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跑通6.SVM简化版本
This commit is contained in:
jiangzhonglian
@@ -8,8 +8,7 @@ Chapter 5 source file for Machine Learing in Action
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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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import matplotlib.pyplot as plt
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def loadDataSet(fileName):
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@@ -95,9 +94,9 @@ def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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# 记录alpha是否已经进行优化，每次循环时设为0，然后再对整个集合顺序遍历
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alphaPairsChanged = 0
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for i in range(m):
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print 'alphas=', alphas
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print 'labelMat=', labelMat
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print 'multiply(alphas, labelMat)=', multiply(alphas, labelMat)
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# print 'alphas=', alphas
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# print 'labelMat=', labelMat
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# print 'multiply(alphas, labelMat)=', multiply(alphas, labelMat)
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# 我们预测的类别 y = w^Tx[i]+b; 其中因为 w = Σ(1~n) a[n]lable[n]x[n]
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fXi = float(multiply(alphas, labelMat).T*(dataMatrix*dataMatrix[i, :].T)) + b
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# 预测结果与真实结果比对，计算误差Ei
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@@ -139,7 +138,7 @@ def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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alphas[j] -= labelMat[j]*(Ei - Ej)/eta
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# 并使用辅助函数，以及L和H对其进行调整
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alphas[j] = clipAlpha(alphas[j], H, L)
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# 检查alpha[j]是否有轻微的改变，如果是的话，就退出for循环。
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# 检查alpha[j]是否只是轻微的改变，如果是的话，就退出for循环。
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if (abs(alphas[j] - alphaJold) < 0.00001):
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print("j not moving enough")
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continue
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@@ -165,11 +164,82 @@ def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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return b, alphas
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def calcWs(alphas, dataArr, classLabels):
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"""
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基于alpha计算w值
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Args:
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alphas 拉格朗日乘子
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dataArr feature数据集
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classLabels 目标变量数据集
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Returns:
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wc 回归系数
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"""
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X = mat(dataArr)
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labelMat = mat(classLabels).transpose()
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m, n = shape(X)
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w = zeros((n, 1))
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for i in range(m):
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w += multiply(alphas[i] * labelMat[i], X[i, :].T)
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return w
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def plotfig_SVM(xMat, yMat, ws, b, alphas):
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"""
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参考地址：
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http://blog.csdn.net/maoersong/article/details/24315633
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http://www.cnblogs.com/JustForCS/p/5283489.html
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http://blog.csdn.net/kkxgx/article/details/6951959
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"""
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xMat = mat(xMat)
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yMat = mat(yMat)
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# b原来是矩阵，先转为数组类型后其数组大小为（1,1），所以后面加[0]，变为(1,)
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b = array(b)[0]
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fig = plt.figure()
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ax = fig.add_subplot(111)
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# 注意flatten的用法
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ax.scatter(xMat[:, 0].flatten().A[0], xMat[:, 1].flatten().A[0])
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# x最大值，最小值根据原数据集dataArr[:, 0]的大小而定
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x = arange(-1.0, 10.0, 0.1)
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# 根据x.w + b = 0 得到，其式子展开为w0.x1 + w1.x2 + b = 0, x2就是y值
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y = (-b-ws[0, 0]*x)/ws[1, 0]
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ax.plot(x, y)
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for i in range(len(yMat)):
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if yMat[i, 0] > 0:
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ax.plot(xMat[i, 0], xMat[i, 1], 'cx')
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else:
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ax.plot(xMat[i, 0], xMat[i, 1], 'kp')
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# 找到支持向量，并在图中标红
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for i in range(100):
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if alphas[i] > 0.0:
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ax.plot(xMat[i, 0], xMat[i, 1], 'ro')
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plt.show()
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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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# b是常量值， alphas是拉格朗日乘子
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b, alphas = smoSimple(dataArr, labelArr, 0.6, 0.001, 40)
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print '/n/n/n'
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print 'b=', b
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print 'alphas[alphas>0]=', alphas[alphas > 0]
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print 'shape(alphas[alphas > 0])=', shape(alphas[alphas > 0])
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for i in range(100):
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if alphas[i] > 0:
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print dataArr[i], labelArr[i]
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# 画图
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ws = calcWs(alphas, dataArr, labelArr)
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plotfig_SVM(dataArr, labelArr, ws, b, alphas)
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def kernelTrans(X, A, kTup): # calc the kernel or transform data to a higher dimensional space
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@@ -383,26 +453,6 @@ def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
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return oS.b, oS.alphas
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def calcWs(alphas, dataArr, classLabels):
