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Nature Inspired Computation and Applications Laboratory School of Computer Science and Technology University of Science and Technology of China Pattern Recognition Lecture 5 Support Vector Machines March 26, 2011
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Nature Inspired Computation and Applications Laboratory 主要内容 1. Hard Margin SVM (硬间隔,假定问题完全可分) 线性 SVM 非线性 SVM 2. Soft Margin SVM (软间隔,更实际的情况) 3. SMO 训练算法 4. 最小二乘 SVM LS-SVM 5. SVM 类型算法的模型选择
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Nature Inspired Computation and Applications Laboratory 线性 SVM n 个训练样本为 对线性可分问题,往往会有多个误差为零的判 定面 线性 SVM 寻求满足以下条件的最优线性判定面 : 1. 可将属于不同类别的训练模式完全分开 2. 在满足条件 1 的所有判定面中,最优判定面具有最大分类间隔 margin 11 {( , ),. ..,( , )} nn yy xx { 1, 1} i y   
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Nature Inspired Computation and Applications Laboratory 线性 SVM 线性支持向量机的基本形式 要将不同类别的所有样本分开,即 考虑等号成立的情况 若为负样本,则其到原点的距离为 若为正样本,则其到原点的距离为 所以,正负样本之间延 w 方向的最短距离是 2 m w () T gb  x w x b y m y i T i ) ( ) ( 裕量 x w w / b m w / b m
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Nature Inspired Computation and Applications Laboratory 线性 SVM 的训练 m 简化为 1 ,则线性支持向量机的基本形式 转化为拉格朗日乘子待定问题(问题 1 2 1 1 minimize ( , ) [ ( ) 1] 2 subject to 0, 1,. .., n T i i i i i L y b in  w α w w x i b y i T i , 1 ) ( subject to 2 min 2 x w w
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Nature Inspired Computation and Applications Laboratory 线性 SVM 的训练 根据 Karush-Kuhn-Tucker 条件,令 L w α 偏导为零,可知 1 1 0, 1,. .., 0 ( ) 1 0 ( ) 1 0 n v i i iv i v n ii i T i i T i i i L w y x v d w L y b yb              wx
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