原数据和代码链接：
链接：
https://pan.baidu.com/s/17ASpLDOKkB3mREGGb8QgBQ
提取码：rtpc
1.定义逻辑回归工具模块 lr_utils.py
# -*- coding: utf-8 -*-
"""
逻辑回归进行图像识别，工具模块
1.计算sigmoid函数
2.计算sigmoid的导函数
3.图像数据转化成向量
4.代价函数计算，L1代价，L2代价
"""
import numpy as np
#sigmoid函数
def basic_sigmoid(x):
'''
Compute sigmoid of x.
Arguments:
x -- A scalar
Return:
s -- sigmoid(x)
'''
sigmoid = 1.0 / (1 + np.exp(-x))
return sigmoid
#sigmoid的导函数
def sigmoid_derivative(x):
"""
Compute the gradient (also called the slope or derivative) of the sigmoid function with respect to its input x.
You can store the output of the sigmoid function into variables and then use it to calculate the gradient.
Arguments:
x -- A scalar or numpy array
Return:
ds -- Your computed gradient.
"""
s = basic_sigmoid(x)
ds = s * (1 - s)
return ds
#图像数据向量化：长宽高分别是width、height和depth的三维图像转化为二维向量
#image2vector() that takes an input of shape (length, height, 3) and returns a vector of shape (length*height*3, 1)
def image2vector(image):
"""
Argument:
image -- a numpy array of shape (length, height, depth)
Returns:
v -- a vector of shape (length*height*depth, 1)
"""
v = image.reshape(image.shape[0] * image.shape[1] * image.shape[2], 1)
return v
#L2范数归一化
def normalizeRows(x):
"""
Implement a function that normalizes each row of the matrix x (to have unit length).
Argument:
x -- A numpy matrix of shape (n, m)
Returns:
x -- The normalized (by row) numpy matrix. You are allowed to modify x.
"""
# Compute x_norm as the norm 2 of x. Use np.linalg.norm(..., ord = 2, axis = ..., keepdims = True)
x_norm = np.linalg.norm(x, axis = 1, keepdims = True)
# Divide x by its norm.
x = x / x_norm
return x
#利用Python的广播，计算softmax函数
def softmax(x):
"""Calculates the softmax for each row of the input x.
Your code should work for a row vector and also for matrices of shape (n, m).
Argument:
x -- A numpy matrix of shape (n,m)
Returns:
s -- A numpy matrix equal to the softmax of x, of shape (n,m)
"""
# Apply exp() element-wise to x. Use np.exp(...).
x_exp = np.exp(x)
# Create a vector x_sum that sums each row of x_exp. Use np.sum(..., axis = 1, keepdims = True).
x_sum = np.sum(x_exp, axis = 1, keepdims = True)
