吳恩達deeplearning.ai課程作業，自己寫的答案。
補充說明：
1. 評論中總有人問為什么直接復制這些notebook運行不了？請不要直接復制粘貼，不可能運行通過的，這個只是notebook中我們要自己寫的那部分，要正確運行還需要其他py文件，請自己到GitHub上下載完整的。這里的部分僅僅是參考用的，建議還是自己按照提示一點一點寫，如果實在卡住了再看答案。個人覺得這樣才是正確的學習方法，況且作業也不算難。
2. 關于評論中有人說我是抄襲，注釋還沒別人詳細，復制下來還運行不過。答復是：做伸手黨之前，請先搞清這個作業是干什么的。大家都是從GitHub上下載原始的作業，然后根據代碼前面的提示（通常會指定函數和公式）來編寫代碼，而且后面還有expected output供你比對，如果程序正確，結果一般來說是一樣的。請不要無腦噴，說什么跟別人的答案一樣的。說到底，我們要做的就是，看他的文字部分，根據提示在代碼中加入部分自己的代碼。我們自己要寫的部分只有那么一小部分代碼。
3. 由于實在很反感無腦噴子，故禁止了下面的評論功能，請見諒。如果有問題，請私信我，在力所能及的范圍內會盡量幫忙。

Deep Neural Network for Image Classification: Application

When you finish this, you will have finished the last programming assignment of Week 4, and also the last programming assignment of this course!

You will use use the functions you’d implemented in the previous assignment to build a deep network, and apply it to cat vs non-cat classification. Hopefully, you will see an improvement in accuracy relative to your previous logistic regression implementation.

After this assignment you will be able to:
- Build and apply a deep neural network to supervised learning.

Let’s get started!

1 - Packages

Let’s first import all the packages that you will need during this assignment.
- numpy is the fundamental package for scientific computing with Python.
- matplotlib is a library to plot graphs in Python.
- h5py is a common package to interact with a dataset that is stored on an H5 file.
- PIL and scipy are used here to test your model with your own picture at the end.
- dnn_app_utils provides the functions implemented in the “Building your Deep Neural Network: Step by Step” assignment to this notebook.
- np.random.seed(1) is used to keep all the random function calls consistent. It will help us grade your work.

import time import numpy as np import h5py import matplotlib.pyplot as plt import scipy from PIL import Image from scipy import ndimage from dnn_app_utils_v2 import *%matplotlib inline plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots plt.rcParams['image.interpolation'] = 'nearest' plt.rcParams['image.cmap'] = 'gray'%load_ext autoreload %autoreload 2np.random.seed(1)

2 - Dataset

You will use the same “Cat vs non-Cat” dataset as in “Logistic Regression as a Neural Network” (Assignment 2). The model you had built had 70% test accuracy on classifying cats vs non-cats images. Hopefully, your new model will perform a better!

Problem Statement: You are given a dataset (“data.h5”) containing:
- a training set of m_train images labelled as cat (1) or non-cat (0)
- a test set of m_test images labelled as cat and non-cat
- each image is of shape (num_px, num_px, 3) where 3 is for the 3 channels (RGB).

Let’s get more familiar with the dataset. Load the data by running the cell below.

train_x_orig, train_y, test_x_orig, test_y, classes = load_data()

The following code will show you an image in the dataset. Feel free to change the index and re-run the cell multiple times to see other images.

# Example of a picture index = 7 plt.imshow(train_x_orig[index]) print ("y = " + str(train_y[0,index]) + ". It's a " + classes[train_y[0,index]].decode("utf-8") + " picture.") y = 1. It's a cat picture.

