人工智能实战_第五次作业_杨佳宁

训练逻辑与门和逻辑或门

作业要求

项目	内容
这个作业属于哪个课程	班级博客
这个作业的要求在哪里	作业要求
我在这个课程的目标是	对于人工智能有一定的了解
这个作业在哪个具体方面帮助我实现目标	了解sigmoid激活函数和交叉熵函损失数，掌握用二分类的思想实现逻辑与门和或门的方法
作业正文	见下
其他参考文献	ai-edu/B-教学案例与实践/B6-神经网络基本原理简明教程-有关实现逻辑非的代码

作业正文

代码

import numpy as np
import matplotlib.pyplot as plt

# x1=0,0,1,1
# x2=0,1,0,1
# y =0,0,0,1
def ReadData_And():
    X = np.array([0,0,1,1,0,1,0,1]).reshape(2,4)
    Y = np.array([0,0,0,1]).reshape(1,4)
    return X,Y
# x1=0,0,1,1
# x2=0,1,0,1
# y =0,1,1,1
def ReadData_Or():
    X = np.array([0,0,1,1,0,1,0,1]).reshape(2,4)
    Y = np.array([0,1,1,1]).reshape(1,4)
    return X,Y

def Sigmoid(x):
    s = 1/(1+np.exp(-x)) 
    return s

def ForwardCalculation(w,b,x):
    z = np.dot(w , x) + b 
    a = Sigmoid(z)
    return a

def BackPropagation(x,y,z):
    m = x.shape[1]
    dZ = z - y
    dB = dZ.sum(axis=1 , keepdims = True)/m
    dW = np.dot(dZ , x.T)/m
    return dW, dB

def UpdateWeights(w, b, dW, dB, eta):
    w = w - eta*dW
    b = b - eta*dB
    return w,b

def CheckLoss(w, b, X, Y):
    m = X.shape[1]
    a = ForwardCalculation(w, b, X)
    # Cross Entropy
    n = np.sum(-(np.multiply(Y, np.log(a)) + np.multiply(1 - Y, np.log(1 - a))))
    loss = n / m
    return loss

# 初始化参数
def InitialWeights(num_input, num_output):
    W = np.zeros((num_output, num_input))
    B = np.zeros((num_output, 1))
    return W, B


def ShowResult(W,B,X,Y):
    w = -W[0,0]/W[0,1]
    b = -B[0,0]/W[0,1]
    x = np.array([0,1])
    y = w * x + b
    plt.plot(x,y)
    # 画出原始样本值
    for i in range(X.shape[1]):
        if Y[0,i] == 0:
            plt.scatter(X[0,i],X[1,i],marker="o",c='b',s=64)
        else:
            plt.scatter(X[0,i],X[1,i],marker="^",c='r',s=64)
    plt.axis([-0.1,1.1,-0.1,1.1])
    plt.show()

if __name__ == '__main__':
    # initialize_data
    eta = 0.5
    eps = 2e-3
    max_epoch = 10000
    # calculate loss to decide the stop condition
    loss = 5
    # create mock up data
    X, Y = ReadData_Or()
    #w, b = np.random.random(),np.random.random()
    w, b = InitialWeights(X.shape[0],Y.shape[0])
    # count of samples
    num_features = X.shape[0]
    num_example = X.shape[1]

    for epoch in range(max_epoch):
        for i in range(num_example):
            # get x and y value for one sample
            x = X[:,i].reshape(num_features,1)
            y = Y[:,i].reshape(1,1)
            # get z from x,y
            z = ForwardCalculation(w, b, x)
            # calculate gradient of w and b
            dW, dB = BackPropagation(x, y, z)
            # update w,b
            w, b = UpdateWeights(w, b, dW, dB, eta)
            # calculate loss for this batch
            loss = CheckLoss(w,b,X,Y)

        if loss < eps:
            break
    print("epoch=",epoch,"loss=",loss,"w=",w,"b=",b)
    ShowResult(w,b,X,Y)