SVM、核方法、SVR基本原理介绍
支持向量
![](https://img.haomeiwen.com/i11128682/20780a3a5e63477b.png)
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![](https://img.haomeiwen.com/i11128682/fd0e31139ca12835.png)
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![](https://img.haomeiwen.com/i11128682/8e8db71a0679bdf9.png)
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![](https://img.haomeiwen.com/i11128682/ca8b5c6b08115714.png)
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线性超平面求解方法
1.引入SVM基本型
![](https://img.haomeiwen.com/i11128682/f865756a3220db66.png)
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![](https://img.haomeiwen.com/i11128682/f0e7c4d8a1f9ca75.png)
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2.利用对偶问题模型建立
![](https://img.haomeiwen.com/i11128682/cdd79cff4c0c7589.png)
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![](https://img.haomeiwen.com/i11128682/6507a63fb912e793.png)
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![](https://img.haomeiwen.com/i11128682/727f6e876c9d94d0.png)
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3.KKT条件
![](https://img.haomeiwen.com/i11128682/f7c19d8ccba78dad.png)
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4.SMO算法求解对偶问题
![](https://img.haomeiwen.com/i11128682/0cbe2169220ad910.png)
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![](https://img.haomeiwen.com/i11128682/7e1386da9065c185.png)
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![](https://img.haomeiwen.com/i11128682/7abb108f8c95d15f.png)
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![](https://img.haomeiwen.com/i11128682/b3d512c127ecd079.png)
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核方法(求解非线性可分问题)
1.核函数
![](https://img.haomeiwen.com/i11128682/0f7cdefb69ff96bd.png)
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![](https://img.haomeiwen.com/i11128682/e5f5329e411069c8.png)
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![](https://img.haomeiwen.com/i11128682/e734235a711e524e.png)
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![](https://img.haomeiwen.com/i11128682/f10c033ad37f02fd.png)
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![](https://img.haomeiwen.com/i11128682/d7389d7e4d78d497.png)
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![](https://img.haomeiwen.com/i11128682/4f7592553bcb28ac.png)
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2.核函数定理
3.常用核函数
![](https://img.haomeiwen.com/i11128682/1eee166eff348267.png)
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软间隔
1.软间隔
![](https://img.haomeiwen.com/i11128682/270a27db7b6a356c.png)
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![](https://img.haomeiwen.com/i11128682/e510d5e593d5b100.png)
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2.损失函数的引入
![](https://img.haomeiwen.com/i11128682/0548fbd3d31de7da.png)
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![](https://img.haomeiwen.com/i11128682/c4cb7e10cc670009.png)
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![](https://img.haomeiwen.com/i11128682/129d31abc8c94162.png)
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3.松弛变量的引入
![](https://img.haomeiwen.com/i11128682/22758f0879e561a0.png)
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![](https://img.haomeiwen.com/i11128682/113f80306df3cbd2.png)
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4.软间隔SVM的对偶问题模型的建立与求解
![](https://img.haomeiwen.com/i11128682/7116ae24f36b5074.png)
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![](https://img.haomeiwen.com/i11128682/64a0a233fb474819.png)
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正则化方法
![](https://img.haomeiwen.com/i11128682/749a6e38d6163b15.png)
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![](https://img.haomeiwen.com/i11128682/ad7a5ddddfad37ba.png)
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SVR(支持向量回归)
1.间隔带的引入
![](https://img.haomeiwen.com/i11128682/e18df23e2faa1ec9.png)
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2.SVR问题模型的建立
![](https://img.haomeiwen.com/i11128682/48f143cf7bf54a4a.png)
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![](https://img.haomeiwen.com/i11128682/cd8cd67176ecd723.png)
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![](https://img.haomeiwen.com/i11128682/06a5137b8152877d.png)
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3.SVR问题模型的求解
![](https://img.haomeiwen.com/i11128682/ebf067a8c66524d1.png)
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![](https://img.haomeiwen.com/i11128682/fcb3dd74d7da7db8.png)
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![](https://img.haomeiwen.com/i11128682/741b35a8fd8d95da.png)
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![](https://img.haomeiwen.com/i11128682/862b6cf97d28789c.png)
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4.SVR核方法
![](https://img.haomeiwen.com/i11128682/8bd81ce03cc820d7.png)
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核方法
![](https://img.haomeiwen.com/i11128682/78a0a2e83474dcdf.png)
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1.表示定理
![](https://img.haomeiwen.com/i11128682/e302f099abc73dea.png)
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![](https://img.haomeiwen.com/i11128682/9c7bb26667827673.png)
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KLDA(核线性判别分析)
![](https://img.haomeiwen.com/i11128682/7c3336734642754d.png)
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![](https://img.haomeiwen.com/i11128682/b265752e2d97346b.png)
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![](https://img.haomeiwen.com/i11128682/ba5bfb7f62ab3ba6.png)
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![](https://img.haomeiwen.com/i11128682/5ee9a3b919122913.png)
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![](https://img.haomeiwen.com/i11128682/c1f012223201260f.png)
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(上文截图来源于周志华的《机器学习》)
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