# Explore your dataset m_train = train_x_orig.shape[0] num_px = train_x_orig.shape[1] m_test = test_x_orig.shape[0]print ("Number of training examples: " + str(m_train)) print ("Number of testing examples: " + str(m_test)) print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)") print ("train_x_orig shape: " + str(train_x_orig.shape)) print ("train_y shape: " + str(train_y.shape)) print ("test_x_orig shape: " + str(test_x_orig.shape)) print ("test_y shape: " + str(test_y.shape)) Number of training examples: 209 Number of testing examples: 50 Each image is of size: (64, 64, 3) train_x_orig shape: (209, 64, 64, 3) train_y shape: (1, 209) test_x_orig shape: (50, 64, 64, 3) test_y shape: (1, 50)

As usual, you reshape and standardize the images before feeding them to the network. The code is given in the cell below.

Figure 1: Image to vector conversion.

# Reshape the training and test examples train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0], -1).T # The "-1" makes reshape flatten the remaining dimensions test_x_flatten = test_x_orig.reshape(test_x_orig.shape[0], -1).T# Standardize data to have feature values between 0 and 1. train_x = train_x_flatten/255. test_x = test_x_flatten/255.print ("train_x's shape: " + str(train_x.shape)) print ("test_x's shape: " + str(test_x.shape)) train_x's shape: (12288, 209) test_x's shape: (12288, 50)

12,28812,288 equals 64×64×364×64×3 which is the size of one reshaped image vector.

3 - Architecture of your model

Now that you are familiar with the dataset, it is time to build a deep neural network to distinguish cat images from non-cat images.

You will build two different models:
- A 2-layer neural network
- An L-layer deep neural network

You will then compare the performance of these models, and also try out different values for LL.

Let’s look at the two architectures.

3.1 - 2-layer neural network

Figure 2: 2-layer neural network.
The model can be summarized as: INPUT -> LINEAR -> RELU -> LINEAR -> SIGMOID -> OUTPUT.

Detailed Architecture of figure 2:
- The input is a (64,64,3) image which is flattened to a vector of size (12288,1)(12288,1).
- The corresponding vector: [x0,x1,...,x12287]T[x0,x1,...,x12287]T is then multiplied by the weight matrix W[1]W[1] of size (n[1],12288)(n[1],12288).
- You then add a bias term and take its relu to get the following vector: [a[1]0,a[1]1,...,a[1]n[1]?1]T[a0[1],a1[1],...,an[1]?1[1]]T.
- You then repeat the same process.
- You multiply the resulting vector by W[2]W[2] and add your intercept (bias).
- Finally, you take the sigmoid of the result. If it is greater than 0.5, you classify it to be a cat.

3.2 - L-layer deep neural network

It is hard to represent an L-layer deep neural network with the above representation. However, here is a simplified network representation:

Figure 3: L-layer neural network.
The model can be summarized as: [LINEAR -> RELU] ×× (L-1) -> LINEAR -> SIGMOID

Detailed Architecture of figure 3:
- The input is a (64,64,3) image which is flattened to a vector of size (12288,1).
- The corresponding vector: [x0,x1,...,x12287]T[x0,x1,...,x12287]T is then multiplied by the weight matrix W[1]W[1] and then you add the intercept b[1]b[1]. The result is called the linear unit.
- Next, you take the relu of the linear unit. This process could be repeated several times for each (W[l],b[l])(W[l],b[l]) depending on the model architecture.
- Finally, you take the sigmoid of the final linear unit. If it is greater than 0.5, you classify it to be a cat.

3.3 - General methodology

As usual you will follow the Deep Learning methodology to build the model:
1. Initialize parameters / Define hyperparameters
2. Loop for num_iterations:
a. Forward propagation
b. Compute cost function
c. Backward propagation
d. Update parameters (using parameters, and grads from backprop)
4. Use trained parameters to predict labels

Let’s now implement those two models!