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"""
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基于alpha计算w值
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Args:
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alphas:
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dataArr:
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classLabels:
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Returns:
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"""
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X = mat(dataArr)
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labelMat = mat(classLabels).transpose()
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m, n = shape(X)
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w = zeros((n, 1))
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for i in range(m):
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w += multiply(alphas[i] * labelMat[i], X[i, :].T)
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return w
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def testRbf(k1=1.3):
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dataArr, labelArr = loadDataSet('testSetRBF.txt')
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b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) # C=200 important
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241
src/python/6.SVM/svm-simple.py
Normal file
241
src/python/6.SVM/svm-simple.py
Normal file
@@ -0,0 +1,241 @@
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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/片刻
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"""
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from numpy import *
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import matplotlib.pyplot as plt
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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 文件名
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Returns:
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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 = []
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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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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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j 返回一个不为i的随机数，在0~m之间的整数值
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"""
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j = 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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"""clipAlpha(调整aj的值，使aj处于 L<=aj<=H)
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Args:
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aj 目标值
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H 最大值
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L 最小值
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Returns:
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aj 目标值
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"""
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if aj > H:
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aj = H
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if L > aj:
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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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"""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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C 松弛变量(常量值)，允许有些数据点可以处于分隔面的错误一侧。
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控制最大化间隔和保证大部分的函数间隔小于1.0这两个目标的权重。
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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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b 模型的常量值
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alphas 拉格朗日乘子
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"""
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dataMatrix = mat(dataMatIn)
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# 矩阵转制 和 .T 一样的功能
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labelMat = mat(classLabels).transpose()
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m, n = shape(dataMatrix)
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# 初始化 b和alphas(alpha有点类似权重值。)
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b = 0
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alphas = mat(zeros((m, 1)))
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# 没有任何alpha改变的情况下遍历数据的次数
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iter = 0
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while (iter < maxIter):
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# w = calcWs(alphas, dataMatIn, classLabels)
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# print("w:", w)
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# 记录alpha是否已经进行优化，每次循环时设为0，然后再对整个集合顺序遍历
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alphaPairsChanged = 0
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for i in range(m):
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# print 'alphas=', alphas
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# print 'labelMat=', labelMat
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# print 'multiply(alphas, labelMat)=', multiply(alphas, labelMat)
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# 我们预测的类别 y = w^Tx[i]+b; 其中因为 w = Σ(1~n) a[n]lable[n]x[n]
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fXi = float(multiply(alphas, labelMat).T*(dataMatrix*dataMatrix[i, :].T)) + b
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# 预测结果与真实结果比对，计算误差Ei
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Ei = fXi - float(labelMat[i])
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# 约束条件 (KKT条件是解决最优化问题的时用到的一种方法。我们这里提到的最优化问题通常是指对于给定的某一函数，求其在指定作用域上的全局最小值。)
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# 0<=alphas[i]<=C，但由于0和C是边界值，我们无法进行优化，因为需要增加一个alphas和降低一个alphas。
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# 表示发生错误的概率：labelMat[i]*Ei 如果超出了 toler， 才需要优化。至于正负号，我们考虑绝对值就对了。
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if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):
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# 如果满足优化的条件，我们就随机选取非i的一个点，进行优化比较
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j = selectJrand(i, m)
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# 预测j的结果
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fXj = float(multiply(alphas, labelMat).T*(dataMatrix*dataMatrix[j, :].T)) + b
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Ej = fXj - float(labelMat[j])
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alphaIold = alphas[i].copy()
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alphaJold = alphas[j].copy()
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# L和H用于将alphas[j]调整到0-C之间。如果L==H，就不做任何改变，直接执行continue语句
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if (labelMat[i] != labelMat[j]):
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L = max(0, alphas[j] - alphas[i])
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H = min(C, C + alphas[j] - alphas[i])
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else:
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L = max(0, alphas[j] + alphas[i] - C)
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H = min(C, alphas[j] + alphas[i])
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if L == H:
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print("L==H")
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continue
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# eta是alphas[j]的最优修改量，如果eta==0，需要退出for循环的当前迭代过程
