神经网络相关（2）

多个神经元的实现——回归问题：  

%matplotlib inline
#IPython的魔法函数，可以在IPython编译器里直接使用，作用是内嵌画图，省略掉plt.show()这一步，直接显示图像

import numpy as np
import matplotlib.pyplot as plt

X = np.arange(-1.0,1.0,0.2)
Y = np.arange(-1.0,1.0,0.2)

Z = np.zeros((10,10))

#权重矩阵 m n 值和神经元数量一致
w_im = np.array([[4.0,4.0],
                 [4.0,4.0]])
w_mo = np.array([[1.0],
                 [-1.0]])


#偏置矩阵 偏置的数量和下层网络的神经元数量一致，为n
b_im = np.array([3.0,-3.0])
b_mo = np.array([0.1])

def middle_layer(x,w,b):
    u = np.dot(x,w) + b
    return 1/(1+np.exp(-u))

def output_layer(x,w,b):
    u = np.dot(x,w) + b
    return u

for i in range(10):
    for j in range(10):
        inp = np.array([X[i],Y[j]])
        mid = middle_layer(inp,w_im,b_im)
        out = output_layer(mid,w_mo,b_mo)
        Z[j][i] = out[0]
        
plt.imshow(Z,"gray",vmin=0.0,vmax=1.0)
plt.colorbar()
plt.show()

%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt

X = np.arange(-1.0,1.0,0.1)
Y = np.arange(-1.0,1.0,0.1)

Z = np.zeros((10,10))

#权重矩阵 m n 值和神经元数量一致
w_im = np.array([[1.0,2.0],
                 [2.0,3.0]])
w_mo = np.array([[-1.0,1.0],
                 [1.0,-1.0]])


#偏置矩阵
b_im = np.array([0.3,-0.3])
b_mo = np.array([0.4,0.1])

def middle_layer(x,w,b):
    u = np.dot(x,w) + b
    return 1/(1+np.exp(-u))

def output_layer(x,w,b):
    u = np.dot(x,w) + b
    return np.exp(u)/np.sum(np.exp(u))

x_1 = []
y_1 = []
x_2 = []
y_2 = []

for i in range(20):
    for j in range(20):
        inp = np.array([X[i],Y[j]])
        mid = middle_layer(inp,w_im,b_im)
        out = output_layer(mid,w_mo,b_mo)
        if out[0] > out[1]:
            x_1.append(X[i])
            y_1.append(Y[j])
        else:
            x_2.append(X[i])
            y_2.append(Y[j])
            
        
plt.scatter(x_1,y_1,marker = "o")
plt.scatter(x_2,y_2,marker = "+")
plt.show()