From ca5860c9f7249b9daa984253c48f65d43b8b5cfe Mon Sep 17 00:00:00 2001 From: jiangzhonglian Date: Mon, 10 Apr 2017 16:20:22 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=E5=88=B06.SVM=20=E5=AF=BB?= =?UTF-8?q?=E6=89=BE=E6=9C=80=E5=A4=A7=E9=97=B4=E9=9A=94?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/6.支持向量机.md | 68 +++++++++++++++++-- images/6.SVM/SVM_1.jpg | Bin 0 -> 157674 bytes images/6.SVM/SVM_2_separating-hyperplane.jpg | Bin 0 -> 149451 bytes images/6.SVM/SVM_3_linearly-separable.jpg | Bin 0 -> 67171 bytes 4 files changed, 62 insertions(+), 6 deletions(-) create mode 100644 images/6.SVM/SVM_1.jpg create mode 100644 images/6.SVM/SVM_2_separating-hyperplane.jpg create mode 100644 images/6.SVM/SVM_3_linearly-separable.jpg diff --git a/docs/6.支持向量机.md b/docs/6.支持向量机.md index 951c3e46..e4c9107c 100644 --- a/docs/6.支持向量机.md +++ b/docs/6.支持向量机.md @@ -1,12 +1,68 @@ - # 6) 支持向量机 -* 基本概念 +![支持向量机_首页](/images/6.SVM/SVM_1.jpg) + +## 支持向量机的概念 + +> 支持向量机(Support Vector Machines, SVM) + +* 支持向量(Support Vector)就是离分隔超平面最近的那些点。 +* 机(Machine)就是表示一种算法,而不是表示机器。 +* SVM有很多种实现,最流行的一种实现是: `序列最小优化(Sequential Minimal Optimization, SMO)算法`。 +* 下面还会介绍一种称为`核函数(kernel)`的方式将SVM扩展到更多数据集上。 +* 实战项目:回顾第1章中手写识别的案例,并考察其能否通过SVM来提高识别的效果。 +* 注意:`SVM几何含义比较直观,但其算法实现较复杂,牵扯大量数学公式的推导。` + +``` +优点:泛化错误率低,计算开销不大,结果易理解。 +缺点:对参数调节和核函数的选择敏感,原始分类器不加修改仅适合于处理二分类问题。 +使用数据类型:数值型和标称型数据。 +``` + +## 基于最大间隔分隔数据 + +* 数据可以通过画一条直线就可以将它们完全分开,这组数据叫`线性可分(linearly separable)`数据。 +* 而这条分隔直线称为`分隔超平面(separating hyperplane)`。 +* 如果数据集上升到1024维呢?那么需要1023维来分隔数据集,也就说需要N-1维的对象来分隔,这个对象叫做`超平面(hyperlane)`,也就是分类的决策边界。 +* ![分隔超平面](/images/6.SVM/SVM_2_separating-hyperplane.jpg) + +## 寻找最大间隔 + +> 为什么寻找最大间隔 + +``` +摘录地址:http://slideplayer.com/slide/8610144 (第12条信息) +Support Vector Machines: Slide 12 Copyright © 2001, 2003, Andrew W. Moore Why Maximum Margin? +denotes +1 denotes -1 f(x,w,b) = sign(w. x - b) The maximum margin linear classifier is the linear classifier with the, um, maximum margin. +This is the simplest kind of SVM (Called an LSVM) Support Vectors are those datapoints that the margin pushes up against + +1.Intuitively this feels safest. +2.If we’ve made a small error in the location of the boundary (it’s been jolted in its perpendicular direction) this gives us least chance of causing a misclassification. +3.CV is easy since the model is immune to removal of any non-support-vector datapoints. +4.There’s some theory that this is a good thing. +5.Empirically it works very very well. + +* * * + +1. 直觉上是安全的 +2. 如果我们在边界的位置发生了一个小错误(它在垂直方向上被颠倒),这给我们最小的错误分类机会。 +3. CV很容易,因为该模型对任何非支持向量数据点的去除是免疫的。 +4. 有一些理论,这是一件好事。 +5. 通常它的工作非常好。 +``` + +* 选择D会比B、C分隔的效果要好很多,原因是上述的5个结论。 +![线性可分](/images/6.SVM/SVM_3_linearly-separable.jpg) + +> 怎么寻找最大间隔 + + + + + + + - * 假设有两组数据,我们可以用一条线将这两个数据集分隔开,这条直线称为分隔超平面 - (当维数很高时称为分隔超平面)。 - * 我们希望找到离分隔超平面最近的点,确保它们离分隔面的距离尽可能远。 - * 支持向量就是离分隔超平面最近的那些点。 * 支持向量机的目标是找出能够最大化训练集数据间隔(margin)的最优分类超平面。 diff --git a/images/6.SVM/SVM_1.jpg b/images/6.SVM/SVM_1.jpg new file mode 100644 index 0000000000000000000000000000000000000000..37c313fa4e81b18479b55b7867cb0a10f30eb573 GIT binary patch literal 157674 zcmb@t2Q*w!`!{+R3?jOO=uC7HC3+`%@15vG8$|DdVDuVMqZ7SHkKP5*`-q8%-us>8 zz5nlB>#lFDTh@JM&N;ucXU{(S+56c~JLf#iKdb}z3NrFC0165K$RR(#!v-M!+RM%w z0F;#h761S+0h9no^}W25l&PAAs*JqS>wld> zb${dH;_&y+j!y2b8nTi!din-5;AP+ufCCT$g22-^7H%#QYHCXV+Wg<{&S(Gi9hheS z+m^Nb)q-%CXHGqa!bd7WceelSU;bP8$kNKq0?9lkvdF^H&B76h9gvvK!o}4ciPMpo z-P7IWFCIiMfgD*Y8YyQ-mv`<~u52{&P8J+&G+Zw^ zU;eH4ch3GE0pLXA-&~+PnfPy+a~=Q)&;tMn_TMt|Q~+pd0|3(D|CT|r0RT@302;?# 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