271 lines
7.4 KiB
Python
271 lines
7.4 KiB
Python
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# -*- coding:UTF-8 -*-
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import matplotlib.pyplot as plt
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import numpy as np
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import random
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"""
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函数说明:读取数据
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Parameters:
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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 - 数据标签
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Author:
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Jack Cui
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Blog:
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http://blog.csdn.net/c406495762
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Zhihu:
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https://www.zhihu.com/people/Jack--Cui/
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Modify:
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2017-09-21
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"""
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def loadDataSet(fileName):
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dataMat = []; labelMat = []
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fr = open(fileName)
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for line in fr.readlines(): #逐行读取，滤除空格等
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lineArr = line.strip().split('\t')
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dataMat.append([float(lineArr[0]), float(lineArr[1])]) #添加数据
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labelMat.append(float(lineArr[2])) #添加标签
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return dataMat,labelMat
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"""
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函数说明:随机选择alpha
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Parameters:
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i - alpha_i的索引值
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m - alpha参数个数
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Returns:
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j - alpha_j的索引值
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Author:
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Jack Cui
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Blog:
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http://blog.csdn.net/c406495762
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Zhihu:
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https://www.zhihu.com/people/Jack--Cui/
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Modify:
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2017-09-21
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"""
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def selectJrand(i, m):
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j = i #选择一个不等于i的j
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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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"""
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函数说明:修剪alpha
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Parameters:
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aj - alpha_j值
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H - alpha上限
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L - alpha下限
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Returns:
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aj - alpah值
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Author:
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Jack Cui
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Blog:
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http://blog.csdn.net/c406495762
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Zhihu:
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https://www.zhihu.com/people/Jack--Cui/
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Modify:
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2017-09-21
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"""
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def clipAlpha(aj,H,L):
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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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"""
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函数说明:数据可视化
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Parameters:
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dataMat - 数据矩阵
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labelMat - 数据标签
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Returns:
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无
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Author:
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Jack Cui
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Blog:
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http://blog.csdn.net/c406495762
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Zhihu:
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https://www.zhihu.com/people/Jack--Cui/
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Modify:
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2017-09-21
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"""
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def showDataSet(dataMat, labelMat):
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data_plus = [] #正样本
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data_minus = [] #负样本
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for i in range(len(dataMat)):
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if labelMat[i] > 0:
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data_plus.append(dataMat[i])
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else:
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data_minus.append(dataMat[i])
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data_plus_np = np.array(data_plus) #转换为numpy矩阵
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data_minus_np = np.array(data_minus) #转换为numpy矩阵
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plt.scatter(np.transpose(data_plus_np)[0], np.transpose(data_plus_np)[1]) #正样本散点图
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plt.scatter(np.transpose(data_minus_np)[0], np.transpose(data_minus_np)[1]) #负样本散点图
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plt.show()
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"""
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函数说明:简化版SMO算法
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Parameters:
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dataMatIn - 数据矩阵
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classLabels - 数据标签
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C - 松弛变量
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toler - 容错率
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maxIter - 最大迭代次数
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Returns:
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无
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Author:
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Jack Cui
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Blog:
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http://blog.csdn.net/c406495762
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Zhihu:
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https://www.zhihu.com/people/Jack--Cui/
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Modify:
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2017-09-23
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"""
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def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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#转换为numpy的mat存储
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dataMatrix = np.mat(dataMatIn); labelMat = np.mat(classLabels).transpose()
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#初始化b参数，统计dataMatrix的维度
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b = 0; m,n = np.shape(dataMatrix)
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#初始化alpha参数，设为0
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alphas = np.mat(np.zeros((m,1)))
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#初始化迭代次数
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iter_num = 0
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#最多迭代matIter次
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while (iter_num < maxIter):
