"><a href="/wiki/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="机器学习">机器学习</a>与<a href="/wiki/%E6%95%B0%E6%8D%AE%E6%8C%96%E6%8E%98" title="数据挖掘">数据挖掘</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Multi-Layer_Neural_Network-Vector-Blank.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Multi-Layer_Neural_Network-Vector-Blank.svg/220px-Multi-Layer_Neural_Network-Vector-Blank.svg.png" decoding="async" width="220" height="105" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Multi-Layer_Neural_Network-Vector-Blank.svg/330px-Multi-Layer_Neural_Network-Vector-Blank.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Multi-Layer_Neural_Network-Vector-Blank.svg/440px-Multi-Layer_Neural_Network-Vector-Blank.svg.png 2x" data-file-width="815" data-file-height="390" /></a></span></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;">范式</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E7%9B%91%E7%9D%A3%E5%AD%A6%E4%B9%A0" title="监督学习">监督学习</a></li> <li><a href="/wiki/%E7%84%A1%E7%9B%A3%E7%9D%A3%E5%AD%B8%E7%BF%92" title="無監督學習">無監督學習</a></li> <li><a href="/wiki/%E7%B7%9A%E4%B8%8A%E6%A9%9F%E5%99%A8%E5%AD%B8%E7%BF%92" title="線上機器學習">線上機器學習</a></li> <li><span class="ilh-all" data-orig-title="元学习 (计算机科学)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Meta-learning (computer science)"><span class="ilh-page"><a href="/w/index.php?title=%E5%85%83%E5%AD%A6%E4%B9%A0_(%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%A7%91%E5%AD%A6)&action=edit&redlink=1" class="new" title="元学习 (计算机科学)（页面不存在）">元学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Meta-learning_(computer_science)" class="extiw" title="en:Meta-learning (computer science)"><span lang="en" dir="auto">Meta-learning (computer science)</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%8D%8A%E7%9B%91%E7%9D%A3%E5%AD%A6%E4%B9%A0" title="半监督学习">半监督学习</a></li> <li><a href="/wiki/%E8%87%AA%E7%9B%91%E7%9D%A3%E5%AD%A6%E4%B9%A0" title="自监督学习">自监督学习</a></li> <li><a href="/wiki/%E5%BC%BA%E5%8C%96%E5%AD%A6%E4%B9%A0" title="强化学习">强化学习</a></li> <li><span class="ilh-all" data-orig-title="基于规则的机器学习" data-lang-code="en" data-lang-name="英语" data-foreign-title="Rule-based machine learning"><span class="ilh-page"><a href="/w/index.php?title=%E5%9F%BA%E4%BA%8E%E8%A7%84%E5%88%99%E7%9A%84%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0&action=edit&redlink=1" class="new" title="基于规则的机器学习（页面不存在）">基于规则的机器学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Rule-based_machine_learning" class="extiw" title="en:Rule-based machine learning"><span lang="en" dir="auto">Rule-based machine learning</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E6%A9%9F%E5%99%A8%E5%AD%B8%E7%BF%92" title="量子機器學習">量子機器學習</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;">问题</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%88%86%E7%B1%BB" title="统计分类">统计分类</a></li> <li><a href="/wiki/%E7%94%9F%E6%88%90%E6%A8%A1%E5%9E%8B" title="生成模型">生成模型</a></li> <li><a href="/wiki/%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="迴歸分析">迴歸分析</a></li> <li><a href="/wiki/%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90" title="聚类分析">聚类分析</a></li> <li><a href="/wiki/%E9%99%8D%E7%BB%B4" title="降维">降维</a></li> <li><span class="ilh-all" data-orig-title="密度估计" data-lang-code="en" data-lang-name="英语" data-foreign-title="density estimation"><span class="ilh-page"><a href="/w/index.php?title=%E5%AF%86%E5%BA%A6%E4%BC%B0%E8%AE%A1&action=edit&redlink=1" class="new" title="密度估计（页面不存在）">密度估计</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/density_estimation" class="extiw" title="en:density estimation"><span lang="en" dir="auto">density estimation</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%BC%82%E5%B8%B8%E6%A3%80%E6%B5%8B" title="异常检测">异常检测</a></li> <li><a href="/wiki/%E6%95%B0%E6%8D%AE%E6%B8%85%E6%B4%97" title="数据清洗">数据清洗</a></li> <li><a href="/wiki/%E8%87%AA%E5%8A%A8%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="自动机器学习">自动机器学习</a></li> <li><a href="/wiki/%E5%85%B3%E8%81%94%E8%A7%84%E5%88%99%E5%AD%A6%E4%B9%A0" title="关联规则学习">关联规则学习</a></li> <li><a href="/wiki/%E8%AA%9E%E6%84%8F%E5%88%86%E6%9E%90" title="語意分析">語意分析</a></li> <li><span class="ilh-all" data-orig-title="结构预测" data-lang-code="en" data-lang-name="英语" data-foreign-title="Structured prediction"><span class="ilh-page"><a href="/w/index.php?title=%E7%BB%93%E6%9E%84%E9%A2%84%E6%B5%8B&action=edit&redlink=1" class="new" title="结构预测（页面不存在）">结构预测</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Structured_prediction" class="extiw" title="en:Structured prediction"><span lang="en" dir="auto">Structured prediction</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%89%B9%E5%BE%81%E5%B7%A5%E7%A8%8B" title="特征工程">特征工程</a></li> <li><a href="/wiki/%E8%A1%A8%E5%BE%81%E5%AD%A6%E4%B9%A0" title="表征学习">表征学习</a></li> <li><span class="ilh-all" data-orig-title="排序学习" data-lang-code="en" data-lang-name="英语" data-foreign-title="Learning to rank"><span class="ilh-page"><a href="/w/index.php?title=%E6%8E%92%E5%BA%8F%E5%AD%A6%E4%B9%A0&action=edit&redlink=1" class="new" title="排序学习（页面不存在）">排序学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Learning_to_rank" class="extiw" title="en:Learning to rank"><span lang="en" dir="auto">Learning to rank</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="语法归纳" data-lang-code="en" data-lang-name="英语" data-foreign-title="Grammar induction"><span class="ilh-page"><a href="/w/index.php?title=%E8%AF%AD%E6%B3%95%E5%BD%92%E7%BA%B3&action=edit&redlink=1" class="new" title="语法归纳（页面不存在）">语法归纳</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Grammar_induction" class="extiw" title="en:Grammar induction"><span lang="en" dir="auto">Grammar induction</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="本体学习" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ontology learning"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%AC%E4%BD%93%E5%AD%A6%E4%B9%A0&action=edit&redlink=1" class="new" title="本体学习（页面不存在）">本体学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ontology_learning" class="extiw" title="en:Ontology learning"><span lang="en" dir="auto">Ontology learning</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%A4%9A%E6%A8%A1%E6%80%81%E5%AD%A6%E4%B9%A0" title="多模态学习">多模态学习</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;"><div style="padding:0.1em 0;line-height:1.2em;"><a href="/wiki/%E7%9B%91%E7%9D%A3%E5%AD%A6%E4%B9%A0" title="监督学习">监督学习</a><br /><span style="font-weight:normal;"><small>(<b><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%88%86%E7%B1%BB" title="统计分类">分类</a></b><span style="font-weight:bold;"> ·</span> <b><a href="/wiki/%E5%9B%9E%E5%BD%92%E5%88%86%E6%9E%90" class="mw-redirect" title="回归分析">回归</a></b>)</small></span></div></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><span class="ilh-all" data-orig-title="学徒学习" data-lang-code="en" data-lang-name="英语" data-foreign-title="Apprenticeship learning"><span class="ilh-page"><a href="/w/index.php?title=%E5%AD%A6%E5%BE%92%E5%AD%A6%E4%B9%A0&action=edit&redlink=1" class="new" title="学徒学习（页面不存在）">学徒学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Apprenticeship_learning" class="extiw" title="en:Apprenticeship learning"><span lang="en" dir="auto">Apprenticeship learning</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%86%B3%E7%AD%96%E6%A0%91%E5%AD%A6%E4%B9%A0" title="决策树学习">决策树学习</a></li> <li><a href="/wiki/%E9%9B%86%E6%88%90%E5%AD%A6%E4%B9%A0" title="集成学习">集成学习</a> <ul><li><a href="/wiki/Bagging%E7%AE%97%E6%B3%95" title="Bagging算法">Bagging</a></li> <li><a href="/wiki/%E6%8F%90%E5%8D%87%E6%96%B9%E6%B3%95" title="提升方法">提升方法</a></li> <li><a href="/wiki/%E9%9A%8F%E6%9C%BA%E6%A3%AE%E6%9E%97" title="随机森林">随机森林</a></li></ul></li> <li><a class="mw-selflink selflink"><i>k</i>-NN</a></li> <li><a href="/wiki/%E7%B7%9A%E6%80%A7%E5%9B%9E%E6%AD%B8" title="線性回歸">線性回歸</a></li> <li><a href="/wiki/%E6%9C%B4%E7%B4%A0%E8%B4%9D%E5%8F%B6%E6%96%AF%E5%88%86%E7%B1%BB%E5%99%A8" title="朴素贝叶斯分类器">朴素贝叶斯</a></li> <li><a href="/wiki/%E4%BA%BA%E5%B7%A5%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C" title="人工神经网络">人工神经网络</a></li> <li><a href="/wiki/%E9%82%8F%E8%BC%AF%E6%96%AF%E8%AB%A6%E8%BF%B4%E6%AD%B8" title="邏輯斯諦迴歸">邏輯斯諦迴歸</a></li> <li><a href="/wiki/%E6%84%9F%E7%9F%A5%E5%99%A8" title="感知器">感知器</a></li> <li><a href="/wiki/%E7%9B%B8%E5%85%B3%E5%90%91%E9%87%8F%E6%9C%BA" title="相关向量机">相关向量机（RVM）</a></li> <li><a