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src/python/06.SVM/svmMLiA.py
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118
src/python/06.SVM/svmMLiA.py
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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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"""
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from numpy import *
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from time import sleep
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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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Returns:
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数据矩阵, 类标签
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"""
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dataMat = []; 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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"""
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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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Args:
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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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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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"""
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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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Args:
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dataMatIn: 数据集
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classLabels: 类别标签
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C: 常数C
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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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dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()
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b = 0; m,n = shape(dataMatrix)
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alphas = mat(zeros((m,1)))
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iter = 0
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while (iter < maxIter):
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alphaPairsChanged = 0
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for i in range(m):
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fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
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Ei = fXi - float(labelMat[i])#if checks if an example violates KKT conditions
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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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j = selectJrand(i,m)
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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(); alphaJold = alphas[j].copy()
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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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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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alphas[j] -= labelMat[j]*(Ei - Ej)/eta
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alphas[j] = clipAlpha(alphas[j],H,L)
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if (abs(alphas[j] - alphaJold) < 0.00001): print("j not moving enough"); continue
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alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])#update i by the same amount as j
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#the update is in the oppostie direction
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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]): 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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alphaPairsChanged += 1
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print("iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))
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if (alphaPairsChanged == 0): iter += 1
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else: iter = 0
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print("iteration number: %d" % iter)
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return b,alphas
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@@ -1,30 +1,155 @@
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# coding=utf-8
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def loadExData():
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return[[1,1,1,0,0],
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[2,2,2,0,0],
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[1,1,1,0,0],
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[5,5,5,0,0],
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[1,1,0,2,2],
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[0,0,0,3,3],
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[0,0,0,1,1]]
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#!/usr/bin/python
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# encoding: utf-8
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from numpy import *
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from numpy import *
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from numpy import linalg as la
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def loadExData():
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# 利用SVD提高推荐效果，菜肴矩阵
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return[[2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5],
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[0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0],
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[3, 3, 4, 0, 3, 0, 0, 2, 2, 0, 0],
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[5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0],
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[4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5],
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[0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4],
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[0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0],
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[0, 0, 0, 3, 0, 0, 0, 0, 4, 5, 0],
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[1, 1, 2, 1, 1, 2, 1, 0, 4, 5, 0]]
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"""
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# 推荐引擎示例矩阵
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return[[4, 4, 0, 2, 2],
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[4, 0, 0, 3, 3],
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[4, 0, 0, 1, 1],
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[1, 1, 1, 2, 0],
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[2, 2, 2, 0, 0],
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[1, 1, 1, 0, 0],
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[5, 5, 5, 0, 0]]
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原矩阵
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return[[1, 1, 1, 0, 0],
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[2, 2, 2, 0, 0],
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[1, 1, 1, 0, 0],
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[5, 5, 5, 0, 0],
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[1, 1, 0, 2, 2],
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[0, 0, 0, 3, 3],
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[0, 0, 0, 1, 1]]
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"""
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# 欧氏距离相似度，假定inA和inB 都是列向量
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# 计算向量的第二范式，相当于计算了欧氏距离
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def ecludSim(inA,inB):
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def ecludSim(inA, inB):
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return 1.0/(1.0 + la.norm(inA - inB))
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# pearsSim()函数会检查是否存在3个或更多的点。
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# corrcoef直接计算皮尔逊相关系数
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def pearsSim(inA,inB):
