2_2逻辑回归在神经网络中的实现

# 2_2Logistic Regression with a Neural Network mindset#

2_2逻辑回归在神经网络中的实现

Welcome to your first (required) programming assignment! You will build a

logistic regression classifier to recognize cats. This assignment will step

you through how to do this with a Neural Network mindset, and so will also

hone your intuitions about deep learning.

Instructions:

- 注意事项：Do not use loops (for/while) in your code, unless the instructions explicitly

ask you to do so.

#

- 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.

## 1、准备实验所要用的包

numpy用于向量计算，h5py识别格式是H5 file的图片，matplotlib画图

First, let’s run the cell below to import all the packages that you will

need during this assignment.

- numpy is the fundamental package for scientific computing

with Python.

- h5py is a common package to interact with a dataset

that is stored on an H5 file.

- matplotlib is a famous library to plot graphs in Python.

- PIL and scipy

are used here to test your model with your own picture at the end.

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

get_ipython().magic(‘matplotlib inline’)

## 2 - 熟悉我们的实验数据(Overview of the Problem set)

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).

You will build a simple image-recognition algorithm that can correctly classify pictures as cat or non-cat.

Let’s get more familiar with the dataset. Load the data by running the following code.

Loading the data (cat/non-cat)

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

train_dataset数据集是209个图片，每个图片都是64*64像素，3表示3种颜色，Red,Blue,Green

test_dataset数据集是50个图片，每个图片都是64*64像素，3表示3种颜色，Red,Blue,Green

We added “_orig” at the end of image datasets (train and test) because we are going to

preprocess them. After preprocessing, we will end up with train_set_x and test_set_x

(the labels train_set_y and test_set_y don’t need any preprocessing).

Each line of your train_set_x_orig and test_set_x_orig is an array representing an image.

You can visualize an example by running the following code. Feel free also to change the

index` value and re-run to see other images.

2.1显示一个不太清晰的图片

index = 5
plt.imshow(train_set_x_orig[index])
print (“y = ” + str(train_set_y[:, index]) + “, it’s a ‘” +
classes[np.squeeze(train_set_y[:, index])].decode(“utf-8”) + “’ picture.”)
plt.show()

classes是一个ndarry类型，保存2个值，一个是b’non-cat’,另一个是b’cat’

np.squeeze是去掉数组中维数为1的向量，如果不加这个函数，decode无法工作

train_set_y是一个(1,209)的一个行向量，train_set_y[:,index]意思是第index列元素的值

Many software bugs in deep learning come from having matrix/vector dimensions that don’t fit.

If you can keep your matrix/vector dimensions straight you will go a long way toward eliminating

many bugs.

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].

2.2输出这几个关键参数的含义

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 (“Number of training examples: m_train = ” + str(m_train))#m_train = 209
print (“Number of testing examples: m_test = ” + str(m_test))#m_test = 50
print (“Height/Width of each image: num_px = ” + str(num_px))#num_px = 64
print (“Each image is of size: (” + str(num_px) + “, ” + str(num_px) + “, 3)”)#(64, 64, 3)
print (“train_set_x shape: ” + str(train_set_x_orig.shape))#(209, 64, 64, 3)
print (“train_set_y shape: ” + str(train_set_y.shape))#(1, 209)，行向量
print (“test_set_x shape: ” + str(test_set_x_orig.shape))#(50, 64, 64, 3)
print (“test_set_y shape: ” + str(test_set_y.shape))#(1, 50)，行向量

**Expected Output for m_train=209, m_test=50 and num_px为64:

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.

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

Reshape the training and test examples

2.3自己添加，测试用的，目的是搞懂图片像素的维度

“””
print(“train_set_x_orig:”)
print(train_set_x_orig)

print(“train_set_x_orig.shape[0]:”)
print(train_set_x_orig.shape[0])#209

print(“train_set_x_orig.shape[1]:”)
print(train_set_x_orig.shape[1])#64

print(“train_set_x_orig.shape[2]:”)
print(train_set_x_orig.shape[2])#64

print(“train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).shape:”)
print(train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).shape)#值为209,12288
“””
train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T#值为12288,209的一个向量
test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T#值为12288,50的一个向量
print(“train_set_x_flatten:”,train_set_x_flatten)

print (“train_set_x_flatten shape: ” + str(train_set_x_flatten.shape))#值为12288,209
print (“train_set_y shape: ” + str(train_set_y.shape))#值为1,209
print (“test_set_x_flatten shape: ” + str(test_set_x_flatten.shape))#值为12288,50
print (“test_set_y shape: ” + str(test_set_y.shape))#值为1,50
print (“sanity check after reshaping: ” + str(train_set_x_flatten[0:5,0]))

