Assignment | 04-week1 -Convolutional Neural Networks: Application Part_2

该系列仅在原课程基础上课后作业部分添加个人学习笔记，如有错误，还请批评指教。在学习了 Andrew Ng 课程的基础上，为了更方便的查阅复习，将其整理成文字。因本人一直在学习英语，所以该系列以英文为主，同时也建议读者以英文为主，中文辅助，以便后期进阶时，为学习相关领域的学术论文做铺垫。- ZJ

Coursera 课程 |deeplearning.ai |网易云课堂

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转载请注明作者和出处：ZJ 微信公众号-「SelfImprovementLab」

CSDN： http://blog.csdn.net/junjun_zhao/article/details/79214866

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Welcome to Course 4’s second assignment! In this notebook, you will:

• Implement helper functions that you will use when implementing a TensorFlow model
• Implement a fully functioning ConvNet using TensorFlow

After this assignment you will be able to:

• Build and train a ConvNet in TensorFlow for a classification problem 对一个分类问题，使用TensorFlow 构建和训练一个卷积神经网络

We assume here that you are already familiar with TensorFlow. If you are not, please refer the TensorFlow Tutorial of the third week of Course 2 (“Improving deep neural networks“).

1.0 - TensorFlow model

In the previous assignment, you built helper functions using numpy to understand the mechanics behind convolutional neural networks. Most practical applications of deep learning today are built using programming frameworks, which have many built-in functions you can simply call.

As usual, we will start by loading in the packages.

import math
import numpy as np
import h5py
import matplotlib.pyplot as plt
import scipy
from PIL import Image
from scipy import ndimage
import tensorflow as tf
from tensorflow.python.framework import ops
from cnn_utils import *

%matplotlib inline
np.random.seed(1)

d:\program files\python36\lib\site-packages\h5py\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
  from ._conv import register_converters as _register_converters

Run the next cell to load the “SIGNS” dataset you are going to use.

# Loading the data (signs)
X_train_orig, Y_train_orig, X_test_orig, Y_test_orig, classes = load_dataset()

As a reminder, the SIGNS dataset is a collection of 6 signs representing numbers from 0 to 5.

The next cell will show you an example of a labelled image in the dataset. Feel free to change the value of index below and re-run to see different examples.

# Example of a picture
index = 6
plt.imshow(X_train_orig[index])
print ("y = " + str(np.squeeze(Y_train_orig[:, index])))

y = 2

In Course 2, you had built a fully-connected network for this dataset. But since this is an image dataset, it is more natural to apply a ConvNet to it.

To get started, let’s examine the shapes of your data.

X_train = X_train_orig/255.
X_test = X_test_orig/255.
Y_train = convert_to_one_hot(Y_train_orig, 6).T
Y_test = convert_to_one_hot(Y_test_orig, 6).T
print ("number of training examples = " + str(X_train.shape[0]))
print ("number of test examples = " + str(X_test.shape[0]))
print ("X_train shape: " + str(X_train.shape))
print ("Y_train shape: " + str(Y_train.shape))
print ("X_test shape: " + str(X_test.shape))
print ("Y_test shape: " + str(Y_test.shape))
conv_layers = {}

number of training examples = 1080
number of test examples = 120
X_train shape: (1080, 64, 64, 3)
Y_train shape: (1080, 6)
X_test shape: (120, 64, 64, 3)
Y_test shape: (120, 6)

1.1 - Create placeholders 占位符

TensorFlow requires that you create placeholders for the input data that will be fed into the model when running the session.

Exercise: Implement the function below to create placeholders for the input image X and the output Y. You should not define the number of training examples for the moment. To do so, you could use “None” as the batch size, it will give you the flexibility to choose it later. Hence X should be of dimension [None, n_H0, n_W0, n_C0] and Y should be of dimension [None, n_y]. Hint.

# GRADED FUNCTION: create_placeholders

def create_placeholders(n_H0, n_W0, n_C0, n_y):
    """
    Creates the placeholders for the tensorflow session.