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def pearsSim(inA, inB):
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# 如果不存在，该函数返回1.0，此时两个向量完全相关。
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if len(inA)< 3 :return 1.0
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return 0.5 + 0.5*corrcoef(inA,inB,rowvar = 0)[0][1]
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if len(inA) < 3:
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return 1.0
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return 0.5 + 0.5*corrcoef(inA, inB, rowvar=0)[0][1]
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# 计算余弦相似度
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def cosSim(inA,inB):
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def cosSim(inA, inB):
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num = float(inA.T*inB)
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denom = la.norm(inA)*la.norm(inB)
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return 0.5 +0.5*(num/denom)
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return 0.5 + 0.5*(num/denom)
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# 基于物品相似度的推荐引擎
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# standEst()函数，用来计算在给定相似度计算方法的条件下，用户对物品的估计评分值。
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# standEst()函数的参数包括数据矩阵、用户编号、物品编号和相似度计算方法
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def standEst(dataMat, user, simMeas, item):
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# 得到数据集中的物品数目
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n = shape(dataMat)[1]
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# 初始化两个评分值
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simTotal = 0.0
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ratSimTotal = 0.0
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# 遍历行中的每个物品（对用户评过分的物品进行遍历，并将它与其他物品进行比较）
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for j in range(n):
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userRating = dataMat[user, j]
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# 如果某个物品的评分值为0，则跳过这个物品
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if userRating == 0:
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continue
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# 寻找两个用户都评级的物品
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# 变量overLap 给出的是两个物品当中已经被评分的那个元素
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overLap = nonzero(logical_and(dataMat[:, item].A>0, dataMat[:, j].A>0))[0]
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# 如果相似度为0，则两着没有任何重合元素，终止本次循环
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if len(overLap) == 0:similarity =0
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# 如果存在重合的物品，则基于这些重合物重新计算相似度。
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else: similarity = simMeas(dataMat[overLap,item], \
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dataMat[overLap,j])
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# print 'the %d and %d similarity is : %f'(iten,j,similarity)
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# 相似度会不断累加，每次计算时还考虑相似度和当前用户评分的乘积
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# similarity 用户相似度， userRating 用户评分
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simTotal += similarity
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ratSimTotal += similarity * userRating
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if simTotal == 0:
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return 0
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# 通过除以所有的评分总和，对上述相似度评分的乘积进行归一化，使得最后评分在0~5之间，这些评分用来对预测值进行排序
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else:
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return ratSimTotal/simTotal
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# recommend()函数，就是推荐引擎，它会调用standEst()函数，产生了最高的N个推荐结果。
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# 如果不指定N的大小，则默认值为3。该函数另外的参数还包括相似度计算方法和估计方法
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def recommend(dataMat, user, N=3, simMeas=cosSim, estMethod=standEst):
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# 寻找未评级的物品
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# 对给定的用户建立一个未评分的物品列表
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unratedItems = nonzero(dataMat[user, :].A == 0)[1]
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# 如果不存在未评分物品，那么就退出函数
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if len(unratedItems) == 0:
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return 'you rated everything'
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# 在所有的未评分物品上进行循环
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itemScores = []
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for item in unratedItems:
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estimatedScore = estMethod(dataMat, user, simMeas, item)
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# 寻找前N个未评级物品，调用standEst()来产生该物品的预测得分，该物品的编号和估计值会放在一个元素列表itemScores中
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itemScores.append((item, estimatedScore))
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# 按照估计得分，对该列表进行排序并返回。列表逆排序，第一个值就是最大值
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return sorted(itemScores, key=lambda jj: jj[1], reverse=True)[: N]
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# 基于SVD的评分估计
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# 在recommend() 中，这个函数用于替换对standEst()的调用，该函数对给定用户给定物品构建了一个评分估计值
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def svdEst(dataMat, user, simMeas, item):
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n = shape(dataMat)[1]
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# 对数据集进行SVD分解
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simTotal = 0.0
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ratSimTotal = 0.0
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# 在SVD分解之后，我们只利用包含了90%能量值的奇异值，这些奇异值会以NumPy数组的形式得以保存
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U, Sigma, VT = la.svd(dataMat)
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# 如果要进行矩阵运算，就必须要用这些奇异值构建出一个对角矩阵
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Sig4 = mat(eye(4) * Sigma[: 4])
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# 利用U矩阵将物品转换到低维空间中，构建转换后的物品
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xformedItems = dataMat.T * U[:, :4] * Sig4.I
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# 对于给定的用户，for循环在用户对应行的元素上进行遍历，
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# 这和standEst()函数中的for循环的目的一样，只不过这里的相似度计算时在低维空间下进行的。
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for j in range(n):
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userRating = dataMat[user, j]
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if userRating == 0 or j == item:
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continue
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# 相似度的计算方法也会作为一个参数传递给该函数
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similarity = simMeas(xformedItems[item, :].T,xformedItems[j, :].T)
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# for 循环中加入了一条print语句，以便了解相似度计算的进展情况。如果觉得累赘，可以去掉
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print 'the %d and %d similarity is: %f' % (item, j, similarity)
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# 对相似度求和
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simTotal += similarity
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# 对相似度及对应评分值的乘积求和
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ratSimTotal += similarity * userRating
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if simTotal == 0:
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return 0
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else:
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# 计算估计评分
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return ratSimTotal/simTotal
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if __name__ == "__main__":
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myMat = mat(loadExData())
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print myMat
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print recommend(myMat, 1, estMethod=svdEst)
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