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面包屑導航結束 --> <!-- 頁面標題開始 --> <div id="n1l1njb9b" class="title"> <h3><a>支持向量機原理<small></small></a></h3> </div> <!-- 頁面標題結束 --> <hr class="featurette-divider"> <!-- 中部開始 --> <div id="n1l1njb9b" class="container"> <!-- 正文 --> <div id="n1l1njb9b" class="lead" id="print"> <p><span style="font-size: x-small;"> </span><a name="bookmark30" style="line-height: 13pt; text-align: justify; background-color: transparent;"></a><span style="font-size: x-small;"><a name="bookmark30" style="line-height: 13pt; text-align: justify; background-color: transparent;"><span id="n1l1njb9b" class="20pt"><span style="font-family: SimSun;">4.</span></span></a><span id="n1l1njb9b" class="20" style="line-height: 13pt; text-align: justify; background-color: transparent;"><span style="font-family: SimSun;"> 2</span></span><span id="n1l1njb9b" class="20" style="line-height: 13pt; text-align: justify; background-color: transparent;">支持向量機原理</span></span></p> <div id="n1l1njb9b" class="Section1"> <p class="21" style="margin-top:0cm;margin-right:0cm;margin-bottom:7.05pt; margin-left:0cm;text-align:justify;text-justify:inter-ideograph;text-indent: 0cm;line-height:11.0pt;mso-line-height-rule:exactly;mso-list:l0 level1 lfo1; tab-stops:16.95pt;background:transparent"><span style="font-size: x-small;"><!--[if !supportLists]--><span style="font-family: SimSun;">4.<span style="font-stretch: normal; line-height: normal; font-family: 'Times New Roman';"> </span></span><!--[endif]--><span id="n1l1njb9b" class="2"><span style="font-family: SimSun;">2. 1</span></span><span id="n1l1njb9b" class="2">支持向量機</span></span></p> <p class="21" style="margin-top:0cm;text-align:justify;text-justify:inter-ideograph; text-indent:26.0pt;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"><span style="font-size: x-small;"><span id="n1l1njb9b" class="2">為了處理模式識別的問題</span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">Vapnik</span></span><span id="n1l1njb9b" class="2">提出了支持向量機的想法，通過的不斷研究和 探索，支持向量機知識理論取得了很大的進展。支持向量機可以被用來尋找線性可分 情況下的最優分類面。最優分類面不僅要求能將兩類不同的數據正確地分類(訓練失 敗率接近0)，而且還要盡可能的使它們的分類間距到達最大。</span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">SVM</span></span><span id="n1l1njb9b" class="2">是為了能夠尋找 到一個滿足分類要求的超平面而被研發出來的，并且它需要使訓練集中的點距離這個 分類面達到的距離最遠，也就是說希望能夠尋找到一個分類面使它雙側的空白地區盡 可能的大。過兩種不同類型的樣本，離分類面最近的，并且能夠平行于最優分類面- 超平面</span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">Hu</span></span><span id="n1l1njb9b" class="2"><span lang="EN-US" style="font-family: SimSun;"> </span></span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">H</span></span><span id="n1l1njb9b" class="2"><sub><span style="font-family: SimSun;">2</span></sub></span><span id="n1l1njb9b" class="2">的訓練樣本就稱為支持向量。</span></span></p> </div> <p><span style="font-size: x-small;"> <!--[if !supportTextWrap]--> <!--[endif]--> </span></p> <p class="21" style="margin-top:12.0pt;text-align:justify;text-justify:inter-ideograph; text-indent:25.0pt;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"><span style="font-size: x-small;"><span id="n1l1njb9b" class="2">大多數條件下，需要訓練的樣本是線性不可分的，為了處理這一問題</span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">Vapnik</span></span><span id="n1l1njb9b" class="2">等 人提出了廣義分類面（松弛子）的想法。針對非線性分類問題利用非線性變換將其轉 化為某個高維空間中的線性問題，然后在這個高維空間上尋找最優分類面。映射空間 可以是有限維也可以是無限維的。分類函數涉及到的只是樣本之間的內積運算，因此 高維度空間只需要進行內積運算即可，這種內積運算的運算形式可通過原空間自定義 的函數來實現，甚至沒有必要知道其變換的形式。</span></span></p> <p class="21" style="margin-top:0cm;text-align:justify;text-justify:inter-ideograph; text-indent:25.0pt;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"><span style="font-size: x-small;"><span id="n1l1njb9b" class="2">依據</span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">Hibert</span></span><span id="n1l1njb9b" class="2"><span style="font-family: SimSun;">-</span></span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">Schmidt</span></span><span id="n1l1njb9b" class="2">定理，任意函數只要能夠符合</span><span id="n1l1njb9b" class="2TimesNewRoman26"><span lang="EN-US">Mercer</span></span><span id="n1l1njb9b" class="2">條件就可以作為計算內 積的函數使用。它能夠實現非線性分類轉變為線性分類，而計算難度卻是一樣的。</span></span></p> <p class="21" style="margin-top:0cm;text-align:justify;text-justify:inter-ideograph; text-indent:25.0pt;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"><span style="font-size: x-small;"><span id="n1l1njb9b" class="2">通俗易懂的說支持向量機就是通過內積核函數將輸入樣本從低維空間映射到一 個高維空間，然后在這個高維空間上尋找最優分類面。