版权声明：流浪者 https://blog.csdn.net/gz153016/article/details/83829808
Logistic_regression.py
"""
You will learn to:
- Build the general architecture of a learning algorithm, including:
- Initializing parameters
- Calculating the cost function and its gradient
- Using an optimization algorithm (gradient descent)
- Gather all three functions above into a main model function, in the right order.
"""
import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage
from lr_utils import load_dataset
import skimage
"""
Problem Statement: You are given a dataset (“data.h5”) containing:
- a training set of m_train images labeled as cat (y=1) or non-cat (y=0)
- a test set of m_test images labeled as cat or non-cat
- each image is of shape (num_px, num_px, 3) where 3 is for the 3 channels (RGB).
Thus, each image is square (height = num_px) and (width = num_px).
图片都是正方形的，也就是width=height=num_px
我们的目的就是构建一个准确的分类方法，来区分输入的图片究竟是否是猫。
"""
# Loading the data(cat/non-cat)
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()
"""
之所以在上面的输入后面都加上_orig是因为接下来我们会对输入进行预处理，预处理之后，我们将其命名为train_set_x,test_set_x。
train_set_orig和test_set_orig的每一行数据都代表着一张图片，我们可以采用索引的方式来查看一下这个图片：
"""
# Example of a picture
index = 208
plt.imshow(train_set_x_orig[index])
print("y = " + str(train_set_y[:,index])+"it is a "+classes[np.squeeze(train_set_y[:, index])].decode("utf-8") + "' picture.")
plt.show()
print("------------------------------------------------------------")
"""
Exercise: Find the values for:
- m_train (number of training examples)
- m_test (number of test examples)
- num_px (= height = width of a training image)
Remember that train_set_x_orig is a numpy-array of shape (m_train, num_px, num_px, 3).
For instance, you can access m_train by writing train_set_x_orig.shape[0].
"""
### START CODE HERE ### (≈ 3 lines of code)
m_train = train_set_x_orig.shape[0]
m_test = test_set_x_orig.shape[0]
num_px = train_set_x_orig.shape[1]
### END CODE HERE ###
print ("Number of training examples: m_train = " + str(m_train))
print("Number of testing examples: m_test = " + str(m_test))
print("Height/Width of each image: num_px = " + str(num_px))
print("Each image is of size:("+str(num_px)+","+str(num_px)+",3)")
print("train_set_x shape:"+str(train_set_x_orig.shape))
print ("train_set_y shape: " + str(train_set_y.shape))
print ("test_set_x shape: " + str(test_set_x_orig.shape))
print ("test_set_y shape: " + str(test_set_y.shape))
print("------------------------------------------------------------")
"""
For convenience, you should now reshape images of shape (num_px, num_px, 3) in a numpy-array of shape (num_px ∗∗ num_px ∗∗ 3, 1).
After this, our training (and test) dataset is a numpy-array where each column represents a flattened image.
There should be m_train (respectively m_test) columns.
Exercise: Reshape the training and test data sets so that images of size (num_px, num_px, 3) are flattened into
single vectors of shape (num_px ∗∗ num_px ∗∗ 3, 1).
A trick 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
"""
train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0],-1).T
test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0],-1).T
print("train_set_x_flatten shape:"+str(train_set_x_flatten.shape))
print("train_set_y shape:"+str(train_set_y.shape))
print("test_set_x_flatten shape:"+str(test_set_x_flatten.shape))
print("test_set_y shape:"+str(test_set_y.shape))
print("sanity check after reshaping:"+str(train_set_x_flatten[0:5,0]))
print("------------------------------------------------------------")
"""
但是在图像中有一种简单的额归一化方法，效果也不错，就是每个样本都除以255（每个通道像素的最大值）。
归一化图像数据的方法为：
"""
train_set_x = train_set_x_flatten/255
test_set_x = test_set_x_flatten/255
"""
The main steps for building a Neural Network are:
1. Define the model structure (such as number of input features)
2. Initialize the model’s parameters
3. Loop:
- Calculate current loss (forward propagation)
- Calculate current gradient (backward propagation)
- Update parameters (gradient descent)
"""
#4.1 - Helper functions
# graded function:sigmoid(激活函数)
def sigmoid(z):
"""
Compute the sigmoid of z
Arguments:
z -- A scalar or numpy array of any size
:param z:
:return s-- sigmoid(z):
"""
s = 1/(1+np.exp(-z))
return s
print("sigmod([0,2])"+str(sigmoid(np.array([0,2]))))
print("-----------------------------------------------")
"""
4.2 - Initializing parameters
Exercise: Implement parameter initialization in the cell below.
