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# 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.

In [1]:
import timeimport numpy as npimport h5pyimport matplotlib.pyplot as pltimport scipyfrom PIL import Imagefrom scipy import ndimagefrom dnn_app_utils_v3 import *%matplotlib inlineplt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plotsplt.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.

In [2]:
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.

In [3]:
# Example of a pictureindex = 25plt.imshow(train_x_orig[index])print ("y = " + str(train_y[0,index]) + ". It's a " + classes[train_y[0,index]].decode("utf-8") +  " picture.")
Out [3]:
y = 1. It's a cat picture.

In [4]:
# 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))
Out [4]:
Number of training examples: 209Number of testing examples: 50Each 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.

In [5]:
# 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 dimensionstest_x_flatten = test_x_orig.reshape(test_x_orig.shape[0], -1).Tprint("train_x_flatten shape = "+str(train_x_flatten.shape))print("test_x_flatten shape = "+str(test_x_flatten.shape))# 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))

Out [5]:
train_x_flatten shape = (12288, 209)test_x_flatten shape = (12288, 50)train_x's shape: (12288, 209)test_x's shape: (12288, 50)

equals $64×64×3$ 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 $L$.
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 .
• The corresponding vector:  is then multiplied by the weight matrix  of size .
• You then add a bias term and take its relu to get the following vector:
• You then repeat the same process.
• You multiply the resulting vector by  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:  is then multiplied by the weight matrix ${W}^{\left[1\right]}$ and then you add the intercept . 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  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 hyperparameters2. 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, cachedef compute_cost(AL, Y):    ...    return costdef linear_activation_backward(dA, cache, activation):    ...    return dA_prev, dW, dbdef update_parameters(parameters, grads, learning_rate):    ...    return parameters

In [6]:
### CONSTANTS DEFINING THE MODEL ####n_x = 12288     # num_px * num_px * 3n_h = 7n_y = 1layers_dims = (n_x, n_h, n_y)

In [7]:
# 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 loop    learning_rate -- learning rate of the gradient descent update rule    print_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 cost    m = 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, W2, b2". Output: "A1, cache1, A2, cache2".        ### START CODE HERE ### (≈ 2 lines of code)        A1, cache1 = linear_activation_forward(X, W1, b1, activation="relu")        A2, cache2 = linear_activation_forward(A1, W2, b2, activation="sigmoid")        ### END CODE HERE ###                # Compute cost        ### START CODE HERE ### (≈ 1 line of code)        cost = compute_cost(A2, Y)        ### END CODE HERE ###                # Initializing backward propagation        dA2 = - (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, activation="sigmoid")        dA0, dW1, db1 = linear_activation_backward(dA1, cache1, activation="relu")        ### END CODE HERE ###                # Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2        grads['dW1'] = dW1        grads['db1'] = db1        grads['dW2'] = dW2        grads['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 parameters        W1 = parameters["W1"]        b1 = parameters["b1"]        W2 = parameters["W2"]        b2 = parameters["b2"]                # Print the cost every 100 training example        if 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 cost    plt.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.

In [8]:
parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True)
Out [8]:
Cost after iteration 0: 0.693049735659989Cost after iteration 100: 0.6464320953428849Cost after iteration 200: 0.6325140647912678Cost after iteration 300: 0.6015024920354665Cost after iteration 400: 0.5601966311605748Cost after iteration 500: 0.515830477276473Cost after iteration 600: 0.4754901313943325Cost after iteration 700: 0.43391631512257495Cost after iteration 800: 0.4007977536203886Cost after iteration 900: 0.35807050113237987Cost after iteration 1000: 0.3394281538366413Cost after iteration 1100: 0.30527536361962654Cost after iteration 1200: 0.2749137728213015Cost after iteration 1300: 0.24681768210614827Cost after iteration 1400: 0.1985073503746611Cost after iteration 1500: 0.17448318112556593Cost after iteration 1600: 0.1708076297809661Cost after iteration 1700: 0.11306524562164737Cost after iteration 1800: 0.09629426845937163Cost after iteration 1900: 0.08342617959726878Cost after iteration 2000: 0.0743907870431909Cost after iteration 2100: 0.06630748132267938Cost after iteration 2200: 0.05919329501038176Cost after iteration 2300: 0.05336140348560564Cost after iteration 2400: 0.048554785628770226
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.