输出第0列从第0个到第4个元素，值为[17 31 56 22 33]

To represent color images, the red, green and blue channels (RGB) must be specified for each pixel,

and so the pixel value is actually a vector of three numbers ranging from 0 to 255.

One common preprocessing step in machine learning is to center and standardize your dataset,

meaning that you substract the mean of the whole numpy array from each example, and then divide

each example by the standard deviation of the whole numpy array. But for picture datasets, it is

simpler and more convenient and works almost as well to just divide every row of the dataset

by 255 (the maximum value of a pixel channel).

initial inputs in order to observe neuron activations. Then you backpropogate with the

gradients to train the model

But, it is extremely important for each feature to have a similar range such that our gradients

don’t explode. You will see that more in detail later in the lectures. !–>

Let’s standardize our dataset.

train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.

What you need to remember:

Common steps for pre-processing a new dataset are:

(1)Figure out the dimensions and shapes of the problem (m_train, m_test, num_px, …)

(2)Reshape the datasets such that each example is now a vector of size (num_px*num_px* 3, 1)

(3)”Standardize” the data

## 3 - General Architecture of the learning algorithm

## 3 - ##一般的方法流程

It’s time to design a simple algorithm to distinguish cat images from non-cat images.

应该用一个算法去区分猫的图片和非猫的图片

You will build a Logistic Regression, using a Neural Network mindset. The following

Figure explains why Logistic Regression is actually a very simple Neural Network!

The cost is then computed by summing over all training examples:

Key steps:

In this exercise, you will carry out the following steps:

(1)Initialize the parameters of the model

(2)Learn the parameters for the model by minimizing the cost

(3)Use the learned parameters to make predictions (on the test set)

(4)Analyse the results and conclude

## 4 - Building the parts of our algorithm

## 4 - 构建自己的算法

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)

You often build 1-3 separately and integrate them into one function we call model().

### 4.1 - 激活函数(Helper functions)

Using your code from “Python Basics”, implement sigmoid(). As you’ve seen in the

figure above, you need to compute sigmoid( w^T x + b) to make predictions. Use np.exp().

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

print (“sigmoid([0, 2]) = ” + str(sigmoid(np.array([0,2]))))#值为[ 0.5 0.88079708]

### 4.2 - 初始化参数(Initializing parameters)

初始化w和b的值

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: 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)

w = np.zeros((dim, 1))#生成一个dim行，1列的向量
b = 0

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

测试上面的initialize_with_zeros函数

dim = 2
w, b = initialize_with_zeros(dim)
print (“w = ” + str(w))#w的值为[[0][0]]
print (“b = ” + str(b))#b的值为0

For image inputs, w will be of shape (num_px*num_px*3, 1).

### 4.3 - 正向传播和反向传播(Forward and Backward propagation)

Now that your parameters are initialized, you can do the “forward” and “backward”

propagation steps for learning the parameters.

Implement a function propagate() that computes the cost function and its gradient.

Forward Propagation:

- You get X

- You compute A

- You calculate the cost function: J

定义传播函数

def propagate(w, b, X, Y):

Implement the cost function and its gradient for the propagation explained above

input 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)前向传播
#print("w.T:",w.T)#w.T: [[1 2]]
#print("np.dot(w.T,X):",np.dot(w.T,X))#np.dot(w.T,X): [[ 7 10]]
#print("np.dot(w.T,X)+b:",np.dot(w.T,X)+b)#np.dot(w.T,X)+b: [[ 9 12]]

A=sigmoid(np.dot(w.T,X)+b)
#print("A1:",A)#A的值为0.99987661，0.99999386

cost=-1/m*np.sum(Y*np.log(A)+(1-Y)*np.log(1-A))

