思路：输入样本X与随机初始权重W相乘，利用sigmoid激活函数输出值，对于二分类问题，用交叉熵损失函数来计算损失值，通过交叉熵损失函数利用链式法则求出W和b的偏导，梯度下降更新W和b即可，（梯度下降又有很多，Momentum,Adam等后面在详细介绍）剩下的就是迭代次数和学习率的问题。

第一课作业直接给了数据集，无须对数据集操作，下面是读取数据集的代码，数据集链接https://download.csdn.net/download/fanzonghao/10539175

命名为：lr_utils.py

 

import numpy as np
import h5pydef load_dataset():train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set featurestrain_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labelstest_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set featurestest_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labelsclasses = np.array(test_dataset["list_classes"][:]) # the list of classestrain_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes
if __name__ == '__main__':train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes=load_dataset()print('训练样本数={}'.format(train_set_x_orig.shape))print('训练样本对应的标签={}'.format(train_set_y_orig.shape))print('前10张训练样本标签={}'.format(train_set_y_orig[:,:10]))print('测试样本数={}'.format(test_set_x_orig.shape))print('测试样本对应的标签={}'.format(test_set_y_orig.shape))print('{}'.format(classes))

可看见打印结果：209个样本，64x64x3。

 

下面通过测试代码看看标签0 1 代表的是什么

 

import cv2
from lr_utils import load_dataset
train_set_x_orig,train_set_y,test_set_x_orig,test_set_y,classes=load_dataset()
cv2.imshow('img0',train_set_x_orig[0])
cv2.waitKey()
cv2.imshow('img2',train_set_x_orig[2])
cv2.waitKey()

可知0代表不是猫，1代表是猫。

由于训练的标签结果是Y=（1，209），X将其拉成一个样本一行向量，X=(209，64*64*3)又W*X=Y,故权重W为（64*64*3,1），最终采用的是样本X=（64*64*3，209），W=（64*64*3,1），计算过程中W要采用转置。

先初始化权重W，激活函数采用sigmoid,输出值A;损失函数采用交叉熵，通过链式法则反向求W和b的导数，在更新W和b即可。计算过程中，注意维度的统一，可用assert 判断。

代码如下：

import numpy as np
from lr_utils import load_dataset
from matplotlib import pyplot as plt
"""
函数功能：逻辑回归实现小猫分类
"""
import cv2
#sigmoid激活函数
def sigmoid(z):s=1.0/(1+np.exp(-z))return s
#初始化权值
def initialize_zeros(dim):w=np.zeros(dim).reshape(dim,1)b=0return w,b
######w(64*64*3,1)#传播过程
def propagate(w,b,X,Y):m=X.shape[1]A=sigmoid(np.dot(w.T,X)+b)assert np.dot(w.T,X).shape==Y.shapecost=-1/m*(np.dot(Y,np.log(A).T)+np.dot((1-Y),np.log(1-A).T))dw=1/m*(np.dot(X,(A-Y).T))db= 1 / m * (np.sum(A-Y))grads={'dw':dw,'db': db}cost=np.squeeze(cost)return cost,grads
'''
函数功能：更新权重 +迭代次数+学习率 返回最终更新的权重和损失值
'''
def optimize(w,b,X,Y,num_iterations,learning_rate,print_cost=False):costs=[]for i in range(num_iterations):cost, grads = propagate(w, b, X, Y)dw=grads['dw']db=grads['db']w = w - learning_rate * dwb = b - learning_rate * dbif i%100==0:costs.append(cost)if print_cost and i%100==0:print('after iteration %i:%f'%(i,cost))params={'w':w,'b':b}grads = {'dw': dw,'db': db}return params,grads,costs
"""
函数功能：实现利用更新好的权重预测小猫
"""
def predict(w,b,X):m = X.shape[1]Y_prediction=np.zeros((1,m))w=w.reshape(X.shape[0],1)A=sigmoid(np.dot(w.T,X)+b)for i in range(A.shape[1]):if A[0,i]>0.5:Y_prediction[0,i]=1else:Y_prediction[0,i]=0return Y_prediction
"""
函数功能：测试函数,在编写过程中,检查W和b的更新,最终注销掉,不调用
"""
def test():dim = 2w, b = initialize_zeros(dim)print('initialize w,b=', w, b)w, b, X, Y = np.array([[1], [2]]), 2, np.array([[1, 2], [3, 4]]), np.array([[1, 0]])cost, grads = propagate(w, b, X, Y)print('cost=', cost)print('dw=', grads['dw'])print('db=', grads['db'])params, grads, costs = optimize(w, b, X, Y, num_iterations=100, learning_rate=0.009, print_cost=False)print('w', params['w'])print('b', params['b'])print('iterations dw=', grads['dw'])print('iterations db=', grads['db'])print('costs=', costs)Y_prediction = predict(w, b, X)print('Y_prediction=', Y_prediction)def model(X_train,Y_train,X_test,Y_test,num_iterations,learning_rate,print_cost):w,b=initialize_zeros(X_train.shape[0])params, grads,costs=optimize(w,b,X_train,Y_train,num_iterations,learning_rate,print_cost=True)Y_prediction_train=predict(params['w'],params['b'],X_train)Y_prediction_test = predict(params['w'], params['b'], X_test)print('train accuracy is {}'.format(np.mean(Y_prediction_train==Y_train)))print('test accuracy is {}'.format(np.mean(Y_prediction_test==Y_test)))d = {"costs":costs,'w':w,'b':b,'Y_prediction_train':Y_prediction_train,'Y_prediction_test':Y_prediction_test,'learning_rate':learning_rate,'num_iterations':num_iterations}return d
if __name__=='__main__':#test()train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()##traintrain_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0],train_set_x_orig.shape[1] *train_set_x_orig.shape[2] * 3).Ttrain_set_x = train_set_x_flatten / 255.train_set_y_flatten = train_set_y.reshape(train_set_y.shape[0], -1)###testtest_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0],test_set_x_orig.shape[1]* test_set_x_orig.shape[2] * 3).Ttest_set_x = test_set_x_flatten / 255.test_set_y_flatten = test_set_y.reshape(test_set_y.shape[0], -1)d=model(train_set_x,train_set_y_flatten,test_set_x,test_set_y_flatten,num_iterations=2000,learning_rate=0.002,print_cost=False)#paint costs lineplt.plot(d['costs'])#print(d['costs'])plt.xlabel('iteration')plt.ylabel('cost')plt.show()#用自带的小猫检测img=cv2.imread('images/my_image2.jpg')imgsize = cv2.resize(img, (64, 64), interpolation=cv2.INTER_CUBIC)cv2.imshow('imgsize', imgsize)cv2.waitKey(0)my_cat=np.array(imgsize.reshape(-1,1))#print(my_cat.shape)My_cat_prediction=predict(d['w'], d['b'], my_cat)print('My_cat_prediction',My_cat_prediction)

打印如下：

测试精度还行,由于样本量少，小猫还是预测错了。