616009755 - 1 第二章 第二章 Bayes Bayes 决策理论...

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Unformatted text preview: 1 第二章 第二章 Bayes Bayes 决策理论 决策理论 2 Bayes Bayes 决策的假设 决策的假设 ¡ 问题:根据高度信息对玉米与杂草 问题:根据高度信息对玉米与杂草 分类。 分类。 3 Bayes Bayes 决策的假设 决策的假设 ¡ 各类别总体概率分布已知 各类别总体概率分布已知 ; ; ¡ 分类数 分类数 已知; 已知; 4 常用的决策 常用的决策 规则 规则-- 1. 1. 最小错误率 最小错误率 杂草 玉米 = = 2 1 ω ω ∑ = = 2 1 ) ( ) | ( ) ( ) | ( ) | ( j j j i i i P x p P x p x P ω ω ω ω ω ( ) ( ) ( ) A B P A P A B P , = 5 用的决策 用的决策 规则 规则-- 1. 1. 最小错误率 最小错误率 ( ) ( ) i j j j i i i j j i x P x p P x p x x P x P x x P x P x x P x P ω ω ω ω ω ω ω ω ω ω ω ω ω ω ∈ = ∈ = < > = = 如果 则 如果 。 归类于杂草 把 之 , 归类于玉米 把 果 ), ( ) | ( max ) ( ) | ( 2 ), | ( max ) | ( 1 ) | ( ) | ( ), | ( ) | ( 2 , 1 2 , 1 2 2 1 1 2 1 6 ( ) ( ) ⎩ ⎨ ⎧ ∈ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ > < + − = − = ⎩ ⎨ ⎧ ∈ < > = 2 1 2 1 2 1 2 1 1 2 2 1 , ) ( ) ( ln ) | ( ln ) | ( ln )] ( ln[ ) ( 4 , ) ( ) ( ) | ( ) | ( ) ( 3 ω ω ω ω ω ω ω ω ω ω ω ω x P P x p x p x l x h x P P x p x p x l 则 若 则 若 常用的决策 常用的决策 规则 规则-- 1. 1. 最小错误率 最小错误率 7 ⎪ ⎩ ⎪ ⎨ ⎧ > > = = = ∫ ∫ ∞ ∞ − ∞ ∞ − ) | ( ) | ( ), | ( ) | ( ) | ( ), | ( ) | ( ) ( ) | ( ) , ( ) ( 2 1 2 1 2 1 x P x P x P x P x P x P x e P x d x p x e P x d x e P e P ω ω ω ω ω ω 当 当 x d P x p x d P x p x d x p x P x d x p x P e P t t t t ) ( ) | ( ) ( ) | ( ) ( ) | ( ) ( ) | ( ) ( 1 1 2 2 1 2 ω ω ω ω ω ω ∫ ∫ ∫ ∫ ∞ + ∞ − +∞ ∞ − + = + = 常用的决策 常用的决策 规则 规则-- 1. 1. 最小错误率 最小错误率 错误率分析 错误率分析 8 ) ( ) ( ) ( ) ( ) | ( ) ( ) | ( ) ( ) ( ) | ( ) ( ) | ( ) , ( ) , ( ) ( 1 1 2 2 1 1 2 2 1 1 2 2 2 1 1 2 2 1 2 1 e P P e P P x d x p P x d x p P P x P P x P x P x P e P ω ω ω ω ω ω ω ω ω ω ω ω + = + = ℜ ∈ + ℜ ∈ = ℜ ∈ + ℜ ∈ = ∫ ∫ ℜ ℜ 常用的决策 常用的决策 规则 规则-- 1. 1. 最小错误率 最小错误率 错误率分析 错误率分析 9 ) ( ) ( 1 2 e P e P 常用的决策 常用的决策 规则 规则-- 1....
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This note was uploaded on 06/02/2010 for the course ELECTRONIC PC2010S taught by Professor Zhangchangshui during the Spring '10 term at Tsinghua University.

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616009755 - 1 第二章 第二章 Bayes Bayes 决策理论...

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