From 9592593d16fc359bfbfd9a39a19c3940bde09d77 Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Sun, 18 Apr 2021 20:43:52 +0800 Subject: [PATCH] Add. Information gain ratio --- .../5.决策树——每次选一边.md | 118 ++++++++++++++++++ .../assets/1618582986891.png | Bin 0 -> 20175 bytes .../assets/1618583056578.png | Bin 0 -> 19306 bytes .../assets/1618583066653.png | Bin 0 -> 28785 bytes .../assets/1618583156554.png | Bin 0 -> 22672 bytes .../assets/1618747519765.png | Bin 0 -> 41203 bytes .../assets/1618747694405.png | Bin 0 -> 162846 bytes .../assets/1618747990121.png | Bin 0 -> 107189 bytes .../assets/1618748039172.png | Bin 0 -> 74808 bytes .../assets/1618748063199.png | Bin 0 -> 25515 bytes .../assets/1618748316870.png | Bin 0 -> 4581 bytes .../assets/1618749594369.png | Bin 0 -> 5795 bytes .../assets/1618749717493.png | Bin 0 -> 9750 bytes 13 files changed, 118 insertions(+) create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618582986891.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618583056578.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618583066653.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618583156554.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618747519765.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618747694405.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618747990121.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618748039172.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618748063199.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618748316870.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618749594369.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618749717493.png diff --git a/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md b/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md index a7485bf..b1d513d 100644 --- a/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md +++ b/机器学习算法理论及应用/李航——统计学习方法/5.决策树——每次选一边.md @@ -95,3 +95,121 @@ Example 如果有1个坏苹果和9个好苹果时,我们可以认为大部分都是坏苹果。内部并不混乱,确定性很大,熵很小。 + + +### 信息增益 + +Information gain + +表示得知特征X的信息而使得类Y的信息的不确定性减少的程度。 + +特征A对训练集D的信息增益g(D,A),定义为集合D的经验熵H(D)与特征A给定条件下D的经验条件熵H(D|A)之差,即:g(D, A) = H(D) - H(D|A) + +当前的信息熵等于划分完(如划分成两个)的信息熵之和。 + + + +**信息增益算法** + +输入:训练数据集D和特征A + +输出:特征A对训练数据集D的信息 + +1. 计算数据集D的经验熵H(D) + + ![1618582986891](assets/1618582986891.png) + +2. 计算特征A对数据集D的经验条件熵H(D|A) + + ![1618583056578](assets/1618583056578.png) + + ![1618583066653](assets/1618583066653.png) + +3. 计算信息增益 + + ![1618583156554](assets/1618583156554.png) + + + +### 举个例子 + +Example + +是否信贷 + +| ID | 年龄 | 有工作 | 有自己房子 | 信贷情况 | 类别 | +| ---- | ---- | ------ | ---------- | -------- | ---- | +| 1 | 青年 | 否 | 否 | 一般 | 否 | +| 2 | 青年 | 否 | 否 | 好 | 否 | +| 3 | 青年 | 是 | 否 | 好 | 是 | +| 4 | 青年 | 是 | 是 | 一般 | 是 | +| 5 | 青年 | 否 | 否 | 一般 | 否 | +| 6 | 中年 | 否 | 否 | 一般 | 否 | +| 7 | 中年 | 否 | 否 | 好 | 否 | +| 8 | 中年 | 是 | 是 | 好 | 是 | +| 9 | 中年 | 否 | 是 | 非常好 | 是 | +| 10 | 中年 | 否 | 是 | 非常好 | 是 | +| 11 | 老年 | 否 | 是 | 非常好 | 是 | +| 12 | 老年 | 否 | 是 | 好 | 是 | +| 13 | 老年 | 是 | 否 | 好 | 是 | +| 14 | 老年 | 是 | 否 | 非常好 | 是 | +| 15 | 老年 | 否 | 否 | 一般 | 否 | + + + +对上表所给的训练数据集D,根据信息增益准则选择最优特征。首先计算经验熵H(D) + +![1618747519765](assets/1618747519765.png) + +> 计算类别:一共15个类别,9个是,6个否 + +然后计算各特征对数据集D的信息增益,分别以A1,A2,A3,A4表示年龄、有工作、有自己房子和信贷情况4个特征,则 + +1. 首先计算年龄![1618747694405](assets/1618747694405.png) + + > H(D)=0.971上面计算了,H(D1)青年,H(D2)中年,H(D3)老年 + +2. 计算有工作 + + ![1618747990121](assets/1618747990121.png) + + > H(D)=0.971,H(D1)是有工作,H(D2)是无工作 + +3. 计算有无房子 + + ![1618748039172](assets/1618748039172.png) + +4. 计算信贷情况 + + ![1618748063199](assets/1618748063199.png) + +有无房子是作为信贷的第一个划分,下降的最快 + + + +### 信息增益比 + +Information gain ratio + +**信息增益比:** + +如果以信息增益为划分依据,存在偏向选择取值较多的特征,信息增益是对这一问题进行矫正。 + +**举例**: + +如上面的例子,后面加入了身份证这个特征,身份证又是唯一的,算法对样本画了个15叉树,一层就搞定了全部的分类。 + +这样会造成一个问题,划分会倾向于特征取值数目较多的,即分的更快。 + +但在预测集上就出现很大的问题了,即预测集的身份证肯定也是唯一的。 + +**定义:** + +特征A对训练数据集D的信息增益比![1618748316870](assets/1618748316870.png)定义为其信息增益g(D,A)与训练数据集D关于特征A的经验熵H(D)之比: + +![1618749594369](assets/1618749594369.png) + +**计算**: + +如上面的年龄,有3个类(青年、中年、老年),![1618749717493](assets/1618749717493.png) + diff --git a/机器学习算法理论及应用/李航——统计学习方法/assets/1618582986891.png 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