href="/wiki/%E6%94%AF%E6%8C%81%E5%90%91%E9%87%8F%E6%9C%BA" title="支持向量机">支持向量机（SVM）</a></li> <li><a href="/wiki/%E8%BF%81%E7%A7%BB%E5%AD%A6%E4%B9%A0" title="迁移学习">迁移学习</a></li> <li><a href="/wiki/%E5%BE%AE%E8%B0%83_(%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0)" title="微调 (深度学习)">微调</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;"><a href="/wiki/%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90" title="聚类分析">聚类分析</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/BIRCH" title="BIRCH">BIRCH</a></li> <li><span class="ilh-all" data-orig-title="CURE算法" data-lang-code="en" data-lang-name="英语" data-foreign-title="CURE algorithm"><span class="ilh-page"><a href="/w/index.php?title=CURE%E7%AE%97%E6%B3%95&action=edit&redlink=1" class="new" title="CURE算法（页面不存在）">CURE算法</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/CURE_algorithm" class="extiw" title="en:CURE algorithm"><span lang="en" dir="auto">CURE algorithm</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%B1%82%E6%AC%A1%E8%81%9A%E7%B1%BB" title="层次聚类">层次</a></li> <li><a href="/wiki/K-%E5%B9%B3%E5%9D%87%E7%AE%97%E6%B3%95" title="K-平均算法"><i>k</i>-平均</a></li> <li><a href="/wiki/%E6%A8%A1%E7%B3%8A%E8%81%9A%E7%B1%BB" title="模糊聚类">Fuzzy</a></li> <li><a href="/wiki/%E6%9C%80%E5%A4%A7%E6%9C%9F%E6%9C%9B%E7%AE%97%E6%B3%95" title="最大期望算法">期望最大化（EM）</a></li> <li><br /><a href="/wiki/DBSCAN" title="DBSCAN">DBSCAN</a></li> <li><a href="/wiki/OPTICS" title="OPTICS">OPTICS</a></li> <li><span class="ilh-all" data-orig-title="均值飘移" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mean shift"><span class="ilh-page"><a href="/w/index.php?title=%E5%9D%87%E5%80%BC%E9%A3%98%E7%A7%BB&action=edit&redlink=1" class="new" title="均值飘移（页面不存在）">均值飘移</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mean_shift" class="extiw" title="en:Mean shift"><span lang="en" dir="auto">Mean shift</span></a></span>）</span></span></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;"><a href="/wiki/%E9%99%8D%E7%BB%B4" title="降维">降维</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E5%9B%A0%E7%B4%A0%E5%88%86%E6%9E%90" title="因素分析">因素分析</a></li> <li><a href="/wiki/%E5%85%B8%E5%9E%8B%E7%9B%B8%E5%85%B3" title="典型相关">CCA</a></li> <li><a href="/wiki/%E7%8B%AC%E7%AB%8B%E6%88%90%E5%88%86%E5%88%86%E6%9E%90" title="独立成分分析">ICA</a></li> <li><a href="/wiki/%E7%B7%9A%E6%80%A7%E5%88%A4%E5%88%A5%E5%88%86%E6%9E%90" title="線性判別分析">LDA</a></li> <li><span class="ilh-all" data-orig-title="非负矩阵分解" data-lang-code="en" data-lang-name="英语" data-foreign-title="Non-negative matrix factorization"><span class="ilh-page"><a href="/w/index.php?title=%E9%9D%9E%E8%B4%9F%E7%9F%A9%E9%98%B5%E5%88%86%E8%A7%A3&action=edit&redlink=1" class="new" title="非负矩阵分解（页面不存在）">NMF</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Non-negative_matrix_factorization" class="extiw" title="en:Non-negative matrix factorization"><span lang="en" dir="auto">Non-negative matrix factorization</span></a></span>）</span></span></li> <li><a href="/wiki/%E4%B8%BB%E6%88%90%E5%88%86%E5%88%86%E6%9E%90" title="主成分分析">PCA</a></li> <li><span class="ilh-all" data-orig-title="适当广义分解" data-lang-code="en" data-lang-name="英语" data-foreign-title="Proper generalized decomposition"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%82%E5%BD%93%E5%B9%BF%E4%B9%89%E5%88%86%E8%A7%A3&action=edit&redlink=1" class="new" title="适当广义分解（页面不存在）">PGD</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Proper_generalized_decomposition" class="extiw" title="en:Proper generalized decomposition"><span lang="en" dir="auto">Proper generalized decomposition</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="t-分布随机邻域嵌入" data-lang-code="en" data-lang-name="英语" data-foreign-title="t-distributed stochastic neighbor embedding"><span class="ilh-page"><a href="/w/index.php?title=T-%E5%88%86%E5%B8%83%E9%9A%8F%E6%9C%BA%E9%82%BB%E5%9F%9F%E5%B5%8C%E5%85%A5&action=edit&redlink=1" class="new" title="T-分布随机邻域嵌入（页面不存在）">t-SNE</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/t-distributed_stochastic_neighbor_embedding" class="extiw" title="en:t-distributed stochastic neighbor embedding"><span lang="en" dir="auto">t-distributed stochastic neighbor embedding</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%A8%80%E7%96%8F%E5%AD%97%E5%85%B8%E5%AD%B8%E7%BF%92" title="稀疏字典學習">SDL</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;"><span class="ilh-all" data-orig-title="结构预测" data-lang-code="en" data-lang-name="英语" data-foreign-title="Structured prediction"><span class="ilh-page"><a href="/w/index.php?title=%E7%BB%93%E6%9E%84%E9%A2%84%E6%B5%8B&action=edit&redlink=1" class="new" title="结构预测（页面不存在）">结构预测</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Structured_prediction" class="extiw" title="en:Structured prediction"><span lang="en" dir="auto">Structured prediction</span></a></span>）</span></span></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E5%9C%96%E6%A8%A1%E5%BC%8F" title="圖模式">圖模式</a> <ul><li><a href="/wiki/%E8%B2%9D%E6%B0%8F%E7%B6%B2%E8%B7%AF" title="貝氏網路">貝氏網路</a></li> <li><a href="/wiki/%E6%A2%9D%E4%BB%B6%E9%9A%A8%E6%A9%9F%E5%9F%9F" title="條件隨機域">條件隨機域</a></li> <li><a href="/wiki/%E9%9A%90%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E6%A8%A1%E5%9E%8B" title="隐马尔可夫模型">隐马尔可夫模型</a></li></ul></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;"><a href="/wiki/%E5%BC%82%E5%B8%B8%E6%A3%80%E6%B5%8B" title="异常检测">异常检测</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E9%9A%A8%E6%A9%9F%E6%8A%BD%E6%A8%A3%E4%B8%80%E8%87%B4" title="隨機抽樣一致">RANSAC</a></li> <li><a class="mw-selflink selflink"><i>k</i>-NN</a></li> <li><span class="ilh-all" data-orig-title="局部异常因子" data-lang-code="en" data-lang-name="英语" data-foreign-title="Local outlier factor"><span class="ilh-page"><a href="/w/index.php?title=%E5%B1%80%E9%83%A8%E5%BC%82%E5%B8%B8%E5%9B%A0%E5%AD%90&action=edit&redlink=1" class="new" title="局部异常因子（页面不存在）">局部异常因子</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Local_outlier_factor" class="extiw" title="en:Local outlier factor"><span lang="en" dir="auto">Local outlier factor</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="Isolation forest" data-lang-code="en" data-lang-name="英语" data-foreign-title="Isolation forest"><span class="ilh-page"><a href="/w/index.php?title=Isolation_forest&action=edit&redlink=1" class="new" title="Isolation forest（页面不存在）">孤立森林</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Isolation_forest" class="extiw" title="en:Isolation forest"><span lang="en" dir="auto">Isolation forest</span></a></span>）</span></span></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;"><a href="/wiki/%E4%BA%BA%E5%B7%A5%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C" title="人工神经网络">人工神经网络</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E8%87%AA%E7%BC%96%E7%A0%81%E5%99%A8" title="自编码器">自编码器</a></li> <li><a href="/wiki/%E8%AA%8D%E7%9F%A5%E8%A8%88%E7%AE%97" title="認知計算">認知計算</a></li> <li><a href="/wiki/%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0" title="深度学习">深度学习</a></li> <li><span class="ilh-all" data-orig-title="DeepDream" data-lang-code="en" data-lang-name="英语" data-foreign-title="DeepDream"><span class="ilh-page"><a href="/w/index.php?title=DeepDream&action=edit&redlink=1" class="new" title="DeepDream（页面不存在）">DeepDream</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/DeepDream" class="extiw" title="en:DeepDream"><span lang="en" dir="auto">DeepDream</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%A4%9A%E5%B1%82%E6%84%9F%E7%9F%A5%E5%99%A8" title="多层感知器">多层感知器</a></li> <li><a href="/wiki/%E5%BE%AA%E7%8E%AF%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C" title="循环神经网络">RNN</a> <ul><li><a href="/wiki/%E9%95%B7%E7%9F%AD%E6%9C%9F%E8%A8%98%E6%86%B6" title="長短期記憶">LSTM</a></li> <li><span class="ilh-all" data-orig-title="门控循环单元" data-lang-code="en" data-lang-name="英语" data-foreign-title="Gated recurrent unit"><span class="ilh-page"><a href="/w/index.php?title=%E9%97%A8%E6%8E%A7%E5%BE%AA%E7%8E%AF%E5%8D%95%E5%85%83&action=edit&redlink=1" class="new" title="门控循环单元（页面不存在）">GRU</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Gated_recurrent_unit" class="extiw" title="en:Gated recurrent unit"><span lang="en" dir="auto">Gated recurrent unit</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="回声状态网络" data-lang-code="en" data-lang-name="英语" data-foreign-title="Echo state network"><span