支持向量機的形式和神經網絡 非常類似<sup>[3</sup>&<sup>37]</sup>。其示意圖如4.3。</span><br clear="all" style="mso-special-character:line-break;page-break-before:always" /> </span></p> <p class="21" style="margin-top:0cm;margin-right:0cm;margin-bottom:8.0pt; margin-left:0cm;text-align:justify;text-justify:inter-ideograph;text-indent: 0cm;line-height:11.0pt;mso-line-height-rule:exactly;mso-list:l1 level1 lfo2; tab-stops:17.7pt;background:transparent"><span style="font-size: x-small;"><!--[if !supportLists]--><span style="font-family: SimSun; letter-spacing: 1pt;">4.<span style="font-stretch: normal; line-height: normal; font-family: 'Times New Roman';"> </span></span><span id="n1l1njb9b" class="2"><span style="font-family: SimSun;">2. 2</span></span><span id="n1l1njb9b" class="2">核函數</span></span></p> <p class="21" style="margin-top:0cm;text-align:justify;text-justify:inter-ideograph; text-indent:0cm;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"><span style="font-size: x-small;"><span id="n1l1njb9b" class="2">內積核函數種類很多，不同的核函數有著不同的應用場合和運算形式。</span></span></p> <p class="21" align="left" style="margin: 0cm 0cm 4.75pt; text-indent: 0cm; line-height: 11pt; background: transparent;"> </p> <p><span style="font-size: x-small;"> <p class="21" align="left" style="margin: 0cm 0cm 4.75pt; text-indent: 0cm; line-height: 11pt; background: transparent;"><span id="n1l1njb9b" class="2Tahoma"><span lang="EN-US"> </span></span></p> </span></p> <p class="21" align="left" style="margin: 0cm 0cm 4.75pt; text-indent: 0cm; line-height: 11pt; background: transparent;"><st1:chsdate year="1899" month="12" day="30" islunardate="False" isrocdate="False" w:st="on"></st1:chsdate><span style="font-size: x-small;"><st1:chsdate year="1899" month="12" day="30" islunardate="False" isrocdate="False" w:st="on"><span id="n1l1njb9b" class="2Tahoma"><span lang="EN-US">4</span></span><span id="n1l1njb9b" class="2TimesNewRoman12"><span lang="EN-US">. </span></span><span id="n1l1njb9b" class="2Tahoma"><span lang="EN-US">2</span></span><span id="n1l1njb9b" class="2TimesNewRoman12"><span lang="EN-US">. </span></span><span id="n1l1njb9b" class="2Tahoma">4</span></st1:chsdate><span id="n1l1njb9b" class="2">支持向量機逆系統</span></span></p> <div><span style="font-size: x-small;"><span id="n1l1njb9b" class="2" style="line-height: 20.1333332061768px; text-align: center;"><span lang="EN-US"> 龍門數控加工中心雙電磁懸浮具有較強的耦合性，為了達到對其解耦本文采用逆 系統解耦控制方法。但是由于電磁懸浮系統是非線性系統因此其逆系統是不易通過計 算推導出來的。為了解決這一問題利用支持向量機非線性回歸任意逼近函數的功能來 擬合雙電磁懸浮系統的逆系統</span><sup>[43</sup>_<sup>45]</sup><span lang="EN-US">。</span></span><span id="n1l1njb9b" class="2" style="line-height: 20.1333332061768px; text-align: center;">支持向量機擬合耦合雙電磁懸浮系統</span><span id="n1l1njb9b" class="2TimesNewRoman26" style="line-height: 20.1333332061768px; text-align: center;"><span lang="EN-US">a</span></span><span id="n1l1njb9b" class="2" style="line-height: 20.1333332061768px; text-align: center;">階逆系 統流程圖如圖<span lang="EN-US" style="font-family: SimSun;">4.4</span>所示。</span></span></div> <p><span style="font-size: x-small;"> <!--[if !supportTextWrap]--> <!--[endif]--> </span></p> <p class="21" style="margin-top:12.7pt;text-align:justify;text-justify:inter-ideograph; text-indent:24.0pt;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"><span style="font-size: x-small;"><span id="n1l1njb9b" class="2">將擬合出來的逆系統串聯在被控系統前將非線性耦合系統解耦并且轉化為具有</span><span id="n1l1njb9b" class="2"> </span><span id="n1l1njb9b" class="2">線性特征的偽線性系統</span><span id="n1l1njb9b" class="2">，</span><span id="n1l1njb9b" class="2">從而降低了解耦后獨立系統的控制難度。</span></span></p> <p class="21" style="margin-top:12.7pt;text-align:justify;text-justify:inter-ideograph; text-indent:24.0pt;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"> </p> <p class="21" style="margin-top:12.7pt;text-align:justify;text-justify:inter-ideograph; text-indent:24.0pt;line-height:23.3pt;mso-line-height-rule:exactly;background: transparent"><span style="font-size:9.0pt;font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman";mso-font-kerning:1.0pt;mso-ansi-language:EN-US;mso-fareast-language: ZH-CN;mso-bidi-language:AR-SA">本文采摘自“數控加工中心龍門磁懸浮系統耦合分析及控制研究”，因為編輯困難導致有些函數、表格、圖片、內容無法顯示，有需要者可以在網絡中查找相關文章！本文由伯特利數控整理發表文章均來自網絡僅供學習參考，轉載請注明！</span></p></div> 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