# Compute softmax(x) by dividing x_exp by x_sum. It should automatically use numpy broadcasting.
s = x_exp / x_sum
return s
#L1代价函数
def L1_loss(yhat, y):
"""
Arguments:
yhat -- vector of size m (predicted labels)
y -- vector of size m (true labels)
Returns:
loss -- the value of the L1 loss function defined above
"""
loss = np.sum(np.abs(y - yhat))
return loss
#L2代价函数
def L2_loss(yhat, y):
# loss = np.sum(np.power(yhat-y, 2))
loss = np.dot(yhat-y, (yhat-y).T)
return loss
if __name__ == '__main__':
print(basic_sigmoid(3))
# x = [1,2,3]
# print(basic_sigmoid(x)) #list会报错，要转成数组
x = np.array([1,2,3])
print(basic_sigmoid(x))
print(sigmoid_derivative(x)) #函数求导
#图像向量化
# This is a 3 by 3 by 2 array, typically images will be (num_px_x, num_px_y,3) where 3 represents the RGB values
image = np.array([[[ 0.67826139, 0.29380381],
[ 0.90714982, 0.52835647],
[ 0.4215251 , 0.45017551]],
[[ 0.92814219, 0.96677647],
[ 0.85304703, 0.52351845],
[ 0.19981397, 0.27417313]],
[[ 0.60659855, 0.00533165],
[ 0.10820313, 0.49978937],
[ 0.34144279, 0.94630077]]])
print(image.shape)
print ("image2vector(image) = " + str(image2vector(image)))
#数据L2归一化处理
x = np.array([[0,3,4],[1,6,4]])
print(normalizeRows(x))
##python 广播运算，就算softmax 函数,每一行相加为1
print(softmax(x))
#计算代价函数
yhat = np.array([.9, 0.2, 0.1, .4, .9])
y = np.array([1, 0, 0, 1, 1])
print('L1 loss:',L1_loss(yhat,y))
print('L2 loss:' ,L2_loss(yhat,y))
2.逻辑回归实现lr.py
# -*- coding: utf-8 -*-
"""
需求：逻辑回归预测图片中是否含有猫
实现思路：
1.加载数据
2.数据预处理：
图像可视化
数据格式整理，将图片数据向量化处理，长宽高分别是width、height和depth的三维图像转化为二维向量，即： (length, height, 3) 转为(length*height*3, 1)
数据标准化处理
3.参数初始化
4.对代价函数最小化，利用梯度下降法求解最优参数
计算参数对应于代价函数的梯度
求解最优参数
5. 利用最优的参数，对数据进行预测
6. 计算预测结果的准确率
7. 绘制代价值和迭代次数，以及学习速率的关系图
结论：学习速率过大，会导致模型不稳定，代价函数出现振荡，训练集的代价函数很低并不意味着模型的训练结果就是好的，可能会出现过拟合现象，要选择合适 的学习速率
- Different learning rates give different costs and thus different predictions results.
- If the learning rate is too large (0.01), the cost may oscillate up and down. It may even diverge (though in this example, using 0.01 still eventually ends up at a good value for the cost).
- A lower cost doesn't mean a better model. You have to check if there is possibly overfitting. It happens when the training accuracy is a lot higher than the test accuracy.
- In deep learning, we usually recommend that you:
- Choose the learning rate that better minimizes the cost function.
- If your model overfits, use other techniques to reduce overfitting.
小知识点：
np.squeeze
np.dot
数组.reshape
when you want to flatten a matrix X of shape (a,b,c,d) to a matrix X_flatten of shape (b ∗∗ c ∗∗ d, a) is to use:
X_flatten = X.reshape(X.shape[0], -1).T # X.T is the transpose of X
"""
import os
os.chdir(r'C:\Users\Administrator\Desktop\DL\逻辑回归\代码整理')
import numpy as np
import h5py #网页爬取
from matplotlib import pyplot as plt
import lr_utils
def load_dataset():
'''
函数说明： 加载数据
'''
train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")
train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features
train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels
test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")
test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features
test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels
classes = np.array(test_dataset["list_classes"][:]) # the list of classes
train_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
def image2vector(dataArr):
'''
函数说明：图像数据转换为列向量(209, 64, 64, 3)表示209张图片，每一张图片是（64，64，3）的图像数据
'''
data_flatten = dataArr.reshape(dataArr.shape[0], -1).T
print(data_flatten.shape)#行 代表特征数， 列 代表样本数
return data_flatten
#初始化参数
def initialize_with_zeros(dim):
"""
This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.