class="ilh-page"><a href="/w/index.php?title=%E5%9B%9E%E5%A3%B0%E7%8A%B6%E6%80%81%E7%BD%91%E7%BB%9C&action=edit&redlink=1" class="new" title="回声状态网络（页面不存在）">ESN</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Echo_state_network" class="extiw" title="en:Echo state network"><span lang="en" dir="auto">Echo state network</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="储备池计算" data-lang-code="en" data-lang-name="英语" data-foreign-title="reservoir computing"><span class="ilh-page"><a href="/w/index.php?title=%E5%82%A8%E5%A4%87%E6%B1%A0%E8%AE%A1%E7%AE%97&action=edit&redlink=1" class="new" title="储备池计算（页面不存在）">储备池计算</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/reservoir_computing" class="extiw" title="en:reservoir computing"><span lang="en" dir="auto">reservoir computing</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E5%8F%97%E9%99%90%E7%8E%BB%E5%B0%94%E5%85%B9%E6%9B%BC%E6%9C%BA" title="受限玻尔兹曼机">受限玻尔兹曼机</a></li> <li><a href="/wiki/%E7%94%9F%E6%88%90%E5%AF%B9%E6%8A%97%E7%BD%91%E7%BB%9C" title="生成对抗网络">GAN</a></li> <li><a href="/wiki/%E8%87%AA%E7%BB%84%E7%BB%87%E6%98%A0%E5%B0%84" title="自组织映射">SOM</a></li> <li><a href="/wiki/%E5%8D%B7%E7%A7%AF%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C" title="卷积神经网络">CNN</a> <ul><li><a href="/wiki/U-Net" title="U-Net">U-Net</a></li></ul></li> <li><a href="/wiki/Transformer%E6%A8%A1%E5%9E%8B" title="Transformer模型">Transformer</a> <ul><li><span class="ilh-all" data-orig-title="Vision transformer" data-lang-code="en" data-lang-name="英语" data-foreign-title="Vision transformer"><span class="ilh-page"><a href="/w/index.php?title=Vision_transformer&action=edit&redlink=1" class="new" title="Vision transformer（页面不存在）">Vision transformer</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Vision_transformer" class="extiw" title="en:Vision transformer"><span lang="en" dir="auto">Vision transformer</span></a></span>）</span></span></li></ul></li> <li><span class="ilh-all" data-orig-title="脉冲神经网络" data-lang-code="en" data-lang-name="英语" data-foreign-title="Spiking neural network"><span class="ilh-page"><a href="/w/index.php?title=%E8%84%89%E5%86%B2%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C&action=edit&redlink=1" class="new" title="脉冲神经网络（页面不存在）">脉冲神经网络</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Spiking_neural_network" class="extiw" title="en:Spiking neural network"><span lang="en" dir="auto">Spiking neural network</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="Memtransistor" data-lang-code="en" data-lang-name="英语" data-foreign-title="Memtransistor"><span class="ilh-page"><a href="/w/index.php?title=Memtransistor&action=edit&redlink=1" class="new" title="Memtransistor（页面不存在）">Memtransistor</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Memtransistor" class="extiw" title="en:Memtransistor"><span lang="en" dir="auto">Memtransistor</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="Electrochemical RAM" data-lang-code="en" data-lang-name="英语" data-foreign-title="Electrochemical RAM"><span class="ilh-page"><a href="/w/index.php?title=Electrochemical_RAM&action=edit&redlink=1" class="new" title="Electrochemical RAM（页面不存在）">电化学RAM</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Electrochemical_RAM" class="extiw" title="en:Electrochemical RAM"><span lang="en" dir="auto">Electrochemical RAM</span></a></span>）</span></span>（ECRAM）</li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;"><a href="/wiki/%E5%BC%BA%E5%8C%96%E5%AD%A6%E4%B9%A0" title="强化学习">强化学习</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Q%E5%AD%A6%E4%B9%A0" title="Q学习">Q学习</a></li> <li><a href="/wiki/SARSA%E7%AE%97%E6%B3%95" title="SARSA算法">SARSA</a></li> <li><a href="/wiki/%E6%97%B6%E5%BA%8F%E5%B7%AE%E5%88%86%E5%AD%A6%E4%B9%A0" title="时序差分学习">时序差分（TD）</a></li> <li><span class="ilh-all" data-orig-title="多智能体强化学习" data-lang-code="en" data-lang-name="英语" data-foreign-title="Multi-agent reinforcement learning"><span class="ilh-page"><a href="/w/index.php?title=%E5%A4%9A%E6%99%BA%E8%83%BD%E4%BD%93%E5%BC%BA%E5%8C%96%E5%AD%A6%E4%B9%A0&action=edit&redlink=1" class="new" title="多智能体强化学习（页面不存在）">多智能体</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Multi-agent_reinforcement_learning" class="extiw" title="en:Multi-agent reinforcement learning"><span lang="en" dir="auto">Multi-agent reinforcement learning</span></a></span>）</span></span> <ul><li><span class="ilh-all" data-orig-title="Self-play (强化学习技术)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Self-play (reinforcement learning technique)"><span class="ilh-page"><a href="/w/index.php?title=Self-play_(%E5%BC%BA%E5%8C%96%E5%AD%A6%E4%B9%A0%E6%8A%80%E6%9C%AF)&action=edit&redlink=1" class="new" title="Self-play (强化学习技术)（页面不存在）">Self-play</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Self-play_(reinforcement_learning_technique)" class="extiw" title="en:Self-play (reinforcement learning technique)"><span lang="en" dir="auto">Self-play (reinforcement learning technique)</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E5%9F%BA%E4%BA%8E%E4%BA%BA%E7%B1%BB%E5%8F%8D%E9%A6%88%E7%9A%84%E5%BC%BA%E5%8C%96%E5%AD%A6%E4%B9%A0" title="基于人类反馈的强化学习">RLHF</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;">与人类学习</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><span class="ilh-all" data-orig-title="主动学习 (机器学习)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Active learning (machine learning)"><span class="ilh-page"><a href="/w/index.php?title=%E4%B8%BB%E5%8A%A8%E5%AD%A6%E4%B9%A0_(%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0)&action=edit&redlink=1" class="new" title="主动学习 (机器学习)（页面不存在）">主动学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Active_learning_(machine_learning)" class="extiw" title="en:Active learning (machine learning)"><span lang="en" dir="auto">Active learning (machine learning)</span></a></span>）</span></span></li> <li><a href="/wiki/%E4%BC%97%E5%8C%85" title="众包">众包</a></li> <li><span class="ilh-all" data-orig-title="Human-in-the-loop" data-lang-code="en" data-lang-name="英语" data-foreign-title="Human-in-the-loop"><span class="ilh-page"><a href="/w/index.php?title=Human-in-the-loop&action=edit&redlink=1" class="new" title="Human-in-the-loop（页面不存在）">Human-in-the-loop</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Human-in-the-loop" class="extiw" title="en:Human-in-the-loop"><span lang="en" dir="auto">Human-in-the-loop</span></a></span>）</span></span></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;">模型诊断</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><span class="ilh-all" data-orig-title="学习曲线 (机器学习)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Learning curve (machine learning)"><span class="ilh-page"><a href="/w/index.php?title=%E5%AD%A6%E4%B9%A0%E6%9B%B2%E7%BA%BF_(%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0)&action=edit&redlink=1" class="new" title="学习曲线 (机器学习)（页面不存在）">学习曲线</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Learning_curve_(machine_learning)" class="extiw" title="en:Learning curve (machine learning)"><span lang="en" dir="auto">Learning curve (machine learning)</span></a></span>）</span></span></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;">数学基础</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><span class="ilh-all" data-orig-title="内核机器" data-lang-code="en" data-lang-name="英语" data-foreign-title="Kernel machines"><span class="ilh-page"><a href="/w/index.php?title=%E5%86%85%E6%A0%B8%E6%9C%BA%E5%99%A8&action=edit&redlink=1" class="new" title="内核机器（页面不存在）">内核机器</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Kernel_machines" class="extiw" title="en:Kernel machines"><span lang="en" dir="auto">Kernel machines</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="偏差–方差困境" data-lang-code="en" data-lang-name="英语" data-foreign-title="Bias–variance tradeoff"><span class="ilh-page"><a href="/w/index.php?title=%E5%81%8F%E5%B7%AE%E2%80%93%E6%96%B9%E5%B7%AE%E5%9B%B0%E5%A2%83&action=edit&redlink=1" class="new" title="偏差–方差困境（页面不存在）">偏差–方差困境</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff" class="extiw" title="en:Bias–variance tradeoff"><span lang="en" dir="auto">Bias–variance tradeoff</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="计算学习理论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Computational learning theory"><span class="ilh-page"><a