4 - Two-layer neural network

Question: Use the helper functions you have implemented in the previous assignment to build a 2-layer neural network with the following structure: LINEAR -> RELU -> LINEAR -> SIGMOID. The functions you may need and their inputs are:

def initialize_parameters(n_x, n_h, n_y):...return parameters def linear_activation_forward(A_prev, W, b, activation):...return A, cache def compute_cost(AL, Y):...return cost def linear_activation_backward(dA, cache, activation):...return dA_prev, dW, db def update_parameters(parameters, grads, learning_rate):...return parameters ### CONSTANTS DEFINING THE MODEL #### n_x = 12288 # num_px * num_px * 3 n_h = 7 n_y = 1 layers_dims = (n_x, n_h, n_y) # GRADED FUNCTION: two_layer_modeldef two_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):"""Implements a two-layer neural network: LINEAR->RELU->LINEAR->SIGMOID.Arguments:X -- input data, of shape (n_x, number of examples)Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)layers_dims -- dimensions of the layers (n_x, n_h, n_y)num_iterations -- number of iterations of the optimization looplearning_rate -- learning rate of the gradient descent update ruleprint_cost -- If set to True, this will print the cost every 100 iterations Returns:parameters -- a dictionary containing W1, W2, b1, and b2"""np.random.seed(1)grads = {}costs = [] # to keep track of the costm = X.shape[1] # number of examples(n_x, n_h, n_y) = layers_dims# Initialize parameters dictionary, by calling one of the functions you'd previously implemented### START CODE HERE ### (≈ 1 line of code)parameters = initialize_parameters(n_x, n_h, n_y)### END CODE HERE #### Get W1, b1, W2 and b2 from the dictionary parameters.W1 = parameters["W1"]b1 = parameters["b1"]W2 = parameters["W2"]b2 = parameters["b2"]# Loop (gradient descent)for i in range(0, num_iterations):# Forward propagation: LINEAR -> RELU -> LINEAR -> SIGMOID. Inputs: "X, W1, b1". Output: "A1, cache1, A2, cache2".### START CODE HERE ### (≈ 2 lines of code)A1, cache1 = linear_activation_forward(X, W1, b1, "relu")A2, cache2 = linear_activation_forward(A1, W2, b2, "sigmoid")### END CODE HERE #### Compute cost### START CODE HERE ### (≈ 1 line of code)cost = compute_cost(A2, Y)### END CODE HERE #### Initializing backward propagationdA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))# Backward propagation. Inputs: "dA2, cache2, cache1". Outputs: "dA1, dW2, db2; also dA0 (not used), dW1, db1".### START CODE HERE ### (≈ 2 lines of code)dA1, dW2, db2 = linear_activation_backward(dA2, cache2, "sigmoid")dA0, dW1, db1 = linear_activation_backward(dA1, cache1, "relu")### END CODE HERE #### Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2grads['dW1'] = dW1grads['db1'] = db1grads['dW2'] = dW2grads['db2'] = db2# Update parameters.### START CODE HERE ### (approx. 1 line of code)parameters = update_parameters(parameters, grads, learning_rate)### END CODE HERE #### Retrieve W1, b1, W2, b2 from parametersW1 = parameters["W1"]b1 = parameters["b1"]W2 = parameters["W2"]b2 = parameters["b2"]# Print the cost every 100 training exampleif print_cost and i % 100 == 0:print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))if print_cost and i % 100 == 0:costs.append(cost)# plot the costplt.plot(np.squeeze(costs))plt.ylabel('cost')plt.xlabel('iterations (per tens)')plt.title("Learning rate =" + str(learning_rate))plt.show()return parameters

Run the cell below to train your parameters. See if your model runs. The cost should be decreasing. It may take up to 5 minutes to run 2500 iterations. Check if the “Cost after iteration 0” matches the expected output below, if not click on the square (?) on the upper bar of the notebook to stop the cell and try to find your error.

parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True) Cost after iteration 0: 0.693049735659989 Cost after iteration 100: 0.6464320953428849 Cost after iteration 200: 0.6325140647912678 Cost after iteration 300: 0.6015024920354665 Cost after iteration 400: 0.5601966311605748 Cost after iteration 500: 0.5158304772764731 Cost after iteration 600: 0.47549013139433255 Cost after iteration 700: 0.43391631512257495 Cost after iteration 800: 0.4007977536203886 Cost after iteration 900: 0.35807050113237976 Cost after iteration 1000: 0.3394281538366413 Cost after iteration 1100: 0.30527536361962654 Cost after iteration 1200: 0.2749137728213016 Cost after iteration 1300: 0.2468176821061484 Cost after iteration 1400: 0.19850735037466105 Cost after iteration 1500: 0.17448318112556638 Cost after iteration 1600: 0.17080762978096967 Cost after iteration 1700: 0.11306524562164705 Cost after iteration 1800: 0.09629426845937154 Cost after iteration 1900: 0.08342617959726867 Cost after iteration 2000: 0.07439078704319087 Cost after iteration 2100: 0.06630748132267934 Cost after iteration 2200: 0.05919329501038172 Cost after iteration 2300: 0.053361403485605606 Cost after iteration 2400: 0.04855478562877019

Expected Output:

**Cost after iteration 0**	0.6930497356599888
**Cost after iteration 100**	0.6464320953428849
**…**	…
**Cost after iteration 2400**	0.048554785628770206

Good thing you built a vectorized implementation! Otherwise it might have taken 10 times longer to train this.

Now, you can use the trained parameters to classify images from the dataset. To see your predictions on the training and test sets, run the cell below.

predictions_train = predict(train_x, train_y, parameters) Accuracy: 1.0

Expected Output:

Accuracy

1.0

predictions_test = predict(test_x, test_y, parameters) Accuracy: 0.72

Expected Output:

Accuracy

0.72

Note: You may notice that running the model on fewer iterations (say 1500) gives better accuracy on the test set. This is called “early stopping” and we will talk about it in the next course. Early stopping is a way to prevent overfitting.

Congratulations! It seems that your 2-layer neural network has better performance (72%) than the logistic regression implementation (70%, assignment week 2). Let’s see if you can do even better with an LL-layer model.

5 - L-layer Neural Network

Question: Use the helper functions you have implemented previously to build an LL-layer neural network with the following structure: [LINEAR -> RELU]××(L-1) -> LINEAR -> SIGMOID. The functions you may need and their inputs are:

def initialize_parameters_deep(layer_dims):...return parameters def L_model_forward(X, parameters):...return AL, caches def compute_cost(AL, Y):...return cost def L_model_backward(AL, Y, caches):...return grads def update_parameters(parameters, grads, learning_rate):...return parameters ### CONSTANTS ### layers_dims = [12288, 20, 7, 5, 1] # 5-layer model # GRADED FUNCTION: L_layer_modeldef L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):#lr was 0.009"""Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID.Arguments:X -- data, numpy array of shape (number of examples, num_px * num_px * 3)Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)layers_dims -- list containing the input size and each layer size, of length (number of layers + 1).learning_rate -- learning rate of the gradient descent update rulenum_iterations -- number of iterations of the optimization loopprint_cost -- if True, it prints the cost every 100 stepsReturns:parameters -- parameters learnt by the model. They can then be used to predict."""np.random.seed(1)costs = [] # keep track of cost# Parameters initialization.### START CODE HERE ###parameters = initialize_parameters_deep(layers_dims)### END CODE HERE #### Loop (gradient descent)for i in range(0, num_iterations):# Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.### START CODE HERE ### (≈ 1 line of code)AL, caches = L_model_forward(X, parameters)### END CODE HERE #### Compute cost.### START CODE HERE ### (≈ 1 line of code)cost = compute_cost(AL, Y)### END CODE HERE #### Backward propagation.### START CODE HERE ### (≈ 1 line of code)grads = L_model_backward(AL, Y, caches)### END CODE HERE #### Update parameters.### START CODE HERE ### (≈ 1 line of code)parameters = update_parameters(parameters, grads, learning_rate)### END CODE HERE #### Print the cost every 100 training exampleif print_cost and i % 100 == 0:print ("Cost after iteration %i: %f" %(i, cost))if print_cost and i % 100 == 0:costs.append(cost)# plot the costplt.plot(np.squeeze(costs))plt.ylabel('cost')plt.xlabel('iterations (per tens)')plt.title("Learning rate =" + str(learning_rate))plt.show()return parameters

You will now train the model as a 5-layer neural network.