Argument:
dim -- size of the w vector we want (or number of parameters in this case)
Returns:
w -- initialized vector of shape (dim, 1)
b -- initialized scalar (corresponds to the bias)
"""
w = np.zeros((dim, 1))
b = 0
assert(w.shape == (dim, 1))
assert(isinstance(b, float) or isinstance(b, int))
return w, b
#正向传播：更新代价，反向传播：更新参数
def propagate(w, b, X, Y):
"""
Implement the cost function and its gradient for the propagation explained above
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of size (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)
Return:
cost -- negative log-likelihood cost for logistic regression
dw -- gradient of the loss with respect to w, thus same shape as w
db -- gradient of the loss with respect to b, thus same shape as b
Tips:
- Write your code step by step for the propagation. np.log(), np.dot()
"""
m = X.shape[1] #样本数
# FORWARD PROPAGATION (FROM X TO COST)
z = np.dot(w.T, X) + b
A = lr_utils.basic_sigmoid(z) # w维度(features,1) x维度(features,samples) b维度(1,1)
cost = -1 / m * np.sum(Y * np.log(A) + (1 - Y) * np.log(1 - A)) #计算代价函数
# BACKWARD PROPAGATION (TO FIND GRAD)
dw = 1 / m * np.dot(X, (A - Y).T)
db = 1 / m * np.sum(A - Y)
### END CODE HERE ###
assert(dw.shape == w.shape)
assert(db.dtype == float)
cost = np.squeeze(cost)
assert(cost.shape == ())
grads = {"dw": dw,
"db": db}
return grads, cost
#利用已经求得的梯度进行参数优化,并返回最后的优化参数，对应梯度值，和代价值
def optimize(w, b, X, Y, num_iterations=2000, learning_rate=0.1, print_cost = False):
"""
This function optimizes w and b by running a gradient descent algorithm
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of shape (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
num_iterations -- number of iterations of the optimization loop
learning_rate -- learning rate of the gradient descent update rule
print_cost -- True to print the loss every 100 steps
Returns:
params -- dictionary containing the weights w and bias b
grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.
Tips:
You basically need to write down two steps and iterate through them:
1) Calculate the cost and the gradient for the current parameters. Use propagate().
2) Update the parameters using gradient descent rule for w and b.
"""
costs = []
for i in range(num_iterations):
# Cost and gradient calculation (≈ 1-4 lines of code)
grads, cost = propagate(w, b, X, Y)
### END CODE HERE ###
# Retrieve derivatives from grads
dw = grads["dw"]
db = grads["db"]
# update rule (≈ 2 lines of code)
### START CODE HERE ###
w = w - learning_rate*dw
b = b - learning_rate*db
# Record the costs
if i % 100 == 0:
costs.append(cost)
# Print the cost every 100 training examples
if print_cost and i % 100 == 0:
print ("Cost after iteration %i: %f" %(i, cost))
params = {"w": w,
"b": b}
grads = {"dw": dw,
"db": db}
return params, grads, costs
def predict(w, b, X):
z = np.dot(w.T, X) + b
yhat = lr_utils.basic_sigmoid(z)
yhat = [ np.around(yhat[0,i]) for i in range(yhat.shape[1]) ] #四舍五入，yhat>0.5为1，<=0.5为0
yhat = np.array(yhat).reshape((1,-1))
return yhat
def accuracy(y, yhat):
rightNum = np.dot(y,yhat.T) + np.dot(1-y,(1-y).T)
accu = float(rightNum) / y.shape[1]
return accu
#合并所有函数 进行模型训练
def model(X_train, y_train, X_test, y_test, num_iterations = 2000, learning_rate = 0.1, print_cost = False):
#初始化参数
dim = X_train.shape[0] #样本特征数目
w, b = initialize_with_zeros(dim)
#利用训练集 优化参数
params, grads, costs = optimize(w, b, X_train, y_train, num_iterations, learning_rate, print_cost)
# print('参数： ',params,'\n代价函数值：',cost)
yhat_train = predict(params['w'], params['b'], X_train)
yhat_test = predict(params['w'], params['b'], X_test)
#模型评估：训练集准确率，测试集准确率
train_accuracy = accuracy(y_train, yhat_train)
test_accuracy = accuracy(y_test, yhat_test)
print('训练集准确率：%f%%'%train_accuracy, ', 测试集准确率: %f%%'%test_accuracy)
d = {"costs": costs,
"yhat_train" : yhat_train,
"yhat_test": yhat_test,
"w" : params['w'],
"b" : params['b'],
"learning_rate" : learning_rate,
"num_iterations": num_iterations}
return d
def plot_cost_iters(costs,learning_rate, num_iterations = 1000):
'''
学习率固定，绘制迭代次数和代价值关系图
'''
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations ')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
def plot_cost_learn(X_train, y_train, X_test, y_test, learning_rates, num_iterations = 1000, print_cost = False):
'''
迭代次数固定，绘制不同的学习率下的代价函数对应值
'''
for i in learning_rates:
print ("learning rate is: " + str(i))
modelRes = model(X_train, y_train, X_test, y_test, num_iterations, i, print_cost)
print ('\n' + "-------------------------------------------------------" + '\n')
#绘制图
plt.plot(modelRes["costs"], label= str(modelRes["learning_rate"]) )
plt.ylabel('cost')
plt.xlabel('iterations')
legend = plt.legend(loc='upper right', shadow=True)
frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()
def imageTest(w, b, my_image):
