python实现感知器（与或运算）
感知器属于一种简单的神经元，在神经网络中通常感知机与神经元的区别就是激活函数的不同，一般常用的激活函数是sigmoid函数，感知器中为阶跃函数。
感知器的输出为：y=f(n)=f(wx+b) //其中，w和b为感知器模型参数，w表示全权值，b表示偏置，wx表示w和x的内积。
在感知层进行学习时，每一个样本都将作为一个刺激输入神经元。输入信号是每一个样本的特征，期望的输出是该样本的类别。当输出与类别不同时，可以通过调整突触权值和偏置值，直到每个样本的输出与类别相同。
原理：输入向量X=(x1,x2,xr)T为样本的特征维，对应权值向量W=(w1,w2,wr)为一组参数。因此线性方程WX+b=0对应于空间中的一条直线。Wi是该直线法向分量，也是权值矩阵的某一行向量；b为直线的截距。该直线确定的判定边界将空间内的不同元素划分为正负两类，通过学习得到感知器模型，对于新的新输入向量可预测其输出类别。
给出一组矩阵，利用神经网络的反向传播功能（BP）来训练一种能够实现逻辑与、或的感知器
import numpy as np
and_samples = [
[0, 0, 0],
[1, 0, 0],
[0, 1, 0],
[1, 1, 1],
]
or_samples = [
[0, 0, 0],
[1, 0, 1],
[0, 1, 1],
[1, 1, 1],
]
def perception(samples):
# 权重
w = np.array([1, 2])
# 偏置
b = 0
a = 1
# 训练10遍
for i in range(10):
for j in range(4):
# 矩阵的第j行的前两个数值
x = np.array(samples[j][:2])
# 将未激活的值输入sigmoid函数 dot:向量的点乘运算
if np.dot(w, x) + b > 0:
y = 1
else:
y = 0
# 真实值
d = np.array(samples[j][2])
delta_b = a * (d - y)
delta_w = a * (d - y) * x
print('No. {} sample [{} {} {} {} {} {} {}]'.format(
i, j, w[0], w[1], b, y, delta_w[0], delta_w[1], delta_b
))
# 更新权重
w = w + delta_w
b = b + delta_b
if __name__ == '__main__':
print('logical and：')
perception(and_samples)
print('logical or：')
perception(or_samples)
Result and：
No. 0 sample [0 1 2 0 0 0 0]
No. 0 sample [1 1 2 0 1 -1 0]
No. 0 sample [2 0 2 -1 1 0 -1]
No. 0 sample [3 0 1 -2 0 1 1]
No. 1 sample [0 1 2 -1 0 0 0]
No. 1 sample [1 1 2 -1 0 0 0]
No. 1 sample [2 1 2 -1 1 0 -1]
No. 1 sample [3 1 1 -2 0 1 1]
No. 2 sample [0 2 2 -1 0 0 0]
No. 2 sample [1 2 2 -1 1 -1 0]
No. 2 sample [2 1 2 -2 0 0 0]
No. 2 sample [3 1 2 -2 1 0 0]
No. 3 sample [0 1 2 -2 0 0 0]
No. 3 sample [1 1 2 -2 0 0 0]
No. 3 sample [2 1 2 -2 0 0 0]
No. 3 sample [3 1 2 -2 1 0 0]
No. 4 sample [0 1 2 -2 0 0 0]
No. 4 sample [1 1 2 -2 0 0 0]
No. 4 sample [2 1 2 -2 0 0 0]
No. 4 sample [3 1 2 -2 1 0 0]
No. 5 sample [0 1 2 -2 0 0 0]
No. 5 sample [1 1 2 -2 0 0 0]
No. 5 sample [2 1 2 -2 0 0 0]
No. 5 sample [3 1 2 -2 1 0 0]
No. 6 sample [0 1 2 -2 0 0 0]
No. 6 sample [1 1 2 -2 0 0 0]
No. 6 sample [2 1 2 -2 0 0 0]
No. 6 sample [3 1 2 -2 1 0 0]
No. 7 sample [0 1 2 -2 0 0 0]
No. 7 sample [1 1 2 -2 0 0 0]
No. 7 sample [2 1 2 -2 0 0 0]
No. 7 sample [3 1 2 -2 1 0 0]
No. 8 sample [0 1 2 -2 0 0 0]
No. 8 sample [1 1 2 -2 0 0 0]
No. 8 sample [2 1 2 -2 0 0 0]
No. 8 sample [3 1 2 -2 1 0 0]
No. 9 sample [0 1 2 -2 0 0 0]
No. 9 sample [1 1 2 -2 0 0 0]
No. 9 sample [2 1 2 -2 0 0 0]
No. 9 sample [3 1 2 -2 1 0 0]
观察发现从第三次训练后，通过神经网络的BP，权重w0,w1和b已经趋于稳定：w0=1,w1=2,b=-2
Result or：
No. 0 sample [0 1 2 0 0 0 0]
No. 0 sample [1 1 2 0 1 0 0]
No. 0 sample [2 1 2 0 1 0 0]
No. 0 sample [3 1 2 0 1 0 0]
No. 1 sample [0 1 2 0 0 0 0]
No. 1 sample [1 1 2 0 1 0 0]
No. 1 sample [2 1 2 0 1 0 0]
No. 1 sample [3 1 2 0 1 0 0]
No. 2 sample [0 1 2 0 0 0 0]
No. 2 sample [1 1 2 0 1 0 0]
No. 2 sample [2 1 2 0 1 0 0]
No. 2 sample [3 1 2 0 1 0 0]
No. 3 sample [0 1 2 0 0 0 0]
No. 3 sample [1 1 2 0 1 0 0]
No. 3 sample [2 1 2 0 1 0 0]
No. 3 sample [3 1 2 0 1 0 0]
No. 4 sample [0 1 2 0 0 0 0]
No. 4 sample [1 1 2 0 1 0 0]
No. 4 sample [2 1 2 0 1 0 0]
No. 4 sample [3 1 2 0 1 0 0]
No. 5 sample [0 1 2 0 0 0 0]
No. 5 sample [1 1 2 0 1 0 0]
No. 5 sample [2 1 2 0 1 0 0]
No. 5 sample [3 1 2 0 1 0 0]
No. 6 sample [0 1 2 0 0 0 0]
No. 6 sample [1 1 2 0 1 0 0]
No. 6 sample [2 1 2 0 1 0 0]
No. 6 sample [3 1 2 0 1 0 0]
No. 7 sample [0 1 2 0 0 0 0]
No. 7 sample [1 1 2 0 1 0 0]
No. 7 sample [2 1 2 0 1 0 0]
No. 7 sample [3 1 2 0 1 0 0]
No. 8 sample [0 1 2 0 0 0 0]
No. 8 sample [1 1 2 0 1 0 0]
No. 8 sample [2 1 2 0 1 0 0]
No. 8 sample [3 1 2 0 1 0 0]
No. 9 sample [0 1 2 0 0 0 0]
No. 9 sample [1 1 2 0 1 0 0]
No. 9 sample [2 1 2 0 1 0 0]
No. 9 sample [3 1 2 0 1 0 0]
对于逻辑或，从输出样本的第一次训练之后，权重和偏置的BP趋于稳定：w0=1,w1=2,b=0