SVM smoSimple

src/python/06.SVM/svmMLiA.py

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+"""
+Created on Nov 4, 2010
+Update on 2017-03-21
+Chapter 5 source file for Machine Learing in Action
+@author: Peter/geekidentity
+"""
+from numpy import *
+from time import sleep
+
+def loadDataSet(fileName):
+    """
+    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
+    Args:
+        fileName: testSet.txt
+
+    Returns:
+        数据矩阵, 类标签
+    """
+    dataMat = []; labelMat = []
+    fr = open(fileName)
+    for line in fr.readlines():
+        lineArr = line.strip().split('\t')
+        dataMat.append([float(lineArr[0]), float(lineArr[1])])
+        labelMat.append(float(lineArr[2]))
+    return dataMat,labelMat
+
+def selectJrand(i,m):
+    """
+    随机选择一个整数
+    Args:
+        i: 第一个alpha的下标
+        m: 所有alpha的数目
+
+    Returns:
+
+    """
+    j=i #we want to select any J not equal to i
+    while (j==i):
+        j = int(random.uniform(0,m))
+    return j
+
+def clipAlpha(aj,H,L):
+    """
+    用于调整大于H或小于L的alpha值
+    Args:
+        aj:
+        H:
+        L:
+
+    Returns:
+
+    """
+    if aj > H:
+        aj = H
+    if L > aj:
+        aj = L
+    return aj
+
+def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
+    """
+    SVM SMO算法的简单实现:
+        创建一个alpha向量并将其初始化为0向量
+        当迭代次数据小于最大迭代次数时(外循环)
+            对数据集中的每个数据向量(内循环):
+                如果该数据向量可以被优化:
+                    随机选择另外一个数据向量
+                    同时优化这两个向量
+                    如果两个向量都不能被优化，退出内循环
+            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
+    Args:
+        dataMatIn: 数据集
+        classLabels: 类别标签
+        C: 常数C
+        toler: 容错率
+        maxIter: 退出前最大的循环次数
+
+    Returns:
+
+    """
+    dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()
+    b = 0; m,n = shape(dataMatrix)
+    alphas = mat(zeros((m,1)))
+    iter = 0
+    while (iter < maxIter):
+        alphaPairsChanged = 0
+        for i in range(m):
+            fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
+            Ei = fXi - float(labelMat[i])#if checks if an example violates KKT conditions
+            if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):
+                j = selectJrand(i,m)
+                fXj = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + b
+                Ej = fXj - float(labelMat[j])
+                alphaIold = alphas[i].copy(); alphaJold = alphas[j].copy()
+                if (labelMat[i] != labelMat[j]):
+                    L = max(0, alphas[j] - alphas[i])
+                    H = min(C, C + alphas[j] - alphas[i])
+                else:
+                    L = max(0, alphas[j] + alphas[i] - C)
+                    H = min(C, alphas[j] + alphas[i])
+                if L==H: print("L==H"); continue
+                eta = 2.0 * dataMatrix[i,:]*dataMatrix[j,:].T - dataMatrix[i,:]*dataMatrix[i,:].T - dataMatrix[j,:]*dataMatrix[j,:].T
+                if eta >= 0: print("eta>=0"); continue
+                alphas[j] -= labelMat[j]*(Ei - Ej)/eta
+                alphas[j] = clipAlpha(alphas[j],H,L)
+                if (abs(alphas[j] - alphaJold) < 0.00001): print("j not moving enough"); continue
+                alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])#update i by the same amount as j
+                                                                        #the update is in the oppostie direction
+                b1 = b - Ei- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[i,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[i,:]*dataMatrix[j,:].T
+                b2 = b - Ej- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[j,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[j,:]*dataMatrix[j,:].T
+                if (0 < alphas[i]) and (C > alphas[i]): b = b1
+                elif (0 < alphas[j]) and (C > alphas[j]): b = b2
+                else: b = (b1 + b2)/2.0
+                alphaPairsChanged += 1
+                print("iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))
+        if (alphaPairsChanged == 0): iter += 1
+        else: iter = 0
+        print("iteration number: %d" % iter)
+    return b,alphas