deeplearning_LogisticRegressionwithaNeuralNetworkmindset

此文为deeplearning课程第二周的编程作业实现一个逻辑回归分类器（识别一个图片中有没有猫）

需要用到的库

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

其中lr_utils中load_dataset是一个用于取得数据的方法，代码实现如下

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

加载数据

train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

建立神经网络的基本步骤

Define the model structure (such as number of input features)

Initialize the model’s parameters

Loop:

Calculate current loss (forward propagation)

Calculate current gradient (backward propagation)

Update parameters (gradient descent)

需要用到的方法

逻辑回归中的sigmod方法

公式：

# GRADED FUNCTION: sigmoid

def sigmoid(z):
"""
Compute the sigmoid of z

Arguments:
z -- A scalar or numpy array of any size.

Return:
s -- sigmoid(z)
"""

### START CODE HERE ### (≈ 1 line of code)
s = 1/(1+np.exp(-z))
### END CODE HERE ###

return s

初始化参数w,b

assert方法用于检查我们初始化的shape是否是正确的

# GRADED FUNCTION: initialize_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.

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)
"""

### START CODE HERE ### (≈ 1 line of code)
w = np.zeros((dim,1))
b = 0
### END CODE HERE ###

assert(w.shape == (dim, 1))
assert(isinstance(b, float) or isinstance(b, int))

return w, b

前向传播与反向传播

返回梯度和代价函数

公式：

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)
### 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

梯度下降使得代价函数最小

返回代价函数最小时的参数w,b ; 梯度；代价函数

公式：

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

预测predict

根据已经算好的参数w,b；对输入的X进行预测，判断这张图片是不是猫

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
### START CODE HERE ### (≈ 1 line of code)
A = sigmoid(np.dot(w.T,X)+b)
### END CODE HERE ###

for i in range(A.shape[1]):

# Convert probabilities A[0,i] to actual predictions p[0,i]
### START CODE HERE ### (≈ 4 lines of code)
if A[0,i]<=0.5:
Y_prediction[0,i] = 0
else:
Y_prediction[0,i] = 1
### END CODE HERE ###

assert(Y_prediction.shape == (1, m))

return Y_prediction

将这些方法组合的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_p
4000
x * 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)
w, b = initialize_with_zeros(X_train.shape[0])

# Gradient descent (≈ 1 line of code)；对训练集进行训练，得到最优的参数
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)；使用w,b这两个最优的参数对训练集合测试集进行判断
Y_prediction_test = predict(w,b,X_test)
Y_prediction_train = predict(w,b,X_train)

### END CODE HERE ###

# Print train/test Errors 分别输出训练集合测试集的误差
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)

最终结果是

Expected Output:

**Train Accuracy**	99.04306220095694 %
**Test Accuracy**	70.0 %

由此可见，此模型存在过拟合的现象

自己输入图片判断

## START CODE HERE ## (PUT YOUR IMAGE NAME)
my_image = "my_image.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))
#调整图片至需要的矩阵大小及shape
my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T
#使用已有参数w,b进行预测(d由之前的model得到)
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.")