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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 4 Linear Discriminant Function March 19 th ,2011
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Nature Inspired Computation and Applications Laboratory 主要内容 引言 线性判别函数和判定面 广义线性判别函数 两类线性可分的情况 感知器准则函数最小化 松弛算法 不可分的情况 最小平方误差方法
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Nature Inspired Computation and Applications Laboratory 引言 本章内容: -假定判别函数的形式已知,而用训练的方法来 估计判别函数的参数值 -介绍各种算法 判别函数的形式: -是 x 的各个分量的线性函数 -或者是关于以 x 为自变量的某些函数的线性函数
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Nature Inspired Computation and Applications Laboratory 判别函数的形式 x 的各个分量的线性函数 关于以 x 为自变量的某些函数的线性函数 权向量: 偏置: b b f g i i i ) ( ) ( x x b x w b g i i i T x w x ) ( ] ,..., , [ 2 1 d w w w w
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Nature Inspired Computation and Applications Laboratory 线性判别函数优点 线性判别的几何意义 处理简便,计算简单 当信息缺乏时,线性分类器对处于最初的、尝试阶段 的分类器来说是很有吸引力的选择
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Nature Inspired Computation and Applications Laboratory 两类分类( 1 两类分类的判定规则: 系统实现结构: ,判定为第二类( 拒绝判定 判定为第一类( 2 1 0 ) ( , 0 ) ( , 0 ) ( C g g C g x x x
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Nature Inspired Computation and Applications Laboratory 两类分类( 2 方程 定义了一个判定面,它把两个类的点分开来。当 函数是线性时,这个平面被称为超平面。 如果 都在判定面上,则 即: 0 ) ( x g x x b b T T x w x w 0 ) ( x x w T
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Nature Inspired Computation and Applications Laboratory 多类分类( 1 设计多类分类的方法: 其他 类分开 类和 个两类问题,每次把 类问题转化为 类分开 类和非 个两类问题,每次把 类问题转化为 j i i i C C K K K C C K K 2 / ) 1 (
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