Python SVM(支持向量机)实现方法完整示例

/* testSet.txt */
3.542485 1.977398 -1
3.018896 2.556416 -1
7.551510 -1.580030 1
2.114999 -0.004466 -1
8.127113 1.274372 1
7.108772 -0.986906 1
8.610639 2.046708 1
2.326297 0.265213 -1
3.634009 1.730537 -1
0.341367 -0.894998 -1
3.125951 0.293251 -1
2.123252 -0.783563 -1
0.887835 -2.797792 -1
7.139979 -2.329896 1
1.696414 -1.212496 -1
8.117032 0.623493 1
8.497162 -0.266649 1
4.658191 3.507396 -1
8.197181 1.545132 1
1.208047 0.213100 -1
1.928486 -0.321870 -1
2.175808 -0.014527 -1
7.886608 0.461755 1
3.223038 -0.552392 -1
3.628502 2.190585 -1
7.407860 -0.121961 1
7.286357 0.251077 1
2.301095 -0.533988 -1
-0.232542 -0.547690 -1
3.457096 -0.082216 -1
3.023938 -0.057392 -1
8.015003 0.885325 1
8.991748 0.923154 1
7.916831 -1.781735 1
7.616862 -0.217958 1
2.450939 0.744967 -1
7.270337 -2.507834 1
1.749721 -0.961902 -1
1.803111 -0.176349 -1
8.804461 3.044301 1
1.231257 -0.568573 -1
2.074915 1.410550 -1
-0.743036 -1.736103 -1
3.536555 3.964960 -1
8.410143 0.025606 1
7.382988 -0.478764 1
6.960661 -0.245353 1
8.234460 0.701868 1
8.168618 -0.903835 1
1.534187 -0.622492 -1
9.229518 2.066088 1
7.886242 0.191813 1
2.893743 -1.643468 -1
1.870457 -1.040420 -1
5.286862 -2.358286 1
6.080573 0.418886 1
2.544314 1.714165 -1
6.016004 -3.753712 1
0.926310 -0.564359 -1
0.870296 -0.109952 -1
2.369345 1.375695 -1
1.363782 -0.254082 -1
7.279460 -0.189572 1
1.896005 0.515080 -1
8.102154 -0.603875 1
2.529893 0.662657 -1
1.963874 -0.365233 -1
8.132048 0.785914 1
8.245938 0.372366 1
6.543888 0.433164 1
-0.236713 -5.766721 -1
8.112593 0.295839 1
9.803425 1.495167 1
1.497407 -0.552916 -1
1.336267 -1.632889 -1
9.205805 -0.586480 1
1.966279 -1.840439 -1
8.398012 1.584918 1
7.239953 -1.764292 1
7.556201 0.241185 1
9.015509 0.345019 1
8.266085 -0.230977 1
8.545620 2.788799 1
9.295969 1.346332 1
2.404234 0.570278 -1
2.037772 0.021919 -1
1.727631 -0.453143 -1
1.979395 -0.050773 -1
8.092288 -1.372433 1
1.667645 0.239204 -1
9.854303 1.365116 1
7.921057 -1.327587 1
8.500757 1.492372 1
1.339746 -0.291183 -1
3.107511 0.758367 -1
2.609525 0.902979 -1
3.263585 1.367898 -1
2.912122 -0.202359 -1
1.731786 0.589096 -1
2.387003 1.573131 -1

# -*- coding:utf-8 -*-
#!python3
__author__ = 'Wsine'
from numpy import *
import matplotlib.pyplot as plt
import operator
import time
def loadDataSet(fileName):
  dataMat = []
  labelMat = []
  with open(fileName) as fr:
    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):
  j = i
  while (j == i):
    j = int(random.uniform(0, m))
  return j
def clipAlpha(aj, H, L):
  if aj > H:
    aj = H
  if L > aj:
    aj = L
  return aj
class optStruct:
  def __init__(self, dataMatIn, classLabels, C, toler):
    self.X = dataMatIn
    self.labelMat = classLabels
    self.C = C
    self.tol = toler
    self.m = shape(dataMatIn)[0]
    self.alphas = mat(zeros((self.m, 1)))
    self.b = 0
    self.eCache = mat(zeros((self.m, 2)))
def calcEk(oS, k):
  fXk = float(multiply(oS.alphas, oS.labelMat).T * (oS.X * oS.X[k, :].T)) + oS.b
  Ek = fXk - float(oS.labelMat[k])
  return Ek
def selectJ(i, oS, Ei):
  maxK = -1
  maxDeltaE = 0
  Ej = 0
  oS.eCache[i] = [1, Ei]
  validEcacheList = nonzero(oS.eCache[:, 0].A)[0]
  if (len(validEcacheList)) > 1:
    for k in validEcacheList:
      if k == i:
        continue
      Ek = calcEk(oS, k)
      deltaE = abs(Ei - Ek)
      if (deltaE > maxDeltaE):
        maxK = k
        maxDeltaE = deltaE
        Ej = Ek
    return maxK, Ej
  else:
    j = selectJrand(i, oS.m)
    Ej = calcEk(oS, j)
  return j, Ej
def updateEk(oS, k):
  Ek = calcEk(oS, k)
  oS.eCache[k] = [1, Ek]
def innerL(i, oS):
  Ei = calcEk(oS, i)
  if ((oS.labelMat[i] * Ei < -oS.tol) and (oS.alphas[i] < oS.C)) or ((oS.labelMat[i] * Ei > oS.tol) and (oS.alphas[i] > 0)):
