人工智能实战2019 第五次作业 焦宇恒 16721088

标题	内容
这个作业属于哪个课程	人工智能实战2019
这个作业的要求在哪里	逻辑与非门
这个作业在哪个具体方面帮助我实现目标	神经网络二分类法

逻辑与门训练样本

X1	X2	Y
0	0	0
0	1	0
1	0	0
1	1	1

逻辑或门训练样本

X1	X2	Y
0	0	0
0	1	1
1	0	1
1	1	1

实验代码

为使篇幅易读，省略部分函数代码

import numpy as np
import matplotlib.pyplot as plt
from pathlib import Path
import math
# 定义对率函数
def Sigmoid(x):
    s=1/(1+np.exp(-x))
    return s

# 前向计算
def ForwardCalculationBatch(W, B, batch_X):
    Z = np.dot(W, batch_X) + B
    A = Sigmoid(Z)
    return A

# 计算损失函数值
def CheckLoss(W, B, X, Y):
    m = X.shape[1]
    A = ForwardCalculationBatch(W,B,X)
    p1 = 1 - Y
    p2 = np.log(1-A)
    p3 = np.log(A)
    p4 = np.multiply(p1 ,p2)
    p5 = np.multiply(Y, p3)
    LOSS = np.sum(-(p4 + p5))  #binary classification
    loss = LOSS / m
    return loss

# 反向计算
# X:input example, Y:lable example, Z:predicated value
def BackPropagationBatch(batch_X, batch_Y, A):
    m = batch_X.shape[1]
    dZ = A - batch_Y
    # dZ列相加，即一行内的所有元素相加
    dB = dZ.sum(axis=1, keepdims=True)/m
    dW = np.dot(dZ, batch_X.T)/m
    return dW, dB

# 更新权重参数
def UpdateWeights(W, B, dW, dB, eta):
    W = W - eta * dW
    B = B - eta * dB
    return W, B

# 推理函数

def Inference(W,B,X_norm,xt):
    xt_normalized = NormalizePredicateData(xt, X_norm)
    A = ForwardCalculationBatch(W,B,xt_normalized)
    return A, xt_normalized

def train(method, X, Y, ForwardCalculationBatch, CheckLoss):
    num_example = X.shape[1]
    num_feature = X.shape[0]
    num_category = Y.shape[0]
    # hyper parameters
    eta, max_epoch,batch_size = InitializeHyperParameters(method,num_example)
    # W(num_category, num_feature), B(num_category, 1)
    W, B = InitialWeights(num_feature, num_category, "zero")
    # calculate loss to decide the stop condition
    loss = 5        # initialize loss (larger than 0)
    error = 1e-3    # stop condition
    dict_loss = {}  # loss history

    # if num_example=200, batch_size=10, then iteration=200/10=20
    max_iteration = (int)(num_example / batch_size)
    for epoch in range(max_epoch):
        print("epoch=%d" %epoch)
        for iteration in range(max_iteration):
            # get x and y value for one sample
            batch_x, batch_y = GetBatchSamples(X,Y,batch_size,iteration)
            # get z from x,y
            batch_a = ForwardCalculationBatch(W, B, batch_x)
            # calculate gradient of w and b
            dW, dB = BackPropagationBatch(batch_x, batch_y, batch_a)
            # update w,b
            W, B = UpdateWeights(W, B, dW, dB, eta)
            
            # calculate loss for this batch
            loss = CheckLoss(W,B,X,Y)
            if method == "SGD":
                if iteration % 10 == 0:
                    print(epoch,iteration,loss,W,B)
                # end if
            else:
                print(epoch,iteration,loss,W,B)
            # end if
            dict_loss[loss] = CData(loss, W, B, epoch, iteration)            
        # end for
        if math.isnan(loss):
            break
        if loss < error:
            break
    # end for
   
# 主程序
if __name__ == '__main__':
    # SGD, MiniBatch, FullBatch
    method = "SGD"
    # read data
    XData = np.array([0, 0, 1, 1, 0, 1, 0, 1]).reshape(2, 4)
    if logic == "and":
    	YData = np.array([0, 0, 0, 1]).reshape(1, 4)
    elif logic == "or"
    	YData = np.array([0, 1, 1, 1]).reshape(1, 4)
    X, X_norm = NormalizeData(XData)
    ShowData(XData, YData)
    Y = ToBool(YData)
    W, B = train(method, X, Y, ForwardCalculationBatch, CheckLoss)
    print("W=",W)
    print("B=",B)
    xt = np.array([5,1,6,9,5,5]).reshape(2,3,order='F')
    result, xt_norm = Inference(W,B,X_norm,xt)
    print("result=",result)
    print(np.around(result))
    ShowResult(X,YData,W,B,xt_norm)

逻辑与门实验结果

epoch=4999, iteration=3, loss=0.008636
W= [[8.83112606 8.82986228]]
B= [[-13.41376608]]
result= [[1. 1. 1.]]
[[1. 1. 1.]]W= [[8.83112606 8.82986228]]
B= [[-13.41376608]]
result= [[1. 1. 1.]]
[[1. 1. 1.]]

逻辑或门实验结果

epoch=4999, iteration=3, loss=0.004591
W= [[10.07943175 10.08022559]]
B= [[-4.57788412]]
result= [[1. 1. 1.]]
[[1. 1. 1.]]