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# 如果ETA为0，那么计算新的alphas[j]就比较麻烦了, 为什么呢？ 因为2个值一样。
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# 2ab <= a^2 + b^2
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eta = 2.0 * dataMatrix[i, :]*dataMatrix[j, :].T - dataMatrix[i, :]*dataMatrix[i,:].T - dataMatrix[j, :]*dataMatrix[j, :].T
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if eta >= 0:
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print("eta>=0")
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continue
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# 计算出一个新的alphas[j]值
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alphas[j] -= labelMat[j]*(Ei - Ej)/eta
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# 并使用辅助函数，以及L和H对其进行调整
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alphas[j] = clipAlpha(alphas[j], H, L)
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# 检查alpha[j]是否只是轻微的改变，如果是的话，就退出for循环。
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if (abs(alphas[j] - alphaJold) < 0.00001):
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print("j not moving enough")
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continue
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# 然后alphas[i]和alphas[j]同样进行改变，虽然改变的大小一样，但是改变的方向正好相反
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alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])
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# 在对alpha[i], alpha[j] 进行优化之后，给这两个alpha值设置一个常数b。
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b1 = b - Ei- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[i,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[i,:]*dataMatrix[j,:].T
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b2 = b - Ej- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[j,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[j,:]*dataMatrix[j,:].T
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if (0 < alphas[i]) and (C > alphas[i]):
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b = b1
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elif (0 < alphas[j]) and (C > alphas[j]):
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b = b2
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else:
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b = (b1 + b2)/2.0
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alphaPairsChanged += 1
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print("iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged))
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# 在for循环外，检查alpha值是否做了更新，如果在更新则将iter设为0后继续运行程序
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if (alphaPairsChanged == 0):
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iter += 1
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else:
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iter = 0
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print("iteration number: %d" % iter)
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return b, alphas
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def calcWs(alphas, dataArr, classLabels):
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"""
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基于alpha计算w值
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Args:
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alphas 拉格朗日乘子
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dataArr feature数据集
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classLabels 目标变量数据集
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Returns:
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wc 回归系数
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"""
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X = mat(dataArr)
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labelMat = mat(classLabels).transpose()
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m, n = shape(X)
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w = zeros((n, 1))
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for i in range(m):
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w += multiply(alphas[i] * labelMat[i], X[i, :].T)
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return w
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def plotfig_SVM(xMat, yMat, ws, b, alphas):
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"""
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参考地址：
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http://blog.csdn.net/maoersong/article/details/24315633
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http://www.cnblogs.com/JustForCS/p/5283489.html
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http://blog.csdn.net/kkxgx/article/details/6951959
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"""
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xMat = mat(xMat)
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yMat = mat(yMat)
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# b原来是矩阵，先转为数组类型后其数组大小为（1,1），所以后面加[0]，变为(1,)
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b = array(b)[0]
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fig = plt.figure()
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ax = fig.add_subplot(111)
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# 注意flatten的用法
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ax.scatter(xMat[:, 0].flatten().A[0], xMat[:, 1].flatten().A[0])
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# x最大值，最小值根据原数据集dataArr[:, 0]的大小而定
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x = arange(-1.0, 10.0, 0.1)
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# 根据x.w + b = 0 得到，其式子展开为w0.x1 + w1.x2 + b = 0, x2就是y值
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y = (-b-ws[0, 0]*x)/ws[1, 0]
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ax.plot(x, y)
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for i in range(len(yMat)):
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if yMat[i, 0] > 0:
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ax.plot(xMat[i, 0], xMat[i, 1], 'cx')
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else:
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ax.plot(xMat[i, 0], xMat[i, 1], 'kp')
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# 找到支持向量，并在图中标红
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for i in range(100):
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if alphas[i] > 0.0:
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ax.plot(xMat[i, 0], xMat[i, 1], 'ro')
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plt.show()
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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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# b是常量值， alphas是拉格朗日乘子
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b, alphas = smoSimple(dataArr, labelArr, 0.6, 0.001, 40)
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print '/n/n/n'
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print 'b=', b
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print 'alphas[alphas>0]=', alphas[alphas > 0]
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print 'shape(alphas[alphas > 0])=', shape(alphas[alphas > 0])
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for i in range(100):
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if alphas[i] > 0:
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print dataArr[i], labelArr[i]
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# 画图
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ws = calcWs(alphas, dataArr, labelArr)
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plotfig_SVM(dataArr, labelArr, ws, b, alphas)
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