from scipy import ndimage
import scipy
# my_image = "cat_in_iran.jpg" # change this to the name of your image file
# We preprocess the image to fit your algorithm.
fname = "images/" + my_image
image = np.array(ndimage.imread(fname, flatten=False))
my_image = scipy.misc.imresize(image, size=(64,64)).reshape((1, 64*64*3)).T #my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T
my_predicted_image = predict(w, b, my_image)
plt.imshow(image)
print ( "预测结果为 : ",np.squeeze(my_predicted_image))
if __name__ == '__main__':
#加载数据
train_set_x, train_set_y, test_set_x, test_set_y, classes = load_dataset()
print(train_set_x.shape)
print(train_set_y.shape)
print(test_set_x.shape)
print(test_set_y.shape)
print(classes.shape)
print(classes)#数据类型为 numpy.bytes_ decode('utf-8') 将字节数据解码为utf-8
# 1代表有猫，0代表无猫
#可视化图片数据
index = 99
plt.imshow(train_set_x[index])
print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode('utf-8')+ "' picture.")
index = 102
plt.imshow(train_set_x[index])
print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode('utf-8')+ "' picture.")
##图像数据向量化
train_set_x_flatten = image2vector(train_set_x)#行 代表特征数， 列 代表样本数
test_set_x_flatten = image2vector(test_set_x)
#参数初始化
dim = train_set_x_flatten.shape[0]
w, b = initialize_with_zeros(dim)
print ("w = " + str(w))
print ("b = " + str(b))
#计算对应参数梯度值
grads, cost = propagate(w, b, train_set_x_flatten, train_set_y)
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))
print ("cost = " + str(cost))
#梯度下降法优化参数
X_train = train_set_x_flatten/255 #数据标准化
y_train = train_set_y
X_test = test_set_x_flatten/255 #数据标准化
y_test = test_set_y
dim = X_train.shape[0]
w, b = initialize_with_zeros(dim) #参数初始化
params, grads, cost = optimize(w, b, X_train, y_train, num_iterations=1000, learning_rate=0.005, print_cost = False)#参数优化
#模型训练
res = model(X_train, y_train, X_test, y_test, num_iterations =5000, learning_rate = 0.0005, print_cost = True)
#抽样查看
index = 6
plt.imshow(test_set_x[index])
print ("y = " + str(test_set_y[0,index]) + ", yhat = ",str(res['yhat_train'][0,index]))
#绘制在同一学习率下的不同迭代次数，对应的代价值
plot_cost_iters(res['costs'],res['learning_rate'],res['num_iterations'])
#固定迭代次数，学习速率和代价函数之间的关系图
plot_cost_learn(X_train, y_train, X_test, y_test, learning_rates=[0.01, 0.005, 0.001, 0.0005, 0.0001], num_iterations = 1500, print_cost = False)
#选择一张自己的图片进行预测
w = res['w']; b = res['b']
my_image = 'cat_in_iran.jpg'
imageTest(w, b, my_image)
my_image = 'my_image2.jpg'
imageTest(w, b, my_image)
3.部分代码运行结果
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