    Arguments:
    n_H0 -- scalar, height of an input image
    n_W0 -- scalar, width of an input image
    n_C0 -- scalar, number of channels of the input
    n_y -- scalar, number of classes

    Returns:
    X -- placeholder for the data input, of shape [None, n_H0, n_W0, n_C0] and dtype "float"
    Y -- placeholder for the input labels, of shape [None, n_y] and dtype "float"
    """

    ### START CODE HERE ### (≈2 lines) "None" as the batch size 
    X = tf.placeholder(name='X', shape=(None, n_H0, n_W0, n_C0), dtype=tf.float32)
    Y = tf.placeholder(name='Y', shape=(None, n_y), dtype=tf.float32)
    ### END CODE HERE ###

    return X, Y

X, Y = create_placeholders(64, 64, 3, 6)
print ("X = " + str(X))
print ("Y = " + str(Y))

X = Tensor("X:0", shape=(?, 64, 64, 3), dtype=float32)
Y = Tensor("Y:0", shape=(?, 6), dtype=float32)

Expected Output

X = Tensor(“Placeholder:0”, shape=(?, 64, 64, 3), dtype=float32)

Y = Tensor(“Placeholder_1:0”, shape=(?, 6), dtype=float32)

1.2 - Initialize parameters

You will initialize weights/filters W1 W 1 and W2 W 2 using tf.contrib.layers.xavier_initializer(seed = 0). You don’t need to worry about bias variables as you will soon see that TensorFlow functions take care of the bias. Note also that you will only initialize the weights/filters for the conv2d functions. TensorFlow initializes the layers for the fully connected part automatically. We will talk more about that later in this assignment.

Exercise: Implement initialize_parameters(). The dimensions for each group of filters are provided below. Reminder - to initialize a parameter W W of shape [1,2,3,4] in Tensorflow, use:

W = tf.get_variable("W", [1,2,3,4], initializer = ...)

More Info.

# GRADED FUNCTION: initialize_parameters 初始化参数 W1， W2

def initialize_parameters():
    """
    Initializes weight parameters to build a neural network with tensorflow. The shapes are:
                        W1 : [4, 4, 3, 8]
                        W2 : [2, 2, 8, 16]
    Returns:
    parameters -- a dictionary of tensors containing W1, W2
    """

    tf.set_random_seed(1)                              # so that your "random" numbers match ours

    ### START CODE HERE ### (approx. 2 lines of code)
    W1 = tf.get_variable('W1', shape=(4, 4, 3, 8),dtype=tf.float32, initializer = tf.contrib.layers.xavier_initializer(seed = 0))
    W2 = tf.get_variable('W2', shape=(2, 2, 8, 16),dtype=tf.float32, initializer = tf.contrib.layers.xavier_initializer(seed = 0))
    ### END CODE HERE ###

    parameters = {"W1": W1,
                  "W2": W2}

    return parameters

tf.reset_default_graph()
with tf.Session() as sess_test:
    parameters = initialize_parameters()
    init = tf.global_variables_initializer()
    sess_test.run(init)
    print("W1 = " + str(parameters["W1"].eval()[1,1,1]))
    print("W2 = " + str(parameters["W2"].eval()[1,1,1]))

W1 = [ 0.00131723  0.1417614  -0.04434952  0.09197326  0.14984085 -0.03514394
 -0.06847463  0.05245192]
W2 = [-0.08566415  0.17750949  0.11974221  0.16773748 -0.0830943  -0.08058
 -0.00577033 -0.14643836  0.24162132 -0.05857408 -0.19055021  0.1345228
 -0.22779644 -0.1601823  -0.16117483 -0.10286498]

* Expected Output:*

W1 =	[ 0.00131723 0.14176141 -0.04434952 0.09197326 0.14984085 -0.03514394 -0.06847463 0.05245192]
W2 =	[-0.08566415 0.17750949 0.11974221 0.16773748 -0.0830943 -0.08058 -0.00577033 -0.14643836 0.24162132 -0.05857408 -0.19055021 0.1345228 -0.22779644 -0.1601823 -0.16117483 -0.10286498]

1.2 - Forward propagation 前向传播

In TensorFlow, there are built-in functions that carry out the convolution steps for you. 有内置函数执行卷积运算

• tf.nn.conv2d(X,W1, strides = [1,s,s,1], padding = ‘SAME’): given an input X X and a group of filters W1 W 1 , this function convolves W1 W 1 ’s filters on X. The third input ([1,f,f,1]) represents the strides for each dimension of the input (m, n_H_prev, n_W_prev, n_C_prev). You can read the full documentation here 卷积层

  • tf.nn.max_pool(A, ksize = [1,f,f,1], strides = [1,s,s,1], padding = ‘SAME’): given an input A, this function uses a window of size (f, f) and strides of size (s, s) to carry out max pooling over each window. You can read the full documentation here池化层

  • tf.nn.relu(Z1): computes the elementwise ReLU of Z1 (which can be any shape). You can read the full documentation here.