href="/w/index.php?title=%E8%AE%A1%E7%AE%97%E5%AD%A6%E4%B9%A0%E7%90%86%E8%AE%BA&action=edit&redlink=1" class="new" title="计算学习理论（页面不存在）">计算学习理论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Computational_learning_theory" class="extiw" title="en:Computational learning theory"><span lang="en" dir="auto">Computational learning theory</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%BB%8F%E9%AA%8C%E9%A3%8E%E9%99%A9%E6%9C%80%E5%B0%8F%E5%8C%96" title="经验风险最小化">经验风险最小化</a></li> <li><span class="ilh-all" data-orig-title="Occam learning" data-lang-code="en" data-lang-name="英语" data-foreign-title="Occam learning"><span class="ilh-page"><a href="/w/index.php?title=Occam_learning&action=edit&redlink=1" class="new" title="Occam learning（页面不存在）">奥卡姆学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Occam_learning" class="extiw" title="en:Occam learning"><span lang="en" dir="auto">Occam learning</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="概率近似正确学习" data-lang-code="en" data-lang-name="英语" data-foreign-title="Probably approximately correct learning"><span class="ilh-page"><a href="/w/index.php?title=%E6%A6%82%E7%8E%87%E8%BF%91%E4%BC%BC%E6%AD%A3%E7%A1%AE%E5%AD%A6%E4%B9%A0&action=edit&redlink=1" class="new" title="概率近似正确学习（页面不存在）">PAC学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Probably_approximately_correct_learning" class="extiw" title="en:Probably approximately correct learning"><span lang="en" dir="auto">Probably approximately correct learning</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6%E4%B9%A0%E7%90%86%E8%AE%BA" title="统计学习理论">统计学习</a></li> <li><a href="/wiki/VC%E7%90%86%E8%AE%BA" title="VC理论">VC理论</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;">大会与出版物</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E7%A5%9E%E7%BB%8F%E4%BF%A1%E6%81%AF%E5%A4%84%E7%90%86%E7%B3%BB%E7%BB%9F%E5%A4%A7%E4%BC%9A" title="神经信息处理系统大会">NeurIPS</a></li> <li><span class="ilh-all" data-orig-title="国际机器学习大会" data-lang-code="en" data-lang-name="英语" data-foreign-title="International Conference on Machine Learning"><span class="ilh-page"><a href="/w/index.php?title=%E5%9B%BD%E9%99%85%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%A4%A7%E4%BC%9A&action=edit&redlink=1" class="new" title="国际机器学习大会（页面不存在）">ICML</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/International_Conference_on_Machine_Learning" class="extiw" title="en:International Conference on Machine Learning"><span lang="en" dir="auto">International Conference on Machine Learning</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%9B%BD%E9%99%85%E8%A1%A8%E5%BE%81%E5%AD%A6%E4%B9%A0%E5%A4%A7%E4%BC%9A" title="国际表征学习大会">ICLR</a></li> <li><span class="ilh-all" data-orig-title="机器学习 (期刊)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Machine Learning (journal)"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0_(%E6%9C%9F%E5%88%8A)&action=edit&redlink=1" class="new" title="机器学习 (期刊)（页面不存在）">ML</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Machine_Learning_(journal)" class="extiw" title="en:Machine Learning (journal)"><span lang="en" dir="auto">Machine Learning (journal)</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="机器学习研究期刊" data-lang-code="en" data-lang-name="英语" data-foreign-title="Journal of Machine Learning Research"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E7%A0%94%E7%A9%B6%E6%9C%9F%E5%88%8A&action=edit&redlink=1" class="new" title="机器学习研究期刊（页面不存在）">JMLR</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Journal_of_Machine_Learning_Research" class="extiw" title="en:Journal of Machine Learning Research"><span lang="en" dir="auto">Journal of Machine Learning Research</span></a></span>）</span></span></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="border-top:1px solid #aaa;text-align:center; background:#ddd;">相关条目</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><span class="ilh-all" data-orig-title="人工智能术语" data-lang-code="en" data-lang-name="英语" data-foreign-title="Glossary of artificial intelligence"><span class="ilh-page"><a href="/w/index.php?title=%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD%E6%9C%AF%E8%AF%AD&action=edit&redlink=1" class="new" title="人工智能术语（页面不存在）">人工智能术语</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Glossary_of_artificial_intelligence" class="extiw" title="en:Glossary of artificial intelligence"><span lang="en" dir="auto">Glossary of artificial intelligence</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="机器学习研究数据集列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="List of datasets for machine-learning research"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E7%A0%94%E7%A9%B6%E6%95%B0%E6%8D%AE%E9%9B%86%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="机器学习研究数据集列表（页面不存在）">机器学习研究数据集列表</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/List_of_datasets_for_machine-learning_research" class="extiw" title="en:List of datasets for machine-learning research"><span lang="en" dir="auto">List of datasets for machine-learning research</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="机器学习概要" data-lang-code="en" data-lang-name="英语" data-foreign-title="Outline of machine learning"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E6%A6%82%E8%A6%81&action=edit&redlink=1" class="new" title="机器学习概要（页面不存在）">机器学习概要</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Outline_of_machine_learning" class="extiw" title="en:Outline of machine learning"><span lang="en" dir="auto">Outline of machine learning</span></a></span>）</span></span></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar" style="line-height:1.6"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84244141">.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output 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.navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%AF%BC%E8%88%AA%E6%A0%8F" title="Template:机器学习导航栏"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%AF%BC%E8%88%AA%E6%A0%8F&action=edit&redlink=1" class="new" title="Template talk:机器学习导航栏（页面不存在）"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0%E5%AF%BC%E8%88%AA%E6%A0%8F" title="Special:编辑页面/Template:机器学习导航栏"><abbr title="编辑该模板">编</abbr></a></li></ul></div></td></tr></tbody></table> <p>在<a href="/wiki/%E6%A8%A1%E5%BC%8F%E8%AF%86%E5%88%AB" title="模式识别">模式识别</a>领域中，<b>最近鄰居法</b>（<b>KNN</b>算法，又譯<b>K-近邻算法</b>）是一种用于<a href="/wiki/%E5%88%86%E7%B1%BB%E9%97%AE%E9%A2%98" class="mw-redirect" title="分类问题">分类</a>和<a href="/wiki/%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="迴歸分析">回归</a>的<a href="/wiki/%E7%84%A1%E6%AF%8D%E6%95%B8%E7%B5%B1%E8%A8%88" title="無母數統計">無母數統計</a>方法<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>，由<a href="/wiki/%E7%BE%8E%E5%9B%BD" title="美国">美国</a>统计学家<a href="/wiki/%E4%BC%8A%E8%8A%99%E7%90%B3%C2%B7%E8%B2%BB%E5%85%8B%E6%96%AF" title="伊芙琳·費克斯">伊芙琳·费克斯</a>和<a href="/wiki/%E5%B0%8F%E7%B4%84%E7%91%9F%E5%A4%AB%C2%B7%E5%8B%9E%E6%A3%AE%C2%B7%E9%9C%8D%E5%A5%87%E6%96%AF" title="小約瑟夫·勞森·霍奇斯">小約瑟夫·霍奇斯</a>于1951年首次提出，后来由<span class="ilh-all" data-orig-title="托馬斯·M·寇弗" data-lang-code="en" data-lang-name="英语" data-foreign-title="Thomas M. Cover"><span class="ilh-page"><a href="/w/index.php?title=%E6%89%98%E9%A6%AC%E6%96%AF%C2%B7M%C2%B7%E5%AF%87%E5%BC%97&action=edit&redlink=1" class="new" title="托馬斯·M·寇弗（页面不存在）">托馬斯·寇弗</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Thomas_M._Cover" class="extiw" title="en:Thomas M. Cover"><span lang="en" dir="auto">Thomas M. Cover</span></a></span>）</span></span>扩展。在这两种情况下，输入包含<span class="ilh-all" data-orig-title="特徵空間(機器學習)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Feature Space"><span class="ilh-page"><a href="/w/index.php?title=%E7%89%B9%E5%BE%B5%E7%A9%BA%E9%96%93(%E6%A9%9F%E5%99%A8%E5%AD%B8%E7%BF%92)&action=edit&redlink=1" class="new" title="特徵空間(機器學習)（页面不存在）">特徵空間</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Feature_Space" class="extiw" title="en:Feature Space"><span lang="en" dir="auto">Feature Space</span></a></span>）</span></span>中的<i><b>k</b></i>个最接近的训练样本。 </p> <dl><dd><ul><li>在<i>k-NN分类</i>中，输出是一个分类族群。一个对象的分类是由其邻居的“多数表决”确定的，<i>k</i>个最近邻居（<i>k</i>为正<a href="/wiki/%E6%95%B4%E6%95%B0" title="整数">整数</a>，通常较小）中最常见的分类决定了赋予该对象的类别。若<i>k</i> = 1，则该对象的类别直接由最近的一个节点赋予。</li></ul></dd></dl> <dl><dd><ul><li>在<i>k-NN回归</i>中，输出是该对象的属性值。该值是其<i>k</i>个最近邻居的值的平均值。</li></ul></dd></dl> <p>最近鄰居法採用向量空間模型來分類，概念為相同類別的案例，彼此的相似度高，而可以藉由計算與已知類別案例之相似度，來評估未知類別案例可能的分類。 </p><p>K-NN是一种<a href="/wiki/%E5%BE%AA%E4%BE%8B%E5%AD%B8%E7%BF%92" title="循例學習">循例學習</a>，或者是局部近似和将所有计算推迟到分类之后的<span class="ilh-all" data-orig-title="惰性学习" data-lang-code="en" data-lang-name="英语" data-foreign-title="lazy learning"><span class="ilh-page"><a href="/w/index.php?title=%E6%83%B0%E6%80%A7%E5%AD%A6%E4%B9%A0&action=edit&redlink=1" class="new" title="惰性学习（页面不存在）">惰性学习</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/lazy_learning" class="extiw" title="en:lazy learning"><span lang="en" dir="auto">lazy learning</span></a></span>）</span></span>。k-近邻算法是所有的<a href="/wiki/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="机器学习">机器学习</a>算法中最简单的之一。 </p><p>无论是分类还是回归，衡量邻居的权重都非常有用，使较近邻居的权重比较远邻居的权重大。例如，一种常见的加权方案是给每个邻居权重赋值为1/ d，其中d是到邻居的距离。<span id="noteTag-cite_ref-sup"><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>註 1<span class="cite-bracket">]</span></a></sup></span> </p><p>邻居都取自一组已经正确分类（在回归的情况下，指属性值正确）的对象。虽然没要求明确的训练步骤，但这也可以当作是此算法的一个训练样本集。 </p><p>k-近邻算法的缺点是对数据的局部结构非常敏感。 </p><p><a href="/wiki/K-%E5%B9%B3%E5%9D%87%E7%AE%97%E6%B3%95" title="K-平均算法">K-平均算法</a>也是流行的机器学习技术，其名稱和k-近邻算法相近，但兩者没有关系。<a href="/wiki/%E6%A0%87%E5%87%86%E5%8C%96_(%E7%BB%9F%E8%AE%A1%E5%AD%A6)" title="标准化 (统计学)">数据标准化</a>可以大大提高该算法的准确性<sup id="cite_ref-:0_3-0" class="reference"><a href="#cite_note-:0-3"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="算法"><span id=".E7.AE.97.E6.B3.95"></span>算法</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=1" title="编辑章节：算法"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:KnnClassification.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/KnnClassification.svg/220px-KnnClassification.svg.png" decoding="async" width="220" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/KnnClassification.svg/330px-KnnClassification.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/KnnClassification.svg/440px-KnnClassification.svg.png 2x" data-file-width="279" data-file-height="252" /></a><figcaption><i>k</i>近邻算法例子。测试样本（绿色圆形）应归入要么是第一类的蓝色方形或是第二类的红色三角形。如果k=3（实线圆圈）它被分配给第二类，因为有2个三角形和只有1个正方形在内侧圆圈之内。如果k=5（虚线圆圈）它被分配到第一类（3个正方形与2个三角形在外侧圆圈之内）。</figcaption></figure> <p>训练样本是多维特征空间向量，其中每个训练样本带有一个类别标签。算法的训练阶段只包含存储的<a href="/wiki/%E7%89%B9%E5%BE%81%E5%90%91%E9%87%8F" class="mw-redirect" title="特征向量">特征向量</a>和训练样本的标签。 </p><p>在分类阶段，<i>k</i>是一个用户定义的常数。一个没有类别标签的向量（查询或测试点）将被归类为最接近该点的<i>k</i>个样本点中最频繁使用的一类。 </p><p>一般情况下，将<a href="/wiki/%E6%AC%A7%E6%B0%8F%E8%B7%9D%E7%A6%BB" class="mw-redirect" title="欧氏距离">欧氏距离</a>作为距离度量，但是这是只适用于<a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E5%B8%83#连续分布" title="概率分布">连续变量</a>。在文本分类这种离散变量情况下，另一个度量——<b>重叠度量</b>（或<a href="/wiki/%E6%B5%B7%E6%98%8E%E8%B7%9D%E7%A6%BB" class="mw-redirect" title="海明距离">海明距离</a>）可以用来作为度量。例如对于基因表达微阵列数据，<i>k</i>-NN也与Pearson和Spearman相关系数结合起来使用。<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>通常情况下，如果运用一些特殊的算法来计算度量的话，<i>k</i>近邻分类精度可显著提高，如运用<a href="/wiki/%E5%A4%A7%E9%97%B4%E9%9A%94%E6%9C%80%E8%BF%91%E9%82%BB%E5%B1%85" title="大间隔最近邻居">大间隔最近邻居</a>或者<a href="/wiki/%E9%82%BB%E9%87%8C%E6%88%90%E5%88%86%E5%88%86%E6%9E%90" title="邻里成分分析">邻里成分分析</a>法。 </p><p>“多数表决”分类会在类别分布偏斜时出现缺陷。也就是说，出现频率较多的样本将会主导测试点的预测结果，因为他们比较大可能出现在测试点的K邻域而测试点的属性又是通过<i>k</i>邻域内的样本计算出来的。<sup id="cite_ref-Coomans_Massart1982_6-0" class="reference"><a href="#cite_note-Coomans_Massart1982-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>解决这个缺点的方法之一是在进行分类时将样本到<i>k</i>个近邻点的距离考虑进去。<i>k</i>近邻点中每一个的分类（对于回归问题来说，是数值）都乘以与测试点之间距离的成反比的权重。另一种克服偏斜的方式是通过数据表示形式的抽象。例如，在<a href="/wiki/%E8%87%AA%E7%BB%84%E7%BB%87%E6%98%A0%E5%B0%84" title="自组织映射">自组织映射</a>（SOM）中，每个节点是相似的点的一个集群的代表（中心），而与它们在原始训练数据的密度无关。<i>K</i>-NN可以应用到SOM中。 </p> <div class="mw-heading mw-heading2"><h2 id="参数选择"><span id=".E5.8F.82.E6.95.B0.E9.80.89.E6.8B.A9"></span>参数选择</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=2" title="编辑章节：参数选择"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>如何选择一个最佳的K值取决于数据。一般情况下，在分类时较大的K值能够减小雜訊的影响，<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> 但会使类别之间的界限变得模糊。一个较好的K值能通过各种启发式技术（见<a href="/wiki/%E8%B6%85%E5%8F%82%E6%95%B0%E4%BC%98%E5%8C%96" title="超参数优化">超参数优化</a>）来获取。 </p><p>噪声和非相关性特征的存在，或特徵尺度与它们的重要性不一致会使K近邻算法的准确性严重降低。对于选取和缩放特征来改善分类已经作了很多研究。一个普遍的做法是利用<a href="/wiki/%E8%BF%9B%E5%8C%96%E7%AE%97%E6%B3%95" title="进化算法">进化算法</a>优化功能扩展<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>，还有一种较普遍的方法是利用训练样本的<a href="/wiki/%E4%BA%92%E4%BF%A1%E6%81%AF" title="互信息">互信息</a>进行选择特征。 </p><p>在二元（两类）分类问题中，选取<i>k</i>为奇数有助于避免两个分类平票的情形。在此问题下，选取最佳经验<i>k</i>值的方法是<a href="/wiki/%E8%87%AA%E5%8A%A9%E6%B3%95" title="自助法">自助法</a>。<sup id="cite_ref-HPS2008_9-0" class="reference"><a href="#cite_note-HPS2008-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="加权最近邻分类器"><span id=".E5.8A.A0.E6.9D.83.E6.9C.80.E8.BF.91.E9.82.BB.E5.88.86.E7.B1.BB.E5.99.A8"></span>加权最近邻分类器</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=3" title="编辑章节：加权最近邻分类器"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><style data-mw-deduplicate="TemplateStyles:r58896141">.mw-parser-output .serif{font-family:Times,serif}</style><span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;"> k</span></span>- 最近邻分类器可以被视为为<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;"> k</span></span>最近邻居分配权重<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7e9fedad8c70c6331b2640b56c23cef8c884e1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.536ex; height:2.843ex;" alt="{\displaystyle 1/k}"></span>以及为所有其他邻居分配<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;"> 0</span></span>权重。这可以推广到加权最近邻分类器。也就是说，第<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r58896141"><span class="serif"><span class="texhtml mvar" style="font-style:italic;margin-left:2px;margin-right:2px;"> i</span></span>近的邻居被赋予权重<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{ni}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{ni}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d76326293e410139d081d073068b9eb32a0777" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.45ex; height:2.009ex;" alt="{\displaystyle w_{ni}}"></span>，其中<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=1}^{n}w_{ni}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=1}^{n}w_{ni}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/167dcdfe9d31faea6f1e6c157cc23fe6e3b39fb7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:11.453ex; height:6.843ex;" alt="{\displaystyle \sum _{i=1}^{n}w_{ni}=1}"></span>。关于加权最近邻分类器的强一致性的类似结果也成立。<sup id="cite_ref-Stone_10-0" class="reference"><a href="#cite_note-Stone-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>设<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{n}^{wnn}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <mi>n</mi> <mi>n</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{n}^{wnn}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e88b657ee88d912408396f8c9ef6af3483bfdf01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.179ex; height:2.509ex;" alt="{\displaystyle C_{n}^{wnn}}"></span>表示权重为<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{w_{ni}\}_{i=1}^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> </msub> <msubsup> <mo fence="false" stretchy="false">}</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{w_{ni}\}_{i=1}^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efaf258e02ccae2b27c279885d6fb898adaf331d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.675ex; height:3.009ex;" alt="{\displaystyle \{w_{ni}\}_{i=1}^{n}}"></span>的加权最近邻分类器。