You have to initialize w as a vector of zeros.
If you don’t know what numpy function to use,
look up np.zeros() in the Numpy library’s documentation.
"""
# Graded Function:Iinitialize_with_zeros
def initialize_with_zeros(dim):
"""
This function creates a vector of zeros of shape (dim,1)for w and initializes b to 0
:param dim -- size of the w vector we want (or number of parameters in this case):
:return:
w -- initialized vetor of shape(dim,1)
b -- initialized scalar (corrsponds 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
dim = 2
w,b = initialize_with_zeros(dim)
print("w = " + str(w))
print("b = " + str(b))
print("----------------------------------")
"""
4.3 - Forward and Backward propagation
Now that your parameters are initialized,
you can do the “forward” and “backward” propagation steps for learning the parameters.
Exercise: Implement a function propagate() that computes the cost function and its gradient.
"""
def propagate(w, b, X, Y):
"""
Implement the cost function ans 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.dot()
"""
m = X.shape[1]
# print("m:"+str(m))
# FORWARD PROPAGATION (FROM X TO COST)
### START CODE HERE ### (≈ 2 lines of code)
A = sigmoid(np.dot(w.T, X) + b) # compute activation
cost = -(1 / m) * np.sum(Y * np.log(A) + (1 - Y) * np.log(1 - A)) # compute cost
### END CODE HERE ###
# BACKWARD PROPAGATION (TO FIND GRAD)
### START CODE HERE ### (≈ 2 lines of code)
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
w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), np.array([[1,0]])
grads, cost = propagate(w, b, X, Y)
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))
print ("cost = " + str(cost))
print("---------------------------------------")
"""Optimization
You have initialized your parameters.
You are also able to compute a cost function and its gradient.
Now, you want to update the parameters using gradient descent.
Exercise: Write down the optimization function.
The goal is to learn w and b by minimizing the cost function J.
For a parameter θ, the update rule is θ=θ−α*dθ, where αis the learning rate.
"""
def optimize(w, b, X, Y, num_iterations, learning_rate, 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)
### START CODE HERE ###
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
### END CODE HERE ###
# 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
params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)
print ("w = " + str(params["w"]))
print ("b = " + str(params["b"]))
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))
print("----------------------------------------------")
"""
Exercise: The previous function will output the learned w and b.
We are able to use w and b to predict the labels for a dataset X.
Implement the predict() function. There is two steps to computing predictions:
Calculate Y^=A=σ(wTX+b)
Convert the entries of a into 0 (if activation <= 0.5) or 1 (if activation > 0.5), stores the predictions in a vector Y_prediction. If you wish, you can use an if/else statement in a for loop (though there is also a way to vectorize this).
