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更新6.支持向量机.md文件
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jiangzhonglian
@@ -115,3 +115,32 @@ SVM的一般流程
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测试算法：十分简单的计算过程就可以实现。
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使用算法：几乎所有分类问题都可以使用SVM，值得一提的是，SVM本身是一个二类分类器，对多类问题应用SVM需要对代码做一些修改。
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```
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* 到目前为止，我们已经了解了一些理论知识，现在我们通过`Code`来实现我们的算法吧。
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## SMO高效优化算法
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> 序列最小优化(Sequential Minimal Optimization, SMO)
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* 创建作者：John Platt
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* 创建时间：1996年
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* SMO用途：用于训练SVM
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* SMO目标：求出一系列alpha和b,一旦求出alpha，就很容易计算出权重向量w并得到分隔超平面。
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* SMO思想：是讲大优化问题分解为多个小优化问题来求解的。
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* SMO原理：每次循环选择两个alpha进行优化处理，一旦找出一对合适的alpha，那么就增大一个同时减少一个。
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* 这里指的合适必须要符合一定的条件
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* 1.这两个alpha必须要在间隔边界之外
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* 2.这两个alpha还没有进行过区间化处理或者不在边界上。
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* 之所以要同时改变2个alpha；原因，我们有一个约束条件：`Σ a[i]*label(i)=0`；如果只是修改一个alpha，很可能导致约束条件失效。
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```
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SMO伪代码大致如下：
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创建一个alpha向量并将其初始化为0向量
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当迭代次数小于最大迭代次数时(外循环)
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对数据集中的每个数据向量(内循环)：
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如果该数据向量可以被优化
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随机选择另外一个数据向量
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同时优化这两个向量
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如果两个向量都不能被优化，退出内循环
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如果所有向量都没被优化，增加迭代数目，继续下一次循环
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```
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100
input/6.SVM/testSet.txt
Executable file
100
input/6.SVM/testSet.txt
Executable file
@@ -0,0 +1,100 @@
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3.542485 1.977398 -1
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3.018896 2.556416 -1
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7.551510 -1.580030 1
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2.114999 -0.004466 -1
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8.127113 1.274372 1
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7.108772 -0.986906 1
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8.610639 2.046708 1
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2.326297 0.265213 -1
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3.634009 1.730537 -1
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0.341367 -0.894998 -1
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3.125951 0.293251 -1
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2.123252 -0.783563 -1
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0.887835 -2.797792 -1
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7.139979 -2.329896 1
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1.696414 -1.212496 -1
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8.117032 0.623493 1
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8.497162 -0.266649 1
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4.658191 3.507396 -1
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8.197181 1.545132 1
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1.208047 0.213100 -1
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1.928486 -0.321870 -1
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2.175808 -0.014527 -1
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7.886608 0.461755 1
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3.223038 -0.552392 -1
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3.628502 2.190585 -1
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7.407860 -0.121961 1
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7.286357 0.251077 1
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2.301095 -0.533988 -1
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-0.232542 -0.547690 -1
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3.457096 -0.082216 -1
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3.023938 -0.057392 -1
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8.015003 0.885325 1
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8.991748 0.923154 1
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7.916831 -1.781735 1
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7.616862 -0.217958 1
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2.450939 0.744967 -1
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7.270337 -2.507834 1
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1.749721 -0.961902 -1
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1.803111 -0.176349 -1
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8.804461 3.044301 1
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1.231257 -0.568573 -1
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2.074915 1.410550 -1
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-0.743036 -1.736103 -1
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3.536555 3.964960 -1
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8.410143 0.025606 1
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7.382988 -0.478764 1
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6.960661 -0.245353 1
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8.234460 0.701868 1
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8.168618 -0.903835 1
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1.534187 -0.622492 -1
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9.229518 2.066088 1
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7.886242 0.191813 1
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2.893743 -1.643468 -1
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1.870457 -1.040420 -1
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5.286862 -2.358286 1
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6.080573 0.418886 1
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2.544314 1.714165 -1
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6.016004 -3.753712 1
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0.926310 -0.564359 -1
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0.870296 -0.109952 -1
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2.369345 1.375695 -1
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1.363782 -0.254082 -1
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7.279460 -0.189572 1
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1.896005 0.515080 -1
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8.102154 -0.603875 1
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2.529893 0.662657 -1
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1.963874 -0.365233 -1
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8.132048 0.785914 1
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8.245938 0.372366 1
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6.543888 0.433164 1
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-0.236713 -5.766721 -1
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8.112593 0.295839 1
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9.803425 1.495167 1
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1.497407 -0.552916 -1
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1.336267 -1.632889 -1
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9.205805 -0.586480 1
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1.966279 -1.840439 -1
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8.398012 1.584918 1
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7.239953 -1.764292 1
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7.556201 0.241185 1
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9.015509 0.345019 1
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8.266085 -0.230977 1
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8.545620 2.788799 1
