小白学习机器学习---第三章(3)：二分类LDA的python实现

上一节理论推导了LDA的实现，下面放上实现的python代码。"""
线性判别分析步骤：
1.把来自两类w1,w2的训练样本集X分成X1与X2

2.计算各类样本的均值向量m1,m2

3.计算样本类内散度矩阵s1,s2

4.计算总的类内散度矩阵 Sw=S1+S2

5.计算Sw的逆矩阵Sw2

6.求解权向量w=Sw2（m1-m2）

7.计算 g(x)=WT(x-1/2(m1+m2)) 根据是否大于0，判断分类

"""
#coding=utf-8
from numpy import *
import matplotlib.pyplot as plt

###导入数据
def createDataSet():
#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
#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

group1=[];group2=[]
i=0
while i<10:
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
group2.append((random.random(2)*20))
i+=1

group1=mat(group1)
group2=mat(group2)
#print(group1)
# print(group2)
return group1,group2

###计算样本均值
def compute_mean(group):
x1=0;x2=0
for a in group:
x1+=array(a)[0][0]
x2+=array(a)[0][1]

x1=x1/len(group)
x2=x2/len(group)
#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
# print('平均值：',x1,x2)
return mat([x1,x2])

###计算样本类内散度矩阵
def compute_scatter(group,mean):
m,d=shape(group)#m为样本个数，d为样本维度

#将所有样本向量-均值向量
group_mean=group-mean#虽然长度不匹配，但是维度匹配就可以计算

#初始化散度矩阵
s_in=mat([[0,0],[0,0]])
for i in range(m):
x=mat(array(group_mean)[i])
# print('x=:',x)
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

#print('s_in',s_in)
return s_in

group1,group2=createDataSet()
mean1=compute_mean(group1)
mean2=compute_mean(group2)
s_in1=compute_scatter(group1,mean1)
s_in2=compute_scatter(group2,mean2)

#求类内总散度
s_sum=s_in1+s_in2
print("类内散度矩阵：",s_sum)
#求类内散度矩阵的逆矩阵
s_rev=s_sum.I ### X.I 返回矩阵X的逆矩阵
print('s_rev:',s_rev)
#求权向量W
meanW=(mean1-mean2).T
print("权向量W：",meanW)
w=dot(s_rev,meanW)
print('w:',w)
print("----------------------")
# for a in group1:
# distance=dot(w.T,a.T)
# mean3=0.5*(mean1+mean2)
# meanD=dot(w.T,mean3.T)
# print(distance-meanD)
# print("-----------------")
# for a in group2:
# distance=dot(w.T,a.T)
# mean3=0.5*(mean1+mean2)
# meanD=dot(w.T,mean3.T)
# print(distance-meanD)

#判断测试集是哪一类
xcord1=[];ycord1=[]
xcord2=[];ycord2=[]

#这两个用来放真实的label分组
xcord3=[];ycord3=[]
xcord4=[];ycord4=[]
w2=array(w)

#通过LDA实现的分类图
for a in group1:
item=array(a)[0]
distance=dot(w.T,a.T)
mean3=0.5*(mean1+mean2)
meanDistance=dot(w.T,mean3.T)
if((distance-meanDistance)>0):
xcord1.append(item[0])
ycord1.append(item[1])
else:
xcord2.append(item[0])
ycord2.append(item[1])
for a in group2:
item=array(a)[0]
distance=dot(w.T,a.T)
mean3=0.5*(mean1+mean2)
meanDistance=dot(w.T,mean3.T)
if((distance-meanDistance)>0):
xcord1.append(item[0])
ycord1.append(item[1])
else:
xcord2.append(item[0])
ycord2.append(item[1])

#画出LDA的分布图
fig=plt.figure()
ax=fig.add_subplot(111)
ax.set_title("LDA")
plt.xlabel('X')
plt.ylabel('Y')
ax.scatter(xcord1,ycord1,s=30,c='red',marker='s')
ax.scatter(xcord2,ycord2,s=30,c='blue')

#画出真实分类图
for a in group1:
item=array(a)[0]
xcord3.append(item[0])
ycord3.append(item[1])
for a in group2:
item=array(a)[0]
xcord4.append(item[0])
ycord4.append(item[1])
fig=plt.figure(num=3)
ax=fig.add_subplot(111)
ax.set_title("realLabel")
plt.xlabel('X')
plt.ylabel('Y')
ax.scatter(xcord3,ycord3,s=30,c='red',marker='s')
ax.scatter(xcord4,ycord4,s=30,c='blue')
plt.show()