"""
# GRADED FUNCTION: predict
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] = 1
else:
Y_prediction[0, i] = 0
assert (Y_prediction.shape == (1, m))
return Y_prediction
print("predictions ="+ str(predict(w,b,X)))
print("-----------------------------------------")
# GRADED FUNCTION: model
def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):
w, b = np.zeros((X_train.shape[0], 1)), 0
parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)
w = parameters["w"]
b = parameters["b"]
Y_prediction_test = predict(w, b, X_test)
Y_prediction_train = predict(w, b, X_train)
Y_prediction_test = predict(w, b, X_test)
Y_prediction_train = predict(w, b, X_train)
print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))
d = {"costs": costs,
"Y_prediction_test": Y_prediction_test,
"Y_prediction_train": Y_prediction_train,
"w": w,
"b": b,
"learning_rate": learning_rate,
"num_iterations": num_iterations}
return d
d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)
"""
训练的准确性接近100%，测试的准确性为70%，说明出现了过拟合的情况，后面会介绍方法解决这个问题。
如果想知道测试数据集中具体的图片预测情况：
"""
index = 1
plt.imshow(test_set_x[:,index].reshape((num_px,num_px,3)))
print("y = " + str(test_set_y[0,index])+", you predicted that it is a \"" + classes[int(d["Y_prediction_test"][0,index])].decode("utf-8") + "\" picture.")
plt.show()
"""
我们还可以打印出梯度和损失函数：
"""
# Plot learning curve (with costs)
costs = np.squeeze(d['costs'])
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title("Learning rate =" + str(d["learning_rate"]))
plt.show()
learning_rates = [0.01, 0.001, 0.0001]
models = {}
for i in learning_rates:
print ("learning rate is: " + str(i))
models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)
print ('\n' + "-------------------------------------------------------" + '\n')
for i in learning_rates:
plt.plot(np.squeeze(models[str(i)]["costs"]), label= str(models[str(i)]["learning_rate"]))
plt.ylabel('cost')
plt.xlabel('iterations')
legend = plt.legend(loc='upper center', shadow=True)
frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()
## START CODE HERE ## (PUT YOUR IMAGE NAME)
my_image = "my_image2.jpg" # change this to the name of your image file
# We preprocess the image to fit your algorithm.
fname = "D:/BaiduYunDownload/image/" + my_image
image = np.array(ndimage.imread(fname, flatten=False))
my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T
my_predicted_image = predict(d["w"], d["b"], my_image)
plt.imshow(image)
print("y = " + str(np.squeeze(my_predicted_image)) + ", your algorithm predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") + "\" picture.")
lr_utils.py
import numpy as np
import h5py
def 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 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
第二版：逻辑回归代码
import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage
from lr_utils import load_dataset
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()
# Example of a picture
index = 208
plt.imshow(train_set_x_orig[index])
#这个代码不清楚
print ("y = " + str(train_set_y[:,index]) + ", it's a '" + classes[np.squeeze(train_set_y[:,index])].decode("utf-8") + "' picture.")
m_train = None
m_test = None
num_px = None
m_train = train_set_x_orig.shape[0]
m_test = test_set_x_orig.shape[0]
num_px = train_set_x_orig.shape[1]
print("-----------数据集信息------------------")
print(str(m_train))
print(str(m_test))
print(str(num_px))
print("(" + str(num_px) + "," + str(num_px) + ",3"+")")
print(str(train_set_x_orig.shape))
print(train_set_y.shape)
print(str(test_set_x_orig.shape))
print(test_set_y.shape)
print("-----------------------------")
train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
print("---------------reshape---------")
print(str(train_set_x_flatten.shape))
print(str(train_set_y.shape))
print(str(test_set_x_flatten.shape))
print(str(test_set_y.shape))
print(str(train_set_x_flatten[0:5,0]))
print("------------------------")
train_set_x = train_set_x_flatten/255
test_set_x = test_set_x_flatten/255
def sigmoid(z):
s = 1/(1 + np.exp(-z))
return s
print("------------测试激活函数-------------")
