2019独角兽企业重金招聘Python工程师标准>>> 
一、感知机算法-原始形式
算法描述：
输入:数据集$T = { (x_{1},y_{1}),(x_{2},y_{2}),..,(x_{n},y_{n})}$，其中$x_{i} \in X = R^{n},y_{i} \in Y={-1,1},i = 1,2,..,N$。学习率$\eta(0<\eta<1)$
输出：$w,b$ ；感知机模型：$f(x) = sign(w \cdot x + b)$
(1).选取初始值$w_{0},b_{0}$
(2).在训练数据中选取$(x_{i},y_{i})$
(3).如果$y_{i}(w\cdot x_{i}+b) \leqslant 0$
$w \leftarrow w + \eta y_{i}x_{i}$
$b \leftarrow b + \eta y_{i}$
(4).转到(2),直到训练集中没有误分类点
%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib.lines import Line2D
import numpy as np
class Perceptron:
def __init__(self):
self.W = []
self.b = 0
self.eta = 0.1
def __decission_func(self,x,y):
return y * self.__clac_Wx_add_b(x)
def __clac_Wx_add_b(self,x):
sum = 0
for i in range(len(x)):
sum += self.W[i]*x[i]
return sum + self.b
def fit(self,X,Y):
num_samples,feat_dim = X.shape
self.W = np.zeros((feat_dim))
self.b = 0
OK = False
while OK == False:
num_Ok = 0
for n in range(num_samples):
xi = X[n,:]
yi = Y[n]
if self.__decission_func(xi,yi) <= 0:
self.W = self.W + self.eta * yi * xi
self.b = self.b + self.eta * yi
else:
num_Ok += 1
if num_Ok == num_samples:
OK = True
def predict(self,x):
return 1 if self.__clac_Wx_add_b(x) > 0 else -1
def clac_y(x,W,b):
return -b / W[0] - W[1] / W[0] * x
X = np.array([[3,3],[4,3],[1,1]])
Y = np.array([1,1,-1])
clf = Perceptron()
clf.fit(X,Y)
color = [str(item/255.) for item in Y]
plt.scatter(X[:,0],X[:,1],c = color,s=300)
plt.text(3,2.5,s='+1')
plt.text(4,2.5,s='+1')
plt.text(1,0.5,s='-1')
print 'W=',clf.W,' b=',clf.b
x = [1,3]
y = []
for i in range(2):
y.append(clac_y(x[i],clf.W,clf.b))
plt.plot(x,y)
#pridect data
xx=[2,5]
rsp = clf.predict(xx)
colr = [str(item/255.) for item in [rsp]]
plt.scatter(xx[0],xx[1],s=100)
sym = '+1' if rsp == 1 else '-1'
plt.text(xx[0],xx[1] - 0.5,s=sym)
W= [ 0.1 0.1] b= -0.3
