## 实验名称：感知机 ### 一、实验目的 1.感知机的基本原理与应用 2.感知机的 python 实现和偏置的加入 3.感知机的局限性与多层感知机 ### 二、实验环境 gedit和xfce终端 ### 三、实验内容及任务感知机是最简单的起源算法。用数学公式表示就是： ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609151300666) 输入信号x1乘权重w1加输入信号x2乘权重w2的值大于阈值y则输出信号为1，小于等于阈值则输入信号为0 与门： ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609151795600) 当(w1，w2，θ) 为(0.5,0.5,0.7)、(0.5,0.5,0.8)、(1.0,1.0,1.0) 时满足要求。与非门： ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609152420965) 当(w1，w2，θ) 为(0.4,0.3,0.5)、(0.5,0.6,0.7)、(1.0,1.0,1.0) 时满足要求。或门： ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609152502772) 当(w1，w2，θ) 为(0.7,0.6,0.5)、(0.8,0.9,0.5)、(1.0,1.0,0.5) 时满足要求。感知机的 python 实现与门： ``` def AND(x1,x2): w1,w2,theta = 1.0，1.0，1.0 tmp = x1 * w1 + x2 * w2 if tmp <= theta: return 0 elif tmp > theta: return 1 if __name__ == '__main__': for xs in [(0, 0), (1, 0), (0, 1), (1, 1)]: y = AND(xs[0], xs[1]) print(str(xs) + " -> " + str(y)) ``` ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609153110176) 与非门： ``` def NAND(x1,x2): w1,w2,theta = 1.0,1.0,1.0 tmp = x1 * w1 + x2 * w2 if tmp <= theta: return 1 elif tmp > theta: return 0 if __name__ == '__main__': for xs in [(0, 0), (1, 0), (0, 1), (1, 1)]: y = NAND(xs[0], xs[1]) print(str(xs) + " -> " + str(y)) ``` ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609153506536) 或门： ``` def OR(s1,s2): w1,w2,theta = 0.7,0.6,0.5 tmp1 = s1 * w1 tmp2 = s2 * w2 if tmp1 >= theta: return 1 elif tmp2 >= theta: return 1 elif tmp1 < theta and tmp2 < theta: return 0 if __name__ == '__main__': for xs in [(0, 0), (1, 0), (0, 1), (1, 1)]: y = OR(xs[0], xs[1]) print(str(xs) + " -> " + str(y)) ``` ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609153547840) 引入偏置后的公式： ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609153627652) 加入偏置后的 python 实现：与门： ``` import numpy as np def AND(x1, x2): x = np.array([x1, x2]) w = np.array([0.5, 0.5]) b = -0.7 tmp = np.sum(w*x) + b if tmp <= 0: return 0 else: return 1 if __name__ == '__main__': for xs in [(0, 0), (1, 0), (0, 1), (1, 1)]: y = AND(xs[0], xs[1]) print(str(xs) + " -> " + str(y)) ``` ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609154035951) 与非门： ``` import numpy as np def NAND(x1, x2): x = np.array([x1, x2]) w = np.array([1.0, 1.0]) b = -1.0 tmp = np.sum(w*x) + b if tmp <= 0: return 1 else: return 0 if __name__ == '__main__': for xs in [(0, 0), (1, 0), (0, 1), (1, 1)]: y = NAND(xs[0], xs[1]) print(str(xs) + " -> " + str(y)) ``` ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609154127861) 或门： ``` import numpy as np def OR(s1, s2): x = np.array([s1, s2]) w = np.array([0.7, 0.6]) b = -0.5 tmp1 = x[0]*w[0]+b tmp2 = x[1]*w[1]+b if tmp1 > 0: return 1 elif tmp2 > 0: return 1 else: return 0 if __name__ == '__main__': for xs in [(0, 0), (1, 0), (0, 1), (1, 1)]: y = OR(xs[0], xs[1]) print(str(xs) + " -> " + str(y)) ``` ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609154162517) 多层感知机的异或门的实现： ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609154213359) ``` def NAND(x1,x2): w1,w2,theta = 1.0,1.0,1.0 tmp = x1 * w1 + x2 * w2 if tmp <= theta: return 1 elif tmp > theta: return 0 def OR(s1,s2): w1,w2,theta = 0.7,0.6,0.5 tmp1 = s1 * w1 tmp2 = s2 * w2 if tmp1 >= theta: return 1 elif tmp2 >= theta: return 1 elif tmp1 < theta and tmp2 < theta: return 0 def AND(s1,s2): w1,w2,theta = 1.0,1.0,1.0 tmp = s1 * w1 + s2 * w2 if tmp <= theta: return 0 elif tmp > theta: return 1 def XOR(x1, x2): s1 = NAND(x1, x2) s2 = OR(x1, x2) h = AND(s1, s2) return h if __name__ == '__main__': for xs in [(0, 0), (1, 0), (0, 1), (1, 1)]: h = XOR(xs[0], xs[1]) print(str(xs) + " -> " + str(h)) ``` ![image.png](https://dn-simplecloud.shiyanlou.com/courses/uid1531766-20201228-1609154283185) ### 四、实验总结感知机的偏置需要注意 numpy 库的使用，多层感知机的异或门没有使用模块导入，直接重新编写了代码。

“信息工程学院18级生产实习-Part1”实验报告