From 4acc814fda4d624949b2c49218465aa01a7eadc5 Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Mon, 12 Apr 2021 21:33:34 +0800 Subject: [PATCH] Add. Learning policy --- .../2.感知机——入门的垫脚石.md | 122 ++++++++++++++++++ .../assets/1618034843122.png | Bin 0 -> 20600 bytes .../assets/1618035195004.png | Bin 0 -> 227447 bytes .../assets/1618232951329.png | Bin 0 -> 7070 bytes .../assets/1618232969849.png | Bin 0 -> 14875 bytes .../assets/1618232989614.png | Bin 0 -> 23879 bytes .../assets/1618233535293.png | Bin 0 -> 14469 bytes .../assets/1618233578508.png | Bin 0 -> 16858 bytes .../assets/1618233886281.png | Bin 0 -> 23891 bytes .../assets/1618234010513.png | Bin 0 -> 65842 bytes .../assets/1618234028471.png | Bin 0 -> 18102 bytes 11 files changed, 122 insertions(+) create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618034843122.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618035195004.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618232951329.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618232969849.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618232989614.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618233535293.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618233578508.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618233886281.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618234010513.png create mode 100644 机器学习算法理论及应用/李航——统计学习方法/assets/1618234028471.png diff --git a/机器学习算法理论及应用/李航——统计学习方法/2.感知机——入门的垫脚石.md b/机器学习算法理论及应用/李航——统计学习方法/2.感知机——入门的垫脚石.md index 10638f5..3fd03aa 100644 --- a/机器学习算法理论及应用/李航——统计学习方法/2.感知机——入门的垫脚石.md +++ b/机器学习算法理论及应用/李航——统计学习方法/2.感知机——入门的垫脚石.md @@ -38,3 +38,125 @@ > 如图中红色线的和的距离肯定比黑色或者黄色的线大。 + + +### 总结 + +1. 一条直线不分错一个点,这就是好的直线。 +2. 模型要尽可能找到好的直线。 +3. 如果没有好的直线,在差的直线中找到好的直线。 +4. 判断直线多差的方式:分错的点到直线的距离求和。 + + + +### 感知机模型 + +Perceptron + +确定终究目标 + +f(x) + +> 我们希望一个函数,如f(x),进来一个豆,它告诉我们是红豆还是绿豆 + +f(x) = sign(w * x + b) + +> sign如图:![1618034843122](assets/1618034843122.png) + +把w * x + b 比作x,相当于给了一个“豆”进来,就只得到两个结果,也就是红豆(+1)或者绿豆(-1)。那么w * x + b 是什么? + +w * x + b是超平面 + +![1618035195004](assets/1618035195004.png) + +> 即那条黄色的分割线,且当豆在线的上面,就是红豆,在下面是绿豆。 +> +> 超平面是n维欧氏空间中余维度等于一的线性子空间,也就是必须是(n-1)维度。即如果是2维,超平面就是1维,如果是3维,超平面就是2维。 + +w * x + b分别代表什么 + +> w是权重,x是特征的实际值,b是偏值 +> +> 比如知道豆的直径,如x1表示某个豆的直径 = w1 * x1 + b1,大于1则是红豆,小于则是绿豆 +> +> 有时候一个特征不一定能区分开来,可能还需要质量,(x1,x2)计算 = (w1, w2) * (x1, x2) +> +> 亦或者还有豆的光滑度,则有x1, x2, x3 ,这样就变成3维了。 + +**正式的说** + +w * x + b 是一个n维空间中的超平面S,其中w是超平面的法向量,b是超平面的截距,这个超平面将特征空间划分成两部分,位于两部分的点分别被分为正负两类。所以,超平面S称为分离超平面。 + +特征空间也就是整个n维空间,样本的每个属性都叫一个特征,特征空间的意思是在这个空间中可以找到样本所有的属性的组合。 + + + +### 感知觉的学习策略 + +Learning policy + +> 求空间中任意一个点X0到超平面S的距离 + +**函数间隔与几何间隔** + +函数间距:![1618232951329](assets/1618232951329.png) + +> 缺点:已知wx + b = 0,当不等于0时(比如1),那如果等比例放大缩小w和b是不是就更小,等同于1/2 (wx + b) = 1/2(wx) + 1/2(b) = 1/2,超平面是没有动的,但是结果却缩小了,那么模型就觉得它知道等比例缩小就能得到更小的结果。 +> +> 这时候就引入几何间距 + +几何间距:![1618232969849](assets/1618232969849.png) + + + +![1618232989614](assets/1618232989614.png) + +> 加入了二范式,相当于有了一个度量的标准,即等比例缩小w时,外面的w也会等比例变化。 + +通俗来讲,函数间距是将你去吃饭的那段路本来要1000m,它改成1km,1就小于1000了,而几何间距就杜绝这种情况,只能都是m或者km + + + +对于误分类数据而已,![1618233535293](assets/1618233535293.png) + +> yi表示真实是+1还是-1 +> +> w*xi+b表示预测的结果 +> +> 绿豆预测成绿豆:预测结果w*xi+b < 0(绿豆),且真实为绿豆(-1)时,则- * -1(wxi + b) < 0。 +> +> 绿豆预测成红豆:w*xi+b > 0,真实为绿豆-1,则- * -1 (wxi + b) > 0。 +> +> 也就是说只要分错,那么数据一定是大于0 + +误分类点xi到超平面S的距离为:![1618233578508](assets/1618233578508.png) + +因此,所有误分类点到超平面S的总距离为:![1618233886281](assets/1618233886281.png) + +> M:误分类点的集合 + + + +### 感知觉的学习策略——原始形式 + +Learning policy + +1. 任选一个超平面w0,b0 + + > 随机初始化,如w0 = 1,可能有多个维度,如x0,x1,x2,那么w也会有w0,w1,w2的随机初始化 + +2. 采用梯度下降法极小化目标函数 + + ![1618234010513](assets/1618234010513.png) + + > L:loss + > + > 这时候用的还是函数间隔,因为感知机的超平面的目标是不分错任何一个点。所以不存在说要某个点到超平面的距离无限的小。 + > + > 也可以用几何间隔,但是会增加计算量,没有必要,但后面基本都是用几何间隔。 + > + > 侧面反映了感知机只能在线性可分的数据集上使用,也就是线性模型。 + +3. 更新w,b + + ![1618234028471](assets/1618234028471.png) \ No newline at end of file diff --git a/机器学习算法理论及应用/李航——统计学习方法/assets/1618034843122.png b/机器学习算法理论及应用/李航——统计学习方法/assets/1618034843122.png new file mode 100644 index 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