Kernel Trick实现svm
04
主要思想及算法流程来自李航的《统计学习方法》和之前推荐的《理解SVM的三重境界》（文末有PDF）
#coding=utf-8
import time
import random
import numpy as np
import math
import copy
a=np.matrix([[1.2,3.1,3.1]])
#print a.astype(int)
#print a.A
class SVM:
def __init__(self,data,kernel,maxIter,C,epsilon):
self.trainData=data
self.C=C #惩罚因子
self.kernel=kernel
self.maxIter=maxIter
self.epsilon=epsilon
self.a=[0 for i in range(len(self.trainData))]
self.w=[0 for i in range(len(self.trainData[0][0]))]
self.eCache=[[0,0] for i in range(len(self.trainData))]
self.b=0
self.xL=[self.trainData[i][0] for i in range(len(self.trainData))]
self.yL=[self.trainData[i][1] for i in range(len(self.trainData))]
def train(self):
#support_Vector=self.__SMO()
self.__SMO()
self.__update()
def __kernel(self,A,B):
#核函数 是对输入的向量进行变形 从低维映射到高维度
res=0
if self.kernel=='Line':
res=self.__Tdot(A,B)
elif self.kernel[0]=='Gauss':
K=0
for m in range(len(A)):
K+=(A[m]-B[m])**2
res=math.exp(-0.5*K/(self.kernel[1]**2))
return res
def __Tdot(self,A,B):
res=0
for k in range(len(A)):
res+=A[k]*B[k]
return res
def __SMO(self):
#SMO是基于 KKT 条件的迭代求解最优化问题算法
#SMO是SVM的核心算法
support_Vector=[]
self.a=[0 for i in range(len(self.trainData))]
pre_a=copy.deepcopy(self.a)
for it in range(self.maxIter):
flag=1
for i in range(len(self.xL)):
#print self.a
#更新 self.a 使用 机器学习实战的求解思路
#计算 j更新
diff=0
self.__update()
#选择有最大误差的j 丹麦理工大学的算法是 对j在数据集上循环, 随机选取i 显然效率不是很高
#机器学习实战 硬币书表述正常 代码混乱且有错误 启发式搜索
Ei=self.__calE(self.xL[i],self.yL[i])
j,Ej=self.__chooseJ(i,Ei)
#计算 L H
(L,H)=self.__calLH(pre_a,j,i)
#思路是先表示为self.a[j] 的唯一变量的函数 再进行求导（一阶导数=0 更新）
kij=self.__kernel(self.xL[i],self.xL[i])+self.__kernel(self.xL[j],self.xL[j])-2*self.__kernel(self.xL[i],self.xL[j])
#print kij,"aa"
if(kij==0):
continue
self.a[j] = pre_a[j] + float(1.0*self.yL[j]*(Ei-Ej))/kij
#下届是L 也就是截距,小于0时为0
#上届是H 也就是最大值,大于H时为H
self.a[j] = min(self.a[j], H)
self.a[j] = max(self.a[j], L)
#self.a[j] = min(self.a[j], H)
#print L,H
self.eCache[j]=[1,self.__calE(self.xL[j],self.yL[j])]
self.a[i] = pre_a[i]+self.yL[i]*self.yL[j]*(pre_a[j]-self.a[j])
self.eCache[i]=[1,self.__calE(self.xL[i],self.yL[i])]
diff=sum([abs(pre_a[m]-self.a[m]) for m in range(len(self.a))])
#print diff,pre_a,self.a
if diff < self.epsilon:
flag=0
pre_a=copy.deepcopy(self.a)
if flag==0:
print (it,"break")
break
#return support_Vector
def __chooseJ(self,i,Ei):
self.eCache[i]=[1,Ei]
chooseList=[]
#print self.eCache
#从误差缓存中得到备选的j的列表 chooseList 误差缓存的作用：解决初始选择问题
for p in range(len(self.eCache)):
if self.eCache[p][0]!=0 and p!=i:
chooseList.append(p)
if len(chooseList)>1:
delta_E=0
maxE=0
j=0
Ej=0
for k in chooseList:
Ek=self.__calE(self.xL[k],self.yL[k])
delta_E=abs(Ek-Ei)
if delta_E>maxE:
maxE=delta_E
j=k
Ej=Ek
return j,Ej
else:
#最初始状态
j=self.__randJ(i)
Ej=self.__calE(self.xL[j],self.yL[j])
return j,Ej
def __randJ(self,i):
j=i
while(j==i):
j=random.randint(0,len(self.xL)-1)
return j
def __calLH(self,pre_a,j,i):
if(self.yL[j]!= self.yL[i]):
return (max(0,pre_a[j]-pre_a[i]),min(self.C,self.C-pre_a[i]+pre_a[j]))
else:
return (max(0,-self.C+pre_a[i]+pre_a[j]),min(self.C,pre_a[i]+pre_a[j]))
def __calE(self,x,y):
#print x,y
y_,q=self.predict(x)
return y_-y
def __calW(self):
self.w=[0 for i in range(len(self.trainData[0][0]))]
for i in range(len(self.trainData)):
for j in range(len(self.w)):
self.w[j]+=self.a[i]*self.yL[i]*self.xL[i][j]
def __update(self):
#更新 self.b 和 self.w
self.__calW()
#得到了self.w 下面求b
#print self.a
maxf1=-99999
min1=99999
for k in range(len(self.trainData)):
y_v=self.__Tdot(self.w,self.xL[k])
#print y_v
if self.yL[k]==-1:
if y_v>maxf1:
maxf1=y_v
else:
if y_v<min1:
min1=y_v
self.b=-0.5*(maxf1+min1)
def predict(self,testData):
pre_value=0
#从trainData 改成 suport_Vector
for i in range(len(self.trainData)):
pre_value+=self.a[i]*self.yL[i]*self.__kernel(self.xL[i],testData)
pre_value+=self.b
#print pre_value,"pre_value"
if pre_value<0:
y=-1
else:
y=1
return y,abs(pre_value-0)
def save(self):
pass
def LoadSVM():
pass
另存为SVM.py
from SVM import *
data=[
[[1,1],1],
[[2,1],1],
[[1,0],1],
[[3,7],-1],
[[4,8],-1],
[[4,10],-1],
]
#如果为gauss核的话 ['Gauss',标准差]
svm=SVM(data,'Line',1000,0.02,0.001)
print (svm.predict([4,0]))
(1, 0.6300000000000001)
print (svm.a)
[0.02, 0.0, 0.0, 0.0, 0.0, 0.02]
print (svm.w)
[-0.06, -0.18000000000000002]
print (svm.b)
0.8700000000000001
参考文献：
https://www.cnblogs.com/pinard/p/6117515.html
https://blog.csdn.net/IT_zxl001/article/details/80488294
https://cuijiahua.com/blog/2017/11/ml_9_svm_2.html
https://blog.csdn.net/sinat_33829806/article/details/78388025
《机器学习实战》第6章