# print(“cost1:”,cost)

# BACKWARD PROPAGATION (TO FIND GRAD)反向传播
dw=1/m*np.dot(X,(A-Y).T)#dw/dz的值
db=1/m*np.sum(A-Y)#

assert(dw.shape == w.shape)
assert(db.dtype == float)
cost = np.squeeze(cost)#把shape为1的维度去掉
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(“w=”,w)#输出w的值[[ 1][ 2]]
print(“b=”,b)#输出b的值为2
print (“dw = ” + str(grads[“dw”]))#dw = [[ 0.99993216][ 1.99980262]]
print (“db = ” + str(grads[“db”]))#db = 0.499935230625
print (“cost2 = ” + str(cost))#cost = 6.00006477319

“”“输出结果为：
w = [[ 1][ 2]]
b = 2
dw = [[ 0.99993216][ 1.99980262]]，在慢慢变小
db = 0.499935230625，在慢慢变小
cost = 6.00006477319
“”“

### 4.4 优化 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.

Write down the optimization function. The goal is to learn w and b by minimizing

the cost function J, For a parameter theta,the update rule is theta = theta - alpha*theta

where alpha is the learning rate.

GRADED FUNCTION: optimize

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)

    grads, cost = propagate(w, b, X, Y)
    # Retrieve derivatives from grads
    dw = grads["dw"]#dw为[0.99993215,1.999802619]
    db = grads["db"]#db为0.499935230625

    # update rule (≈ 2 lines of code)
    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

w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), np.array([[1,0]])
params, grads, costs = optimize(w, b, X, Y, num_iterations= 1000, 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(“costs:”,costs)

“””
输出结果为：
w = [[ 0.1124579 ][ 0.23106775]]
b = 1.55930492484
dw = [[ 0.90158428][ 1.76250842]]，变化幅度比上次大
db = 0.430462071679，变化幅度比上次大
costs: 根据观察，迭代次数越多，逐步变小
(1、)num_iterations= 100时，cost的值为：
[6.0000647731922054, 5.9528238404019787, 5.9055835580118288, 5.8583439731360443
1.7829431852935509, 1.7418687698781761, 1.7012327949342381,..1.4681764883914099]
(2、)num_iterations= 1000时，cost的值为：
[6.0000647731922054, 5.9528238404019787, 5.9055835580118288, 5.8583439731360443,
1.7829431852935509, 1.7418687698781761, 1.7012327949342381,..1.4681764883914099
….0.45007550362095522, 0.44996277790930794, 0.44985009639693085…0.44872570768284936]
“”“

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:

1. Calculate sigmod(w.T*x+b)

2. 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/elsestatement in afor` loop (though there is also a way to vectorize this).

4.5 函数预测(predict)

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)
#print("A2:",A)用于测试
for i in range(A.shape[1]):
    # Convert probabilities A[0,i] to actual predictions p[0,i]
    if A[0, i] <= 0.5:#A的值为: [[ 0.99987661  0.99999386]]
        Y_prediction[0, i] = 0
    else:
        Y_prediction[0, i] = 1

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

w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), np.array([[1,0]])
print (“predictions = ” + str(predict(w, b, X)))#预测的结果为[[1,1]]

You’ve implemented several functions that:

(1)Initialize (w,b)

(2)Optimize the loss iteratively to learn parameters (w,b):

- computing the cost and its gradient

- updating the parameters using gradient descent

(3)Use the learned (w,b) to predict the labels for a given set of examples

## 5 - 在模型中合并所有函数(Merge all functions into a model )

You will now see how the overall model is structured by putting together all the building blocks

(functions implemented in the previous parts) together, in the right order.

Implement the model function. Use the following notation:

- Y_prediction for your predictions on the test set

- Y_prediction_train for your predictions on the train set

- w, costs, grads for the outputs of optimize()

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.
"""
# (1)initialize parameters with zeros (≈ 1 line of code)
w, b = initialize_with_zeros(X_train.shape[0])

# (2)Gradient descent
parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)

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

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

# (5)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

d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000,
learning_rate = 0.005, print_cost = True)

print(“d[‘costs’]:”,d[‘costs’])#输出costs的值

Comment:Training accuracy is close to 100%. This is a good sanity check: your model is working

and has high enough capacity to fit the training data. Test error is 68%. It is actually not bad for

this simple model, given the small dataset we used and that logistic regression is a linear classifier.

