# 深入浅出Logistic Regression之二分类

## 实战逻辑回归二元分类

### 1.加载数据集

```import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage
train_dataset = h5py.File('./train_catvnoncat.h5', "r")
#训练数据集
train_set_x_orig = np.array(train_dataset["train_set_x"][:])
#训练数据集的类别
train_set_y_orig = np.array(train_dataset["train_set_y"][:])
test_dataset = h5py.File('./test_catvnoncat.h5', "r")
#测试数据集
test_set_x_orig = np.array(test_dataset["test_set_x"][:])
#测试数据集的类别
test_set_y_orig = np.array(test_dataset["test_set_y"][:])
#所有数据的分类集合
classes = np.array(test_dataset["list_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```

### 2.得到数据的信息和简单的数据处理

```#训练数据集实例的size
m_train = train_set_x_orig.shape[0]
#测试数据集实例的size
m_test = test_set_x_orig.shape[0]
#每个实例的px
num_px = train_set_x_orig.shape[1]

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))
## 输出为
Number of training examples: m_train = 209
Number of testing examples: m_test = 50
Height/Width of each image: num_px = 64
Each image is of size: (64, 64, 3)
train_set_x shape: (209, 64, 64, 3)
train_set_y shape: (1, 209)
test_set_x shape: (50, 64, 64, 3)
test_set_y shape: (1, 50)```

X_flatten = X.reshape(X.shape[0], -1).T

```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))
##输出
train_set_x_flatten shape: (12288, 209)
train_set_y shape: (1, 209)
test_set_x_flatten shape: (12288, 50)
test_set_y shape: (1, 50)
#为了我们更方便的进行机器学习，我们需要对数据进行预处理，标准化数据。
train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.```

### 3.开始建立我们算法模型

#### 3.1 帮助函数(sigmod function)和初始化参数模型

```def sigmoid(z):
"""
Compute the sigmoid of z
Arguments:
z -- A scalar or numpy array of any size.
Return:
s -- sigmoid(z)
"""
s = 1/(1+np.exp(-z))
return s
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```

### 前向传播和反向传播梯度下降算法

```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]
# FORWARD PROPAGATION (FROM X TO COST)
A = sigmoid(w.T.dot(X)+b)                                     # compute activation
cost = -1/m*np.sum(np.dot(np.log(A),Y.T)+np.dot(np.log(1-A),(1-Y).T))                        # compute cost
# BACKWARD PROPAGATION (TO FIND GRAD)
dw = 1/m*np.dot(X,(A-Y).T)
db = 1/m*np.sum(np.subtract(A,Y))
### END CODE HERE ###
assert(dw.shape == w.shape)
assert(db.dtype == float)
cost = np.squeeze(cost)
assert(cost.shape == ())
"db": db}
## 下面我们需要进行优化求解
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 ###

# 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}

"db": db}

### 进行预测

```def predict(w, b, X):
'''
Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)

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)

Returns:
Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X
'''

m = X.shape[1]
Y_prediction = np.zeros((1,m))
w = w.reshape(X.shape[0], 1)

# Compute vector "A" predicting the probabilities of a cat being present in the picture
A = sigmoid(np.dot(w.T,X)+b)
Y_prediction=np.where(A<=0.5,0,1)
assert(Y_prediction.shape == (1, m))

return Y_prediction```

### model

```# GRADED FUNCTION: model

def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):
"""
Builds the logistic regression model by calling the function you've implemented previously

Arguments:
X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)
Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)
X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)
Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)
num_iterations -- hyperparameter representing the number of iterations to optimize the parameters
learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()
print_cost -- Set to true to print the cost every 100 iterations

Returns:
d -- dictionary containing information about the model.
"""

### START CODE HERE ###

# initialize parameters with zeros (≈ 1 line of code)
dim = X_train.shape[0]
w, b = initialize_with_zeros(dim)
# Gradient descent (≈ 1 line of code)
parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations , learning_rate , print_cost )

# Retrieve parameters w and b from dictionary "parameters"
w = parameters["w"]
b = parameters["b"]

# Predict test/train set examples (≈ 2 lines of code)
Y_prediction_train = predict(w,b,X_train)
Y_prediction_test = predict(w,b,X_test)

### END CODE HERE ###

# Print train/test Errors
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```

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