二分类LDA的py...

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  """
  
  
  
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  线性判别分析步骤：
  
  
  
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  1.把来自两类w1,w2的训练样本集X分成X1与X2
  
  
  
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  2.计算各类样本的均值向量m1,m2
  
  
  
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  3.计算样本类内散度矩阵s1,s2
  
  
  
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  4.计算总的类内散度矩阵 Sw=S1+S2
  
  
  
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  5.计算Sw的逆矩阵Sw2
  
  
  
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  6.求解权向量w=Sw2（m1-m2）
  
  
  
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  7.计算 g(x)=WT(x-1/2(m1+m2)) 根据是否大于0，判断分类
  
  
  
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  """
  
  
  
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  #coding=utf-8
  
  
  
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  from
  numpy
  import
  *
  
  
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  import
  matplotlib.pyplot
  as
  plt
  
  
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  ###导入数据
  
  
  
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  def createDataSet():
  
  
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  #group1=[[0.697,0.460],[0.774,0.376],[0.634,0.264],[0.608,0.318],[0.556,0.215],[0.403,0.211],[0.481,0.149],[0.437,0.211]]#好瓜
  
  
  
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  #group2=[[0.666,0.091],[0.243,0.267],[0.245,0.057],[0.343,0.099],[0.639,0.161],[0.657,0.198],[0.360,0.370],[0.593,0.042]]#烂瓜
  
  
  
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  group1=[];group2=[]
  
  
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  i=
  0
  
  
  
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  while
  i<
  10
  :
  
  
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  group1.append(random.random(
  2
  )*
  3
  )
  #random.random(i) ： 生成具有i个元素的[],每个元素取值为0到1
  
  
  
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  group2.append((random.random(
  2
  )*
  20
  ))
  
  
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  i+=
  1
  
  
  
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  group1=mat(group1)
  
  
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  group2=mat(group2)
  
  
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  #print(group1)
  
  
  
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  # print(group2)
  
  
  
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  return
  group1,group2
  
  
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  ###计算样本均值
  
  
  
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  def compute_mean(group):
  
  
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  x1=
  0
  ;x2=
  0
  
  
  
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  for
  a
  in
  group:
  
  
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  x1+=array(a)[
  0
  ][
  0
  ]
  
  
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  x2+=array(a)[
  0
  ][
  1
  ]
  
  
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  x1=x1/len(group)
  
  
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  x2=x2/len(group)
  
  
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  #m=np.mean(group,0) np.mean(group,0) # 压缩行，对各列求均值,返回一个1*n矩阵，若为1，则对各行求均值，返回m*1矩阵，若为2，则对所有数求一个均值，返回一个数
  
  
  
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  # print('平均值：',x1,x2)
  
  
  
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  return
  mat([x1,x2])
  
  
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  ###计算样本类内散度矩阵
  
  
  
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  def compute_scatter(group,mean):
  
  
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  m,d=shape(group)
  #m为样本个数，d为样本维度
  
  
  
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  #将所有样本向量-均值向量
  
  
  
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  group_mean=group-mean
  #虽然长度不匹配，但是维度匹配就可以计算
  
  
  
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  #初始化散度矩阵
  
  
  
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  s_in=mat([[
  0
  ,
  0
  ],[
  0
  ,
  0
  ]])
  
  
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  for
  i
  in
  range(m):
  
  
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  x=mat(array(group_mean))
  
  
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  # print('x=:',x)
  
  
  
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  s_in=s_in+dot(x.T,x)
  ###X.T 获得矩阵X的转置,dot为矩阵乘法运算
  
  
  
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  #print('s_in',s_in)
  
  
  
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  return
  s_in
  
  
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  group1,group2=createDataSet()
  
  
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  mean1=compute_mean(group1)
  
  
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  mean2=compute_mean(group2)
  
  
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  s_in1=compute_scatter(group1,mean1)
  
  
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  s_in2=compute_scatter(group2,mean2)
  
  
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  #求类内总散度
  
  
  
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  s_sum=s_in1+s_in2
  
  
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  print(
  "类内散度矩阵："
  ,s_sum)
  
  
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  #求类内散度矩阵的逆矩阵
  
  
  
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  s_rev=s_sum.I
  ### X.I 返回矩阵X的逆矩阵
  
  
  