    j, Ej = selectJ(i, oS, Ei)
    alphaIold = oS.alphas[i].copy()
    alphaJold = oS.alphas[j].copy()
    if (oS.labelMat[i] != oS.labelMat[j]):
      L = max(0, oS.alphas[j] - oS.alphas[i])
      H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i])
    else:
      L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C)
      H = min(oS.C, oS.alphas[j] + oS.alphas[i])
    if (L == H):
      # print("L == H")
      return 0
    eta = 2.0 * oS.X[i, :] * oS.X[j, :].T - oS.X[i, :] * oS.X[i, :].T - oS.X[j, :] * oS.X[j, :].T
    if eta >= 0:
      # print("eta >= 0")
      return 0
    oS.alphas[j] -= oS.labelMat[j] * (Ei - Ej) / eta
    oS.alphas[j] = clipAlpha(oS.alphas[j], H, L)
    updateEk(oS, j)
    if (abs(oS.alphas[j] - alphaJold) < 0.00001):
      # print("j not moving enough")
      return 0
    oS.alphas[i] += oS.labelMat[j] * oS.labelMat[i] * (alphaJold - oS.alphas[j])
    updateEk(oS, i)
    b1 = oS.b - Ei - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.X[i, :] * oS.X[i, :].T - oS.labelMat[j] * (oS.alphas[j] - alphaJold) * oS.X[i, :] * oS.X[j, :].T
    b2 = oS.b - Ei - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.X[i, :] * oS.X[j, :].T - oS.labelMat[j] * (oS.alphas[j] - alphaJold) * oS.X[j, :] * oS.X[j, :].T
    if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]):
      oS.b = b1
    elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]):
      oS.b = b2
    else:
      oS.b = (b1 + b2) / 2.0
    return 1
  else:
    return 0
def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
  """
  输入：数据集, 类别标签, 常数C, 容错率, 最大循环次数
  输出：目标b, 参数alphas
  """
  oS = optStruct(mat(dataMatIn), mat(classLabels).transpose(), C, toler)
  iterr = 0
  entireSet = True
  alphaPairsChanged = 0
  while (iterr < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
    alphaPairsChanged = 0
    if entireSet:
      for i in range(oS.m):
        alphaPairsChanged += innerL(i, oS)
      # print("fullSet, iter: %d i:%d, pairs changed %d" % (iterr, i, alphaPairsChanged))
      iterr += 1
    else:
      nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
      for i in nonBoundIs:
        alphaPairsChanged += innerL(i, oS)
        # print("non-bound, iter: %d i:%d, pairs changed %d" % (iterr, i, alphaPairsChanged))
      iterr += 1
    if entireSet:
      entireSet = False
    elif (alphaPairsChanged == 0):
      entireSet = True
    # print("iteration number: %d" % iterr)
  return oS.b, oS.alphas
def calcWs(alphas, dataArr, classLabels):
  """
  输入：alphas, 数据集, 类别标签
  输出：目标w
  """
  X = mat(dataArr)
  labelMat = mat(classLabels).transpose()
  m, n = shape(X)
  w = zeros((n, 1))
  for i in range(m):
    w += multiply(alphas[i] * labelMat[i], X[i, :].T)
  return w
def plotFeature(dataMat, labelMat, weights, b):
  dataArr = array(dataMat)
  n = shape(dataArr)[0]
  xcord1 = []; ycord1 = []
  xcord2 = []; ycord2 = []
  for i in range(n):
    if int(labelMat[i]) == 1:
      xcord1.append(dataArr[i, 0])
      ycord1.append(dataArr[i, 1])
    else:
      xcord2.append(dataArr[i, 0])
      ycord2.append(dataArr[i, 1])
  fig = plt.figure()
  ax = fig.add_subplot(111)
  ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
  ax.scatter(xcord2, ycord2, s=30, c='green')
  x = arange(2, 7.0, 0.1)
  y = (-b[0, 0] * x) - 10 / linalg.norm(weights)
  ax.plot(x, y)
  plt.xlabel('X1'); plt.ylabel('X2')
  plt.show()
def main():
  trainDataSet, trainLabel = loadDataSet('testSet.txt')
  b, alphas = smoP(trainDataSet, trainLabel, 0.6, 0.0001, 40)
  ws = calcWs(alphas, trainDataSet, trainLabel)
  print("ws = \n", ws)
  print("b = \n", b)
  plotFeature(trainDataSet, trainLabel, ws, b)
if __name__ == '__main__':
  start = time.clock()
  main()
  end = time.clock()
  print('finish all in %s' % str(end - start))