统计学习方法 李航 第二章习题

2.1Minsky和Papert指出：感知机因为是线性模型，所以不能表示复杂的函数，如异或。验证感知机为什么不能表示异或

2.2模仿例题2.1，构建从训练数据集求感知机模型的例子

import numpy as np
import matplotlib.pyplot as plt

class showPicture:
def __init__(self,data,w,b):
self.b = b
self.w = w
plt.figure(1)
plt.title('Plot 1', size=14)
plt.xlabel('x-axis', size=14)
plt.ylabel('y-axis', size=14)

xData = np.linspace(0, 5, 100)
yData = self.expression(xData)
plt.plot(xData, yData, color='r', label='y1 data')

plt.scatter(data[0][0],data[0][1],s=50)
plt.scatter(data[1][0],data[1][1],s=50)
plt.scatter(data[2][0],data[2][1],marker='x',s=50,)
plt.savefig('2d.png',dpi=75)
def expression(self,x):
y = (-self.b - self.w[0]*x)/self.w[1]
return y
def show(self):
plt.show()
class perceptron:
def __init__(self,x,y,a=1):
self.x = x
self.y = y
self.w = np.zeros((x.shape[1],1))
self.b = 0
self.a = 1
def sign(self,w,b,x):
result = 0
y = np.dot(x,w)+b
return int(y)
def train(self):
flag = True
length = len(self.x)
while flag:
count = 0
for i in range(length):
tmpY = self.sign(self.w,self.b,self.x[i,:])
if tmpY*self.y[i]<=0:
tmp = self.y[i]*self.a*self.x[i,:]
tmp = tmp.reshape(self.w.shape)
self.w = tmp +self.w
self.b = self.b + self.y[i]
count +=1
if count == 0:
flag = False
return self.w,self.b

2.3证明：样本集线性可分的充要条件是正实例点集所构成的凸壳和负实例点集构成的凸壳不相交