运用对偶的（对应原始）感知机算法实现线性分类。
参考书目：《统计学习方法》(李航)
算法原理：
代码实现：
环境：win7 32bit + Anaconda3 +spyder
和原始算法的实现基本框架是类似的，只是判断和权值的更新算法有点变化。
# -*- coding: utf-8 -*-
"""
Created on Fri Nov 18 01:29:35 2016 @author: Administrator
""" import numpy as np
from matplotlib import pyplot as plt # train matrix
def get_train_data():
M1 = np.random.random((100,2))
# 将label加到最后，方便后面操作
M11 = np.column_stack((M1,np.ones(100))) M2 = np.random.random((100,2)) - 0.7
M22 = np.column_stack((M2,np.ones(100)*(-1)))
# 合并两类，并将位置索引加到最后
MA = np.vstack((M11,M22))
MA = np.column_stack((MA,range(0,200))) # 作图操作
plt.plot(M1[:,0],M1[:,1], 'ro')
plt.plot(M2[:,0],M2[:,1], 'go')
# 为了美观，根据数据点限制之后分类线的范围
min_x = np.min(M2)
max_x = np.max(M1)
# 分隔x,方便作图
x = np.linspace(min_x, max_x, 100)
# 此处返回 x 是为了之后作图方便
return MA,x # GRAM计算
def get_gram(MA):
GRAM = np.empty(shape=(200,200))
for i in range(len(MA)):
for j in range(len(MA)):
GRAM[i,j] = np.dot(MA[i,][:2], MA[j,][:2])
return GRAM # 方便在train函数中识别误分类点
def func(alpha,b,xi,yi,yN,index,GRAM):
pa1 = alpha*yN
pa2 = GRAM[:,index]
num = yi*(np.dot(pa1,pa2)+b)
return num # 训练training data
def train(MA, alpha, b, GRAM, yN):
# M 存储每次处理后依旧处于误分类的原始数据
M = []
for sample in MA:
xi = sample[0:2]
yi = sample[-2]
index = int(sample[-1])
# 如果为误分类，改变alpha,b
# n 为学习率
if func(alpha,b,xi,yi,yN,index,GRAM) <= 0:
alpha[index] += n
b += n*yi
M.append(sample)
if len(M) > 0:
# print('迭代...')
train(M, alpha, b, GRAM, yN)
return alpha,b # 作出分类线的图
def plot_classify(w,b,x, rate0):
y = (w[0]*x+b)/((-1)*w[1])
plt.plot(x,y)
plt.title('Accuracy = '+str(rate0)) # 随机生成testing data 并作图
def get_test_data():
M = np.random.random((50,2))
plt.plot(M[:,0],M[:,1],'*y')
return M
# 对传入的testing data 的单个样本进行分类
def classify(w,b,test_i):
if np.sign(np.dot(w,test_i)+b) == 1:
return 1
else:
return 0 # 测试数据，返回正确率
def test(w,b,test_data):
right_count = 0
for test_i in test_data:
classx = classify(w,b,test_i)
if classx == 1:
right_count += 1
rate = right_count/len(test_data)
return rate if __name__=="__main__":
MA,x= get_train_data()
test_data = get_test_data()
GRAM = get_gram(MA)
yN = MA[:,2]
xN = MA[:,0:2]
# 定义初始值
alpha = [0]*200
b = 0
n = 1
# 初始化最优的正确率
rate0 = 0 # print(alpha,b)
# 循环不同的学习率n,寻求最优的学习率，即最终的rate0
# w0,b0为对应的最优参数
for i in np.linspace(0.01,1,100):
n = i
alpha,b = train(MA, alpha, b, GRAM, yN)
alphap = np.column_stack((alpha*yN,alpha*yN))
w = sum(alphap*xN)
rate = test(w,b,test_data)
# print(w,b)
rate = test(w,b,test_data)
if rate > rate0:
rate0 = rate
w0 = w
b0 = b
print('Until now, the best result of the accuracy on test data is '+str(rate))
print('with w='+str(w0)+' b='+str(b0))
print('---------------------------------------------')
# 在选定最优的学习率后，作图
plot_classify(w0,b0,x,rate0)
plt.show()
输出：