Run the cell below to train your model. The cost should decrease on every iteration. It may take up to 5 minutes to run 2500 iterations. Check if the “Cost after iteration 0” matches the expected output below, if not click on the square (?) on the upper bar of the notebook to stop the cell and try to find your error.

parameters = L_layer_model(train_x, train_y, layers_dims, num_iterations = 2500, print_cost = True) Cost after iteration 0: 0.771749 Cost after iteration 100: 0.672053 Cost after iteration 200: 0.648263 Cost after iteration 300: 0.611507 Cost after iteration 400: 0.567047 Cost after iteration 500: 0.540138 Cost after iteration 600: 0.527930 Cost after iteration 700: 0.465477 Cost after iteration 800: 0.369126 Cost after iteration 900: 0.391747 Cost after iteration 1000: 0.315187 Cost after iteration 1100: 0.272700 Cost after iteration 1200: 0.237419 Cost after iteration 1300: 0.199601 Cost after iteration 1400: 0.189263 Cost after iteration 1500: 0.161189 Cost after iteration 1600: 0.148214 Cost after iteration 1700: 0.137775 Cost after iteration 1800: 0.129740 Cost after iteration 1900: 0.121225 Cost after iteration 2000: 0.113821 Cost after iteration 2100: 0.107839 Cost after iteration 2200: 0.102855 Cost after iteration 2300: 0.100897 Cost after iteration 2400: 0.092878

Expected Output:

Cost after iteration 0	0.771749
Cost after iteration 100	0.672053
…	…
Cost after iteration 2400	0.092878

pred_train = predict(train_x, train_y, parameters) Accuracy: 0.985645933014

Train Accuracy

0.985645933014

pred_test = predict(test_x, test_y, parameters) Accuracy: 0.8

Expected Output:

Test Accuracy

0.8

Congrats! It seems that your 5-layer neural network has better performance (80%) than your 2-layer neural network (72%) on the same test set.

This is good performance for this task. Nice job!

Though in the next course on “Improving deep neural networks” you will learn how to obtain even higher accuracy by systematically searching for better hyperparameters (learning_rate, layers_dims, num_iterations, and others you’ll also learn in the next course).

6) Results Analysis

First, let’s take a look at some images the L-layer model labeled incorrectly. This will show a few mislabeled images.

print_mislabeled_images(classes, test_x, test_y, pred_test)

A few type of images the model tends to do poorly on include:
- Cat body in an unusual position
- Cat appears against a background of a similar color
- Unusual cat color and species
- Camera Angle
- Brightness of the picture
- Scale variation (cat is very large or small in image)

7) 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)!

## START CODE HERE ## my_image = "cat3.jpg" # change this to the name of your image file my_label_y = [1] # the true class of your image (1 -> cat, 0 -> non-cat) ## END CODE HERE ##fname = "images/" + my_image image = np.array(ndimage.imread(fname, flatten=False)) my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((num_px*num_px*3,1)) my_predicted_image = predict(my_image, my_label_y, parameters)plt.imshow(image) print ("y = " + str(np.squeeze(my_predicted_image)) + ", your L-layer model predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") + "\" picture.") Accuracy: 1.0 y = 1.0, your L-layer model predicts a "cat" picture.

References:

• for auto-reloading external module: http://stackoverflow.com/questions/1907993/autoreload-of-modules-in-ipython

總結

以上是生活随笔為你收集整理的吴恩达深度学习课程deeplearning.ai课程作业：Class 1 Week 4 assignment4_2的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。