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alphaPairsChanged = 0
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for i in range(m):
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#步骤1：计算误差Ei
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fXi = float(np.multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
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Ei = fXi - float(labelMat[i])
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#优化alpha，设定一定的容错率。
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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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#随机选择另一个与alpha_i成对优化的alpha_j
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j = selectJrand(i,m)
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#步骤1：计算误差Ej
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fXj = float(np.multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + b
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Ej = fXj - float(labelMat[j])
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#保存更新前的aplpha值，使用深拷贝
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alphaIold = alphas[i].copy(); alphaJold = alphas[j].copy();
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#步骤2：计算上下界L和H
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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: print("L==H"); continue
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#步骤3：计算eta
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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: print("eta>=0"); continue
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#步骤4：更新alpha_j
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alphas[j] -= labelMat[j]*(Ei - Ej)/eta
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#步骤5：修剪alpha_j
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alphas[j] = clipAlpha(alphas[j],H,L)
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if (abs(alphas[j] - alphaJold) < 0.00001): print("alpha_j变化太小"); continue
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#步骤6：更新alpha_i
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alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])
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#步骤7：更新b_1和b_2
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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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#步骤8：根据b_1和b_2更新b
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if (0 < alphas[i]) and (C > alphas[i]): b = b1
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elif (0 < alphas[j]) and (C > alphas[j]): b = b2
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else: b = (b1 + b2)/2.0
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#统计优化次数
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alphaPairsChanged += 1
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#打印统计信息
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print("第%d次迭代 样本:%d, alpha优化次数:%d" % (iter_num,i,alphaPairsChanged))
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#更新迭代次数
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if (alphaPairsChanged == 0): iter_num += 1
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else: iter_num = 0
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print("迭代次数: %d" % iter_num)
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return b,alphas
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"""
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函数说明:分类结果可视化
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Parameters:
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dataMat - 数据矩阵
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w - 直线法向量
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b - 直线解决
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Returns:
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无
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Author:
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Jack Cui
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Blog:
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http://blog.csdn.net/c406495762
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Zhihu:
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https://www.zhihu.com/people/Jack--Cui/
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Modify:
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2017-09-23
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"""
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def showClassifer(dataMat, w, b):
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#绘制样本点
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data_plus = [] #正样本
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data_minus = [] #负样本
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for i in range(len(dataMat)):
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if labelMat[i] > 0:
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data_plus.append(dataMat[i])
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else:
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data_minus.append(dataMat[i])
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data_plus_np = np.array(data_plus) #转换为numpy矩阵
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data_minus_np = np.array(data_minus) #转换为numpy矩阵
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plt.scatter(np.transpose(data_plus_np)[0], np.transpose(data_plus_np)[1], s=30, alpha=0.7) #正样本散点图
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plt.scatter(np.transpose(data_minus_np)[0], np.transpose(data_minus_np)[1], s=30, alpha=0.7) #负样本散点图
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#绘制直线
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x1 = max(dataMat)[0]
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x2 = min(dataMat)[0]
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a1, a2 = w
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b = float(b)
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a1 = float(a1[0])
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a2 = float(a2[0])
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y1, y2 = (-b- a1*x1)/a2, (-b - a1*x2)/a2
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plt.plot([x1, x2], [y1, y2])
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#找出支持向量点
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for i, alpha in enumerate(alphas):
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if abs(alpha) > 0:
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x, y = dataMat[i]
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plt.scatter([x], [y], s=150, c='none', alpha=0.7, linewidth=1.5, edgecolor='red')
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plt.show()
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"""
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函数说明:计算w
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Parameters:
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dataMat - 数据矩阵
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labelMat - 数据标签
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alphas - alphas值
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Returns:
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无
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Author:
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Jack Cui
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Blog:
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http://blog.csdn.net/c406495762
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Zhihu:
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https://www.zhihu.com/people/Jack--Cui/
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Modify:
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2017-09-23
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"""
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def get_w(dataMat, labelMat, alphas):
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alphas, dataMat, labelMat = np.array(alphas), np.array(dataMat), np.array(labelMat)
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w = np.dot((np.tile(labelMat.reshape(1, -1).T, (1, 2)) * dataMat).T, alphas)
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return w.tolist()
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if __name__ == '__main__':
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dataMat, labelMat = loadDataSet('testSet.txt')
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b,alphas = smoSimple(dataMat, labelMat, 0.6, 0.001, 40)
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w = get_w(dataMat, labelMat, alphas)
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showClassifer(dataMat, w, b)
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