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9.295969 1.346332 1
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2.404234 0.570278 -1
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2.037772 0.021919 -1
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1.727631 -0.453143 -1
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1.979395 -0.050773 -1
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8.092288 -1.372433 1
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1.667645 0.239204 -1
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9.854303 1.365116 1
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7.921057 -1.327587 1
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8.500757 1.492372 1
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1.339746 -0.291183 -1
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3.107511 0.758367 -1
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2.609525 0.902979 -1
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3.263585 1.367898 -1
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2.912122 -0.202359 -1
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1.731786 0.589096 -1
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2.387003 1.573131 -1
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@@ -1,49 +1,50 @@
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#!/usr/bin/python
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# coding:utf8
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"""
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Created on Nov 4, 2010
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Update on 2017-03-21
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Chapter 5 source file for Machine Learing in Action
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@author: Peter/geekidentity
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@author: Peter/geekidentity/片刻
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"""
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from numpy import *
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import pylab
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from time import sleep
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def main():
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dataArr, labelArr = loadDataSet('testSet.txt')
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smoSimple(dataArr, labelArr, 0.6, 0.001, 40)
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def loadDataSet(fileName):
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"""
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对文件进行逐行解析，从而得到第行的类标签和整个数据矩阵
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Args:
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fileName: testSet.txt
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fileName 文件名
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Returns:
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数据矩阵, 类标签
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dataMat 数据矩阵
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labelMat 类标签
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"""
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dataMat = []; labelMat = []
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dataMat = []
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labelMat = []
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fr = open(fileName)
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for line in fr.readlines():
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lineArr = line.strip().split('\t')
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dataMat.append([float(lineArr[0]), float(lineArr[1])])
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labelMat.append(float(lineArr[2]))
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return dataMat,labelMat
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return dataMat, labelMat
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def selectJrand(i,m):
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def selectJrand(i, m):
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"""
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随机选择一个整数
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Args:
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i: 第一个alpha的下标
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m: 所有alpha的数目
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Returns:
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"""
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j=i #we want to select any J not equal to i
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while (j==i):
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j = int(random.uniform(0,m))
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return j
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def clipAlpha(aj,H,L):
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"""
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用于调整大于H或小于L的alpha值
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@@ -51,7 +52,6 @@ def clipAlpha(aj,H,L):
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aj:
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H:
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L:
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Returns:
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"""
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@@ -61,17 +61,10 @@ def clipAlpha(aj,H,L):
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aj = L
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return aj
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def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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"""
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SVM SMO算法的简单实现:
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创建一个alpha向量并将其初始化为0向量
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当迭代次数据小于最大迭代次数时(外循环)
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对数据集中的每个数据向量(内循环):
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如果该数据向量可以被优化:
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随机选择另外一个数据向量
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同时优化这两个向量
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如果两个向量都不能被优化，退出内循环
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如果所有向量都没有被优化，增加迭代数目，继续下一次循环
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"""smoSimple
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Args:
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dataMatIn: 数据集
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classLabels: 类别标签
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@@ -80,7 +73,6 @@ def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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可以通过调节该参数达到不同的结果。
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toler: 容错率
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maxIter: 退出前最大的循环次数
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Returns:
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"""
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@@ -132,6 +124,13 @@ def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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return b,alphas
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if __name__ == "__main__":
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# 获取特征和目标变量
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dataArr, labelArr = loadDataSet('input/6.SVM/testSet.txt')
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# print labelArr
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# smoSimple(dataArr, labelArr, 0.6, 0.001, 40)
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def kernelTrans(X, A, kTup): # calc the kernel or transform data to a higher dimensional space
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"""
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核转换函数
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@@ -566,5 +565,3 @@ def smoPK(dataMatIn, classLabels, C, toler, maxIter): # full Platt SMO
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print("iteration number: %d" % iter)
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return oS.b, oS.alphas
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if __name__ == "__main__":
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main()
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