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  print(
  's_rev:'
  ,s_rev)
  
  
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  #求权向量W
  
  
  
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  meanW=(mean1-mean2).T
  
  
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  print(
  "权向量W："
  ,meanW)
  
  
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  w=dot(s_rev,meanW)
  
  
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  print(
  'w:'
  ,w)
  
  
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  print(
  "----------------------"
  )
  
  
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  # for a in group1:
  
  
  
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  # distance=dot(w.T,a.T)
  
  
  
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  # mean3=0.5*(mean1+mean2)
  
  
  
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  # meanD=dot(w.T,mean3.T)
  
  
  
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  # print(distance-meanD)
  
  
  
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  # print("-----------------")
  
  
  
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  # for a in group2:
  
  
  
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  # distance=dot(w.T,a.T)
  
  
  
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  # mean3=0.5*(mean1+mean2)
  
  
  
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  # meanD=dot(w.T,mean3.T)
  
  
  
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  # print(distance-meanD)
  
  
  
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  #判断测试集是哪一类
  
  
  
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  xcord1=[];ycord1=[]
  
  
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  xcord2=[];ycord2=[]
  
  
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  #这两个用来放真实的label分组
  
  
  
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  xcord3=[];ycord3=[]
  
  
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  xcord4=[];ycord4=[]
  
  
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  w2=array(w)
  
  
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  #通过LDA实现的分类图
  
  
  
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  for
  a
  in
  group1:
  
  
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  item=array(a)[
  0
  ]
  
  
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  distance=dot(w.T,a.T)
  
  
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  mean3=
  0.5
  *(mean1+mean2)
  
  
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  meanDistance=dot(w.T,mean3.T)
  
  
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  if
  ((distance-meanDistance)>
  0
  ):
  
  
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  xcord1.append(item[
  0
  ])
  
  
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  ycord1.append(item[
  1
  ])
  
  
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  else
  :
  
  
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  xcord2.append(item[
  0
  ])
  
  
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  ycord2.append(item[
  1
  ])
  
  
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  for
  a
  in
  group2:
  
  
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  item=array(a)[
  0
  ]
  
  
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  distance=dot(w.T,a.T)
  
  
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  mean3=
  0.5
  *(mean1+mean2)
  
  
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  meanDistance=dot(w.T,mean3.T)
  
  
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  if
  ((distance-meanDistance)>
  0
  ):
  
  
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  xcord1.append(item[
  0
  ])
  
  
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  ycord1.append(item[
  1
  ])
  
  
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  else
  :
  
  
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  xcord2.append(item[
  0
  ])
  
  
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  ycord2.append(item[
  1
  ])
  
  
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  #画出LDA的分布图
  
  
  
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  fig=plt.figure()
  
  
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  ax=fig.add_subplot(
  111
  )
  
  
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  ax.set_title(
  "LDA"
  )
  
  
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  plt.xlabel(
  'X'
  )
  
  
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  plt.ylabel(
  'Y'
  )
  
  
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  ax.scatter(xcord1,ycord1,s=
  30
  ,c=
  'red'
  ,marker=
  's'
  )
  
  
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  ax.scatter(xcord2,ycord2,s=
  30
  ,c=
  'blue'
  )
  
  
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  #画出真实分类图
  
  
  
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  for
  a
  in
  group1:
  
  
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  item=array(a)[
  0
  ]
  
  
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  xcord3.append(item[
  0
  ])
  
  
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  ycord3.append(item[
  1
  ])
  
  
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  for
  a
  in
  group2:
  
  
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  item=array(a)[
  0
  ]
  
  
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  xcord4.append(item[
  0
  ])
  
  
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  ycord4.append(item[
  1
  ])
  
  
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  fig=plt.figure(num=
  3
  )
  
  
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  ax=fig.add_subplot(
  111
  )
  
  
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  ax.set_title(
  "realLabel"
  )
  
  
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  plt.xlabel(
  'X'
  )
  
  
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  plt.ylabel(
  'Y'
  )
  
  
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  ax.scatter(xcord3,ycord3,s=
  30
  ,c=
  'red'
  ,marker=
  's'
  )
  
  
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  ax.scatter(xcord4,ycord4,s=
  30
  ,c=
  'blue'
  )
  
  
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  plt.show()
  
  
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