根据类别分布的规律性条件，超额风险具有以下渐近展开<sup id="cite_ref-Samworth12_11-0" class="reference"><a href="#cite_note-Samworth12-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {R}}_{\mathcal {R}}(C_{n}^{wnn})-{\mathcal {R}}_{\mathcal {R}}(C^{Bayes})=\left(B_{1}s_{n}^{2}+B_{2}t_{n}^{2}\right)\{1+o(1)\},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <mi>n</mi> <mi>n</mi> </mrow> </msubsup> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">R</mi> </mrow> </mrow> </msub> <mo stretchy="false">(</mo> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>a</mi> <mi>y</mi> <mi>e</mi> <mi>s</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msubsup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msubsup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <mo>)</mo> </mrow> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>+</mo> <mi>o</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {R}}_{\mathcal {R}}(C_{n}^{wnn})-{\mathcal {R}}_{\mathcal {R}}(C^{Bayes})=\left(B_{1}s_{n}^{2}+B_{2}t_{n}^{2}\right)\{1+o(1)\},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02f064c830dbca4fcd695427bcc45c7aeb1b1196" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:54.866ex; height:3.343ex;" alt="{\displaystyle {\mathcal {R}}_{\mathcal {R}}(C_{n}^{wnn})-{\mathcal {R}}_{\mathcal {R}}(C^{Bayes})=\left(B_{1}s_{n}^{2}+B_{2}t_{n}^{2}\right)\{1+o(1)\},}"></span></dd></dl> <p>对常数 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fa091eb428443c9c5c5fcf32a69d3665c89e00c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle B_{1}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/199944d59dcc18842dfd1deab6000a1d1dadcbae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.818ex; height:2.509ex;" alt="{\displaystyle B_{2}}"></span> 当 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{n}^{2}=\sum _{i=1}^{n}w_{ni}^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msubsup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{n}^{2}=\sum _{i=1}^{n}w_{ni}^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed6dbd702b3141f1649ce10ccff3bac0acd55299" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:12.599ex; height:6.843ex;" alt="{\displaystyle s_{n}^{2}=\sum _{i=1}^{n}w_{ni}^{2}}"></span> 并且 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{n}=n^{-2/d}\sum _{i=1}^{n}w_{ni}\{i^{1+2/d}-(i-1)^{1+2/d}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> </msub> <mo fence="false" stretchy="false">{</mo> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>i</mi> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{n}=n^{-2/d}\sum _{i=1}^{n}w_{ni}\{i^{1+2/d}-(i-1)^{1+2/d}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd32f71ab3cd0784e73324108ecb05be734cd7de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:40.4ex; height:6.843ex;" alt="{\displaystyle t_{n}=n^{-2/d}\sum _{i=1}^{n}w_{ni}\{i^{1+2/d}-(i-1)^{1+2/d}\}}"></span>。 </p><p>最佳加权方案<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \{w_{ni}^{*}\}_{i=1}^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <msubsup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <msubsup> <mo fence="false" stretchy="false">}</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{w_{ni}^{*}\}_{i=1}^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f97b387c9e937fac91f0644ac895c5c95d9a4921" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.675ex; height:3.009ex;" alt="{\displaystyle \{w_{ni}^{*}\}_{i=1}^{n}}"></span>用于平衡上面显示中的两个项，如下所示：令 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k^{*}=\lfloor Bn^{\frac {4}{d+4}}\rfloor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mo fence="false" stretchy="false">⌊</mo> <mi>B</mi> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mrow> <mi>d</mi> <mo>+</mo> <mn>4</mn> </mrow> </mfrac> </mrow> </msup> <mo fence="false" stretchy="false">⌋</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k^{*}=\lfloor Bn^{\frac {4}{d+4}}\rfloor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cbecc881f1b8637b3d4d4527fd1671f5be252fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.059ex; height:4.176ex;" alt="{\displaystyle k^{*}=\lfloor Bn^{\frac {4}{d+4}}\rfloor }"></span>， </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{ni}^{*}={\frac {1}{k^{*}}}\left[1+{\frac {d}{2}}-{\frac {d}{2{k^{*}}^{2/d}}}\{i^{1+2/d}-(i-1)^{1+2/d}\}\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mn>2</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo fence="false" stretchy="false">{</mo> <msup> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mo>−</mo> <mo stretchy="false">(</mo> <mi>i</mi> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> </mrow> </msup> <mo fence="false" stretchy="false">}</mo> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{ni}^{*}={\frac {1}{k^{*}}}\left[1+{\frac {d}{2}}-{\frac {d}{2{k^{*}}^{2/d}}}\{i^{1+2/d}-(i-1)^{1+2/d}\}\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbfa4058134234385c31544db3e657c4b242ab34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:50.643ex; height:6.176ex;" alt="{\displaystyle w_{ni}^{*}={\frac {1}{k^{*}}}\left[1+{\frac {d}{2}}-{\frac {d}{2{k^{*}}^{2/d}}}\{i^{1+2/d}-(i-1)^{1+2/d}\}\right]}"></span> 对 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=1,2,\dots ,k^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=1,2,\dots ,k^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ea7e974f7466c9dedfe409ea013bc719264872b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.703ex; height:2.676ex;" alt="{\displaystyle i=1,2,\dots ,k^{*}}"></span> 并且</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{ni}^{*}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{ni}^{*}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bd3d5b77d7fef0dabd4326ee85b04fa244fa988" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.711ex; height:2.843ex;" alt="{\displaystyle w_{ni}^{*}=0}"></span> 对 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i=k^{*}+1,\dots ,n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>=</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i=k^{*}+1,\dots ,n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c2f2e5c12f3febcefe0aae189d44031daf8e79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.742ex; height:2.676ex;" alt="{\displaystyle i=k^{*}+1,\dots ,n}"></span>.</dd></dl> <p>利用最优权重，超额风险的渐近展开中的主项是<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {O}}(n^{-{\frac {4}{d+4}}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mrow> <mi>d</mi> <mo>+</mo> <mn>4</mn> </mrow> </mfrac> </mrow> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}(n^{-{\frac {4}{d+4}}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07280735a8852d609ffd3942647d7e3255697f05" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.804ex; height:4.176ex;" alt="{\displaystyle {\mathcal {O}}(n^{-{\frac {4}{d+4}}})}"></span>。当使用<span class="ilh-all" data-orig-title="自助聚合" data-lang-code="en" data-lang-name="英语" data-foreign-title="bootstrap aggregating"><span class="ilh-page"><a href="/w/index.php?title=%E8%87%AA%E5%8A%A9%E8%81%9A%E5%90%88&action=edit&redlink=1" class="new" title="自助聚合（页面不存在）">bagged 最近邻分类器</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/bootstrap_aggregating" class="extiw" title="en:bootstrap aggregating"><span lang="en" dir="auto">bootstrap aggregating</span></a></span>）</span></span>时，类似的结果也是如此。 </p> <div class="mw-heading mw-heading2"><h2 id="属性"><span id=".E5.B1.9E.E6.80.A7"></span>属性</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=4" title="编辑章节：属性"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>原始朴素的算法通过計算测试点到存储样本点的距离是比较容易实现的，但它属于计算密集型的，特别是当训练样本集变大时，计算量也会跟着增大。多年来，许多用来减少不必要距离评价的近邻搜索算法已经被提出来。使用一种合适的近邻搜索算法能使K近邻算法的计算变得简单许多。 </p><p>近邻算法具有较强的一致性结果。随着数据趋于无限，算法保证错误率不会超过贝叶斯算法错误率的两倍<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>。对于一些K值，K近邻保证错误率不会超过贝叶斯的。 </p> <div class="mw-heading mw-heading2"><h2 id="决策边界"><span id=".E5.86.B3.E7.AD.96.E8.BE.B9.E7.95.8C"></span>决策边界</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=5" title="编辑章节：决策边界"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>近邻算法能用一种有效的方式隐含的计算<a href="/wiki/%E5%86%B3%E7%AD%96%E8%BE%B9%E7%95%8C" title="决策边界">决策边界</a>。另外，它也可以显式的计算决策边界，以及有效率的这样做计算，使得计算复杂度是边界复杂度的函数。<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="连续变量估计"><span id=".E8.BF.9E.E7.BB.AD.E5.8F.98.E9.87.8F.E4.BC.B0.E8.AE.A1"></span>连续变量估计</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=6" title="编辑章节：连续变量估计"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>K近邻算法也适用于连续变量估计，比如适用反距离加权平均多个K近邻点确定测试点的值。该算法的功能有： </p> <ol><li>从目标区域抽样计算欧式或马氏距离；</li> <li>在交叉验证后的RMSE基础上选择启发式最优的K邻域；</li> <li>计算多元k-最近邻居的距离倒数加权平均。</li></ol> <div class="mw-heading mw-heading2"><h2 id="發展"><span id=".E7.99.BC.E5.B1.95"></span>發展</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=7" title="编辑章节：發展"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>然而k最近鄰居法因為計算量相當的大，所以相當的耗時，Ko與Seo提出一演算法<b>TCFP</b>（<b>t</b>ext <b>c</b>ategorization using <b>f</b>eature <b>p</b>rojection），嘗試利用<span class="ilh-all" data-orig-title="特徵投影法" data-lang-code="en" data-lang-name="英语" data-foreign-title="feature projection"><span class="ilh-page"><a href="/w/index.php?title=%E7%89%B9%E5%BE%B5%E6%8A%95%E5%BD%B1%E6%B3%95&action=edit&redlink=1" class="new" title="特徵投影法（页面不存在）">特徵投影法</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/feature_projection" class="extiw" title="en:feature projection"><span lang="en" dir="auto">feature projection</span></a></span>）</span></span>來降低與分類無關的特徵對於系統的影響，並藉此提昇系統效能，其實驗結果顯示其分類效果與k最近鄰居法相近，但其運算所需時間僅需k最近鄰居法運算時間的五十分之一。 </p><p>除了針對文件分類的效率，尚有研究針對如何促進<i>k</i>最近鄰居法在文件分類方面的效果，如Han等人於2002年嘗試利用<a href="/wiki/%E8%B2%AA%E5%BF%83%E6%B3%95" class="mw-redirect" title="貪心法">貪心法</a>，針對文件分類實做可調整權重的k最近鄰居法<b>WAkNN</b>（<b>w</b>eighted <b>a</b>djusted <b>k</b> <b>n</b>earest <b>n</b>eighbor），以促進分類效果；而Li等人於2004年提出由於不同分類的文件本身有數量上有差異，因此也應該依照訓練集合中各種分類的文件數量，選取不同數目的最近鄰居，來參與分類。 </p> <div class="mw-heading mw-heading2"><h2 id="参见"><span id=".E5.8F.82.E8.A7.81"></span>参见</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=8" title="编辑章节：参见"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r79074265">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="div-col"> <ul><li><a href="/wiki/%E6%9C%80%E9%82%BB%E8%BF%91%E6%90%9C%E7%B4%A2" title="最邻近搜索">最邻近搜索</a></li> <li><a href="/wiki/%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90" title="聚类分析">聚类分析</a></li> <li><a href="/wiki/%E6%95%B0%E6%8D%AE%E6%8C%96%E6%8E%98" title="数据挖掘">数据挖掘</a></li> <li><a href="/wiki/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="机器学习">机器学习</a></li> <li><a href="/wiki/%E6%A8%A1%E5%BC%8F%E8%AF%86%E5%88%AB" title="模式识别">模式识别</a></li> <li><a href="/wiki/%E9%A2%84%E6%B5%8B%E5%88%86%E6%9E%90" title="预测分析">预测分析</a></li> <li><a href="/wiki/%E7%BB%B4%E6%95%B0%E7%81%BE%E9%9A%BE" title="维数灾难">维数灾难</a></li> <li><a href="/wiki/%E4%B8%BB%E6%88%90%E5%88%86%E5%88%86%E6%9E%90" title="主成分分析">主成分分析</a></li> <li><a href="/wiki/%E6%9C%80%E5%B0%8F%E5%93%88%E5%B8%8C" title="最小哈希">最小哈希</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="注释"><span id=".E6.B3.A8.E9.87.8A"></span>注释</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=9" title="编辑章节：注释"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="references-NoteFoot"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">这个方案是一个<a href="/wiki/%E7%BA%BF%E6%80%A7%E6%8F%92%E5%80%BC" title="线性插值">线性插值</a>的推广。</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="參考文獻"><span id=".E5.8F.83.E8.80.83.E6.96.87.E7.8D.BB"></span>參考文獻</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=10" title="编辑章节：參考文獻"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="引用"><span id=".E5.BC.95.E7.94.A8"></span>引用</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=11" title="编辑章节：引用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation journal">Altman, N. S. <a rel="nofollow" class="external text" href="https://archive.org/details/sim_american-statistician_1992-08_46_3/page/175">An introduction to kernel and nearest-neighbor nonparametric regression</a>. The American Statistician. 1992, <b>46</b> (3): 175–185. <a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00031305.1992.10475879"><span title="數位物件識別號">doi:10.1080/00031305.1992.10475879</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=An+introduction+to+kernel+and+nearest-neighbor+nonparametric+regression&rft.aufirst=N.+S.&rft.aulast=Altman&rft.date=1992&rft.genre=article&rft.issue=3&rft.jtitle=The+American+Statistician&rft.pages=175-185&rft.volume=46&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_american-statistician_1992-08_46_3%2Fpage%2F175&rft_id=info%3Adoi%2F10.1080%2F00031305.1992.10475879&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-:0-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_3-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Piryonesi S. Madeh; El-Diraby Tamer E. Role of Data Analytics in Infrastructure Asset Management: Overcoming Data Size and Quality Problems. Journal of Transportation Engineering, Part B: Pavements. 2020-06-01, <b>146</b> (2): 04020022. <a rel="nofollow" class="external text" href="https://doi.org/10.1061%2FJPEODX.0000175"><span title="數位物件識別號">doi:10.1061/JPEODX.0000175</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=Role+of+Data+Analytics+in+Infrastructure+Asset+Management%3A+Overcoming+Data+Size+and+Quality+Problems&rft.au=El-Diraby+Tamer+E.&rft.au=Piryonesi+S.+Madeh&rft.date=2020-06-01&rft.genre=article&rft.issue=2&rft.jtitle=Journal+of+Transportation+Engineering%2C+Part+B%3A+Pavements&rft.pages=04020022&rft.volume=146&rft_id=info%3Adoi%2F10.1061%2FJPEODX.0000175&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite class="citation book">Hastie, Trevor. <a rel="nofollow" class="external text" href="https://archive.org/details/elementsofstatis0000hast">The elements of statistical learning : data mining, inference, and prediction : with 200 full-color illustrations</a>. Tibshirani, Robert., Friedman, J. H. (Jerome H.). New York: Springer. 2001. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-387-95284-5" title="Special:网络书源/0-387-95284-5"><span title="国际标准书号">ISBN</span> 0-387-95284-5</a>. <a rel="nofollow" class="external text" href="//www.worldcat.org/oclc/46809224"><span title="OCLC">OCLC 46809224</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.au=Hastie%2C+Trevor.&rft.btitle=The+elements+of+statistical+learning+%3A+data+mining%2C+inference%2C+and+prediction+%3A+with+200+full-color+illustrations&rft.date=2001&rft.genre=book&rft.isbn=0-387-95284-5&rft.place=New+York&rft.pub=Springer&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felementsofstatis0000hast&rft_id=info%3Aoclcnum%2F46809224&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation journal">Jaskowiak, P. A.; Campello, R. J. G. B. Comparing Correlation Coefficients as Dissimilarity Measures for Cancer Classification in Gene Expression Data. Brazilian Symposium on Bioinformatics (BSB 2011): 1–8. <span class="plainlinks"><a rel="nofollow" class="external text" href="//citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.993"><span title="CiteSeerX">CiteSeerX 10.1.1.208.993</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=Comparing+Correlation+Coefficients+as+Dissimilarity+Measures+for+Cancer+Classification+in+Gene+Expression+Data&rft.au=Campello%2C+R.+J.+G.+B.&rft.aufirst=P.+A.&rft.aulast=Jaskowiak&rft.genre=article&rft.pages=1-8&rft_id=%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.208.993&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Coomans_Massart1982-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Coomans_Massart1982_6-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">D. Coomans; D.L. Massart. Alternative k-nearest neighbour rules in supervised pattern recognition: Part 1. k-Nearest neighbour classification by using alternative voting rules. <a href="/w/index.php?title=Analytica_Chimica_Acta&action=edit&redlink=1" class="new" title="Analytica Chimica Acta（页面不存在）">Analytica Chimica Acta</a>. 1982, <b>136</b>: 15–27. <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0003-2670%2801%2995359-0"><span title="數位物件識別號">doi:10.1016/S0003-2670(01)95359-0</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=Alternative+k-nearest+neighbour+rules+in+supervised+pattern+recognition%3A+Part+1.+k-Nearest+neighbour+classification+by+using+alternative+voting+rules&rft.au=D.+Coomans&rft.au=D.L.+Massart&rft.date=1982&rft.genre=article&rft.jtitle=Analytica+Chimica+Acta&rft.pages=15-27&rft.volume=136&rft_id=info%3Adoi%2F10.1016%2FS0003-2670%2801%2995359-0&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Everitt, B. S., Landau, S., Leese, M. and Stahl, D.（2011）Miscellaneous Clustering Methods, in Cluster Analysis, 5th Edition, John Wiley & Sons, Ltd, Chichester, UK.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Nigsch F, Bender A, van Buuren B, Tissen J, Nigsch E, Mitchell JB (2006). "Melting point prediction employing k-nearest neighbor algorithms and genetic parameter optimization". Journal of Chemical Information and Modeling 46 (6): 2412–2422. doi:10.1021/ci060149f. <a class="external mw-magiclink-pmid" rel="nofollow" href="//www.ncbi.nlm.nih.gov/pubmed/17125183?dopt=Abstract">PMID 17125183</a>.</span> </li> <li id="cite_note-HPS2008-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-HPS2008_9-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Hall P, Park BU, Samworth RJ. <a rel="nofollow" class="external text" href="https://archive.org/details/sim_annals-of-statistics_2008-10_36_5/page/2135">Choice of neighbor order in nearest-neighbor classification</a>. <a href="/w/index.php?title=Annals_of_Statistics&action=edit&redlink=1" class="new" title="Annals of Statistics（页面不存在）">Annals of Statistics</a>. 