But no worries, you’ll build an even better classifier next week!

Also, you see that the model is clearly overfitting the training data. Later in this specialization

you will learn how to reduce overfitting, for example by using regularization. Using the code

below (and changing the index variable) you can look at predictions on pictures of the test set.

Example of a picture that was wrongly classified.

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()

Plot cost function and the gradients learning curve (with costs)

costs = np.squeeze(d[‘costs’])

print(“costs2:”,costs)用于测试

plt.plot(costs)
plt.ylabel(‘cost’)
plt.xlabel(‘iterations (per hundreds)’)
plt.title(“Learning rate =” + str(d[“learning_rate”]))
plt.show()

Interpretation:

You can see the cost decreasing. It shows that the parameters are being learned.

However, you see that you could train the model even more on the training set.

Try to increase the number of iterations in the cell above and rerun the cells. You

might see that the training set accuracy goes up, but the test set accuracy goes down.

This is called overfitting.

## 6 - 特征值分析（Further analysis (optional/ungraded exercise)）

Congratulations on building your first image classification model. Let’s analyze it

further, and examine possible choices for the learning rate

#### Choice of learning rate

#(1)In order for Gradient Descent to work you must choose the learning rate wisely.

The learning rate determines how rapidly we update the parameters. If the learning rate

is too large we may “overshoot” the optimal value. Similarly, if it is too small we

will need too many iterations to converge to the best values. That’s why it is crucial

to use a well-tuned learning rate.

#(2)Let’s compare the learning curve of our model with several choices of learning rates

Run the cell below. This should take about 1 minute. Feel free also to try different

values than the three we have initialized the learning_rates variable to contain,

and see what happens.

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(“models[str(i)][costs]:”, models[str(i)][“costs”])
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()

“””
程序输出结果为：
learning rate is: 0.01
train accuracy: 99.52153110047847 %

test accuracy: 68.0 %

learning rate is: 0.001
train accuracy: 88.99521531100478 %

test accuracy: 64.0 %

learning rate is: 0.0001
train accuracy: 68.42105263157895 %
test accuracy: 36.0 %
“”“

“””

- 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:

(1)Choose the learning rate that better minimizes the cost function.

(2)If your model overfits, use other techniques to reduce overfitting.

(We’ll talk about this in later videos.)

“”“

## 7 - 用自己的图片测试模型(Test with your own image (optional/ungraded exercise) )

Congratulations on finishing this assignment. You can use your own image and

see the output of your model. To do that:

1. Click on “File” in the upper bar of this notebook, then click “Open”

to go on your Coursera Hub.

2. Add your image to this Jupyter Notebook’s directory, in the “images” folder

3. Change your image’s name in the following code

4. Run the code and check if the algorithm is right (1 = cat, 0 = non-cat)!

my_image = “xiangmao.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=(num_px,num_px)).reshape((1, num_px*num_px*3)).T

改变图片的尺寸，变为训练集的大小

my_predicted_image = predict(d[“w”], d[“b”], my_image)

plt.imshow(image)
plt.show()
print(“y = ” + str(np.squeeze(my_predicted_image)) + “, your algorithm predicts a \”” +
classes[int(np.squeeze(my_predicted_image)),].decode(“utf-8”) + “\” picture.”)

What to remember from this assignment:

1. Preprocessing the dataset is important.

2. You implemented each function separately: initialize(), propagate(), optimize(). Then you built a model().

3. Tuning the learning rate (which is an example of a “hyperparameter”) can make a big difference to the

algorithm. You will see more examples of this later in this course!

Finally, if you’d like, we invite you to try different things on this Notebook. Make sure you submit before

trying anything. Once you submit, things you can play with include:

- Play with the learning rate and the number of iterations

- Try different initialization methods and compare the results

- Test other preprocessings (center the data, or divide each row by its standard deviation)

Bibliography:

- http://www.wildml.com/2015/09/implementing-a-neural-network-from-scratch/

- https://stats.stackexchange.com/questions/211436/why-do-we-normalize-images-by-subtracting-the-datasets-image-mean-and-not-the-c