print("sigmoid([0, 2]) = " + str(sigmoid(np.array([0,2]))))
print("------------测试激活函数------------")
def initialize_with_zeros(dim):
w, b = np.zeros((dim,1)), 0
assert(w.shape == (dim, 1))
assert (isinstance(b, float) or isinstance(b, int))
return w, b
print("----------测试初始化-----------")
dim = 2
w, b = initialize_with_zeros(dim)
print("w = " + str(w))
print(str(w.shape))
print("b = " + str(b))
print("----------测试初始化-----------")
def propagate(w, b, X, Y):
m = X.shape[1]
A = sigmoid(np.dot(w.T, X)+b)
cost = -(1/m)*np.sum(Y*np.log(A) + (1-Y)*np.log(1-A))
dw = 1/m*np.dot(X,(A - Y).T)
db = 1/m*np.sum(A - Y)
assert (dw.shape == w.shape)
assert (db.dtype == float)
cost = np.squeeze(cost)
assert (cost.shape == ())
grads = {"dw": dw,
"db": db}
return grads, cost
print("------------传播---------------------")
w, b, X, Y, = np.array([[1.],[2.]]), 2., np.array([[1.,2.,-1.], [3.,4.,-3.2]]), np.array([[1,0,1]])
grads, cost = propagate(w, b, X, Y)
print("dw = " + str(grads["dw"]))
print("db = " + str(grads["db"]))
print("cost = " + str(cost))
print("------------传播---------------------")
def optimizie(w, b, X, Y,num_iterations, learning_rate, print_cost = False):
costs = []
for i in range(num_iterations):
grads, cost = propagate(w, b, X, Y)
dw = grads["dw"]
db =grads["db"]
w = w - learning_rate * dw
b = b - learning_rate * db
if i % 100 == 0:
costs.append(cost)
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
params, grads, costs = optimizie(w, b, X, Y, num_iterations=100, learning_rate=0.009, print_cost=False)
print("-----------------优化---------------")
print("w = " + str(params["w"]))
print("b = " + str(params["b"]))
print("dw= " + str(grads["dw"]))
print("db = " + str(grads["db"]))
print("-----------------优化---------------")
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)
# print("A.shape:" + str(A.shape))
# print("A[0,0]"+ str(A[0,2]))
# A[0,0],A[0,1],A[0,2] 遍历了 A
for i in range(A.shape[1]):
if A[0, i]<=0.5:
Y_prediction[0, i] = 0
else:
Y_prediction[0, i] = 1
assert(Y_prediction.shape == (1, m))
return Y_prediction
print("--------------------预测--------------")
w = np.array([[0.1124579],[0.23106775]])
b = -0.3
x = np.array([[1.,-1.1,-3.2],[1.2,2.,0.1]])
print ("predictions = " + str(predict(w, b, X)))
print("--------------------预测--------------")
def model(X_train, Y_train, X_test, Y_test, num_iterations = 200, learning_rate = 0.5, print_cost = False):
w, b =initialize_with_zeros(X_train.shape[0])
parameters, grads, costs = optimizie(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)
w = parameters["w"]
b = parameters["b"]
Y_prediction_test = predict(w, b, X_test)
Y_prediction_train = predict(w, b, X_train)
print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))
d = {"costs": costs,
"Y_prediction_test": Y_prediction_test,
"Y_prediction_train": Y_prediction_train,
"w": w,
"b": b,
"learning_rate": learning_rate,
"num_iterations": num_iterations}
return d
d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations =1000, learning_rate = 0.005, print_cost = True)
print("-------------尝试不同的学习率-------------")
learning_rates = [0.01, 0.001, 0.0001]
models = {}
for i in learning_rates:
print ("learning rate is: " + str(i))
models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)
print ('\n' + "-------------------------------------------------------" + '\n')
for i in learning_rates:
plt.plot(np.squeeze(models[str(i)]["costs"]), label= str(models[str(i)]["learning_rate"]))
plt.ylabel('cost')
plt.xlabel('iterations')
legend = plt.legend(loc='upper center', shadow= True)
frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()
## START CODE HERE ## (PUT YOUR IMAGE NAME)
my_image = "my_cat.jpg" # change this to the name of your image file
## END CODE HERE ##
# 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=(num_px,num_px)).reshape((1, num_px*num_px*3)).T #待解释
my_predicted_image = predict(d["w"], d["b"], my_image)
plt.imshow(image)
print("y = " + str(np.squeeze(my_predicted_image)) + ", your algorithm predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") + "\" picture.")