2008, <b>36</b> (5): 2135–2152. <a rel="nofollow" class="external text" href="https://doi.org/10.1214%2F07-AOS537"><span title="數位物件識別號">doi:10.1214/07-AOS537</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=Choice+of+neighbor+order+in+nearest-neighbor+classification&rft.au=Hall+P%2C+Park+BU%2C+Samworth+RJ&rft.date=2008&rft.genre=article&rft.issue=5&rft.jtitle=Annals+of+Statistics&rft.pages=2135-2152&rft.volume=36&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_annals-of-statistics_2008-10_36_5%2Fpage%2F2135&rft_id=info%3Adoi%2F10.1214%2F07-AOS537&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Stone-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Stone_10-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Stone C. J. <a rel="nofollow" class="external text" href="https://archive.org/details/sim_annals-of-statistics_1977-07_5_4/page/595">Consistent nonparametric regression</a>. <a href="/w/index.php?title=Annals_of_Statistics&action=edit&redlink=1" class="new" title="Annals of Statistics（页面不存在）">Annals of Statistics</a>. 1977, <b>5</b> (4): 595–620. <a rel="nofollow" class="external text" href="https://doi.org/10.1214%2Faos%2F1176343886"><span title="數位物件識別號">doi:10.1214/aos/1176343886</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=Consistent+nonparametric+regression&rft.au=Stone+C.+J.&rft.date=1977&rft.genre=article&rft.issue=4&rft.jtitle=Annals+of+Statistics&rft.pages=595-620&rft.volume=5&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_annals-of-statistics_1977-07_5_4%2Fpage%2F595&rft_id=info%3Adoi%2F10.1214%2Faos%2F1176343886&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-Samworth12-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Samworth12_11-0">^</a></b></span> <span class="reference-text"><cite class="citation journal">Samworth R. J. <a rel="nofollow" class="external text" href="https://archive.org/details/sim_annals-of-statistics_2012-10_40_5/page/2733">Optimal weighted nearest neighbour classifiers</a>. <a href="/w/index.php?title=Annals_of_Statistics&action=edit&redlink=1" class="new" title="Annals of Statistics（页面不存在）">Annals of Statistics</a>. 2012, <b>40</b> (5): 2733–2763. <span class="plainlinks"><a rel="nofollow" class="external text" href="//arxiv.org/abs/1101.5783"><span title="arXiv">arXiv:1101.5783</span></a> <span typeof="mw:File"><span title="可免费查阅"><img alt="可免费查阅" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png" decoding="async" width="9" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/14px-Lock-green.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/18px-Lock-green.svg.png 2x" data-file-width="512" data-file-height="813" /></span></span></span>. <a rel="nofollow" class="external text" href="https://doi.org/10.1214%2F12-AOS1049"><span title="數位物件識別號">doi:10.1214/12-AOS1049</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=Optimal+weighted+nearest+neighbour+classifiers&rft.au=Samworth+R.+J.&rft.date=2012&rft.genre=article&rft.issue=5&rft.jtitle=Annals+of+Statistics&rft.pages=2733-2763&rft.volume=40&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_annals-of-statistics_2012-10_40_5%2Fpage%2F2733&rft_id=info%3Aarxiv%2F1101.5783&rft_id=info%3Adoi%2F10.1214%2F12-AOS1049&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Cover TM, Hart PE (1967). "Nearest neighbor pattern classification". IEEE Transactions on Information Theory 13 (1): 21–27. doi:10.1109/TIT.1967.1053964.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Bremner D, Demaine E, Erickson J, Iacono J, Langerman S, Morin P, Toussaint G (2005). "Output-sensitive algorithms for computing nearest-neighbor decision boundaries". Discrete and Computational Geometry 33 (4): 593–604. doi:10.1007/s00454-004-1152-0</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="来源"><span id=".E6.9D.A5.E6.BA.90"></span>来源</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=12" title="编辑章节：来源"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r80540462">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .refbegin-100{font-size:100%}</style><div class="refbegin" style=""> <ul><li>E. H. Han, G. Karypis and V. Kumar, Text categorization using weight adjusted k-Nearest Neighbor classification, Pacific-Asia Conference on Knowledge Discovery and Data Mining, pp. 53–65, 2001.</li> <li>Y. J. Ko and Y. J. Seo, Text categorization using feature projections, Proceedings of the Nineteenth international conference on Computational linguistics, Volume 1, pp. 1–7, 2002.</li> <li>B. L. Li, Q. Lu and S. W. Yu, An adaptive k-nearest neighbor text categorization strategy, ACM Transactions on Asian Language Information Processing, Volume 3 , Issue 4, pp. 215–226, 2004.</li></ul> <p>}} </p> </div> <div class="mw-heading mw-heading2"><h2 id="拓展阅读"><span id=".E6.8B.93.E5.B1.95.E9.98.85.E8.AF.BB"></span>拓展阅读</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=K-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&action=edit&section=13" title="编辑章节：拓展阅读"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.1422">When Is "Nearest Neighbor" Meaningful?</a>（<a rel="nofollow" class="external text" href="//web.archive.org/web/20090726012702/http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.1422">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li> <li><cite class="citation book"><a href="/w/index.php?title=Belur_V._Dasarathy&action=edit&redlink=1" class="new" title="Belur V. Dasarathy（页面不存在）">Belur V. Dasarathy</a> (编). Nearest Neighbor (NN) Norms: NN Pattern Classification Techniques. 1991. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-8186-8930-7" title="Special:网络书源/0-8186-8930-7"><span title="国际标准书号">ISBN</span> 0-8186-8930-7</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.au=Belur+V.+Dasarathy&rft.btitle=Nearest+Neighbor+%28NN%29+Norms%3A+NN+Pattern+Classification+Techniques&rft.date=1991&rft.genre=book&rft.isbn=0-8186-8930-7&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation book">Shakhnarovish, Darrell, and Indyk (编). Nearest-Neighbor Methods in Learning and Vision. <a href="/wiki/MIT_Press" class="mw-redirect" title="MIT Press">MIT Press</a>. 2005. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/0-262-19547-X" title="Special:网络书源/0-262-19547-X"><span title="国际标准书号">ISBN</span> 0-262-19547-X</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.au=Shakhnarovish%2C+Darrell%2C+and+Indyk&rft.btitle=Nearest-Neighbor+Methods+in+Learning+and+Vision&rft.date=2005&rft.genre=book&rft.isbn=0-262-19547-X&rft.pub=MIT+Press&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation journal">Mäkelä H Pekkarinen A. Estimation of forest stand volumes by Landsat TM imagery and stand-level field-inventory data. <a href="/w/index.php?title=Forest_Ecology_and_Management&action=edit&redlink=1" class="new" title="Forest Ecology and Management（页面不存在）">Forest Ecology and Management</a>. 2004-07-26, <b>196</b> (2–3): 245–255. <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.foreco.2004.02.049"><span title="數位物件識別號">doi:10.1016/j.foreco.2004.02.049</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3AK-%E8%BF%91%E9%82%BB%E7%AE%97%E6%B3%95&rft.atitle=Estimation+of+forest+stand+volumes+by+Landsat+TM+imagery+and+stand-level+field-inventory+data&rft.au=M%C3%A4kel%C3%A4+H+Pekkarinen+A&rft.date=2004-07-26&rft.genre=article&rft.issue=2%E2%80%933&rft.jtitle=Forest+Ecology+and+Management&rft.pages=245-255&rft.volume=196&rft_id=info%3Adoi%2F10.1016%2Fj.foreco.2004.02.049&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></li> <li>Fast k nearest neighbor search using <a href="/wiki/GPU" class="mw-redirect" title="GPU">GPU</a>. In Proceedings of the CVPR Workshop on Computer Vision on GPU, Anchorage, Alaska, USA, June 2008. V. Garcia and E. Debreuve and M. Barlaud.</li> <li><a rel="nofollow" class="external text" href="http://www.scholarpedia.org/article/K-nearest_neighbor">Scholarpedia article on <i>k</i>-NN</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210128122727/http://www.scholarpedia.org/article/K-nearest_neighbor">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li> <li><a rel="nofollow" class="external text" href="https://code.google.com/p/google-all-pairs-similarity-search/">google-all-pairs-similarity-search</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20160116173026/https://code.google.com/p/google-all-pairs-similarity-search/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" 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