In [9]:
print("train_x shape = "+str(train_x.shape))print("train_y shape = "+str(train_y.shape))predictions_train = predict(train_x, train_y, parameters)
Out [9]:
train_x shape = (12288, 209)train_y shape = (1, 209)Accuracy: 1.0
Expected Output:
 Accuracy 1

In [10]:
print("test_x shape = "+str(test_x.shape))print("test_y shape = "+str(test_y.shape))predictions_test = predict(test_x, test_y, parameters)
Out [10]:
test_x shape = (12288, 50)test_y shape = (1, 50)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 -layer model.

## 5 - L-layer Neural Network

Question: Use the helper functions you have implemented previously to build an $L$-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(layers_dims):    ...    return parameters def L_model_forward(X, parameters):    ...    return AL, cachesdef compute_cost(AL, Y):    ...    return costdef L_model_backward(AL, Y, caches):    ...    return gradsdef update_parameters(parameters, grads, learning_rate):    ...    return parameters
In [11]:
### CONSTANTS ###layers_dims = [12288, 20, 7, 5, 1] #  4-layer model

In [12]:
# 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 rule    num_iterations -- number of iterations of the optimization loop    print_cost -- if True, it prints the cost every 100 steps        Returns:    parameters -- parameters learnt by the model. They can then be used to predict.    """    np.random.seed(1)    costs = []                         # keep track of cost        # Parameters initialization. (≈ 1 line of code)    ### 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 example        if 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 cost    plt.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 4-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.

In [13]:
parameters = L_layer_model(train_x, train_y, layers_dims, num_iterations = 2500, print_cost = True)
Out [13]:
Cost after iteration 0: 0.771749Cost after iteration 100: 0.672053Cost after iteration 200: 0.648263Cost after iteration 300: 0.611507Cost after iteration 400: 0.567047Cost after iteration 500: 0.540138Cost after iteration 600: 0.527930Cost after iteration 700: 0.465477Cost after iteration 800: 0.369126Cost after iteration 900: 0.391747Cost after iteration 1000: 0.315187Cost after iteration 1100: 0.272700Cost after iteration 1200: 0.237419Cost after iteration 1300: 0.199601Cost after iteration 1400: 0.189263Cost after iteration 1500: 0.161189Cost after iteration 1600: 0.148214Cost after iteration 1700: 0.137775Cost after iteration 1800: 0.129740Cost after iteration 1900: 0.121225Cost after iteration 2000: 0.113821Cost after iteration 2100: 0.107839Cost after iteration 2200: 0.102855Cost after iteration 2300: 0.100897Cost 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

In [14]:
print("train_x shape = "+str(train_x.shape))print("train_y shape = "+str(train_y.shape))pred_train = predict(train_x, train_y, parameters)
Out [14]:
train_x shape = (12288, 209)train_y shape = (1, 209)Accuracy: 0.985645933014

Expected Output:
 Train Accuracy 0.985646

In [15]:
print("test_x shape = "+str(test_x.shape))print("test_y shape = "+str(test_y.shape))pred_test = predict(test_x, test_y, parameters)
Out [15]:
test_x shape = (12288, 50)test_y shape = (1, 50)Accuracy: 0.8
Expected Output:
 Test Accuracy 0.8

Congrats! It seems that your 4-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.

In [16]:
print_mislabeled_images(classes, test_x, test_y, pred_test)
Out [16]:

A few types 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)

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" folder3. Change your image's name in the following code4. Run the code and check if the algorithm is right (1 = cat, 0 = non-cat)!

In [17]:
## START CODE HERE ##my_image = "my_image.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_imageimage = 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_image = my_image/255.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.")
Out [17]:

Accuracy: 1.0y = 1.0, your L-layer model predicts a "cat" picture.

I tried to provide optimized solutions like vectorized implementation for each assignment. If you think that more optimization can be done, then suggest the corrections / improvements in the comments.

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Feel free to ask doubts in the comment section. I will try my best to solve it.
If you find this helpful by any mean like, comment and share the post.
This is the simplest way to encourage me to keep doing such work.

Thanks and Regards,
-Akshay P. Daga

1. Hi sir , in week 4 assignment at 2 layer model I am getting an error as" cost not defined"and my code is looks pretty same as the one you have posted please can you tell me what's wrong in my code

1. yes even for me .. please suggest something what to do

2. Have you tried running all the cell in proper given sequence. Because, In jupyter notebook a particular cell might be dependent on previous cell.
I think, there in no problem in code. You are doing something wrong with the executing the code.