  • tf.contrib.layers.flatten(P): given an input P, this function flattens each example into a 1D vector it while maintaining the batch-size. It returns a flattened tensor with shape [batch_size, k]. You can read the full documentation [here.] 将样本转化成一维的样本(https://www.tensorflow.org/api_docs/python/tf/contrib/layers/flatten)

  • tf.contrib.layers.fully_connected(F, num_outputs): given a the flattened input F, it returns the output computed using a fully connected layer. You can read the full documentation here.全连接

  • In the last function above (tf.contrib.layers.fully_connected), the fully connected layer automatically initializes weights in the graph and keeps on training them as you train the model. Hence, you did not need to initialize those weights when initializing the parameters. 全连接层自动初始化权重，不需要管

    Exercise:

    Implement the forward_propagation function below to build the following model: CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTED. You should use the functions above.

    In detail, we will use the following parameters for all the steps:
    - Conv2D: stride 1, padding is “SAME”
    - ReLU
    - Max pool: Use an 8 by 8 filter size and an 8 by 8 stride, padding is “SAME”
    - Conv2D: stride 1, padding is “SAME”
    - ReLU
    - Max pool: Use a 4 by 4 filter size and a 4 by 4 stride, padding is “SAME”
    - Flatten the previous output.
    - FULLYCONNECTED (FC) layer: Apply a fully connected layer without an non-linear activation function. Do not call the softmax here. This will result in 6 neurons in the output layer, which then get passed later to a softmax. In TensorFlow, the softmax and cost function are lumped together into a single function, which you’ll call in a different function when computing the cost. 这里不需要采用非线性的激活函数，也无需调用 softmax 函数，因为该函数已经被整合到代价函数中

    # GRADED FUNCTION: forward_propagation
    
    def forward_propagation(X, parameters):
        """
        Implements the forward propagation for the model:
        CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTED
    
        Arguments:
        X -- input dataset placeholder, of shape (input size, number of examples)
        parameters -- python dictionary containing your parameters "W1", "W2"
                      the shapes are given in initialize_parameters
    
        Returns:
        Z3 -- the output of the last LINEAR unit
        """
    
        # Retrieve the parameters from the dictionary "parameters" 
        W1 = parameters['W1']
        W2 = parameters['W2']
    
        ### START CODE HERE ###
        # CONV2D: stride of 1, padding 'SAME'
        Z1 = tf.nn.conv2d(input=X, filter=W1, strides = [1,1,1,1], padding = 'SAME')
        # RELU
        A1 = tf.nn.relu(Z1)
        # MAXPOOL: window 8x8, sride 8, padding 'SAME'
        P1 = tf.nn.max_pool(value=A1,ksize = [1,8,8,1], strides = [1,8,8,1], padding = 'SAME')
        # CONV2D: filters W2, stride 1, padding 'SAME'
        Z2 = tf.nn.conv2d(input=P1, filter=W2, strides = [1,1,1,1], padding = 'SAME')
        # RELU
        A2 = tf.nn.relu(Z2)
        # MAXPOOL: window 4x4, stride 4, padding 'SAME'
        P2 = tf.nn.max_pool(value=A2, ksize = [1, 4, 4, 1], strides = [1, 4, 4, 1], padding = 'SAME')
        # FLATTEN
        P  = tf.contrib.layers.flatten(P2)
        # FULLY-CONNECTED without non-linear activation function (not not call softmax).
        # 6 neurons in output layer. Hint: one of the arguments should be "activation_fn=None" 
        Z3 = tf.contrib.layers.fully_connected(P,6, activation_fn=None)
        ### END CODE HERE ###
    
        return Z3

    tf.reset_default_graph()
    
    with tf.Session() as sess:
        np.random.seed(1)
        X, Y = create_placeholders(64, 64, 3, 6)
        parameters = initialize_parameters()
        Z3 = forward_propagation(X, parameters)
        init = tf.global_variables_initializer()
        sess.run(init)
        a = sess.run(Z3, {X: np.random.randn(2,64,64,3), Y: np.random.randn(2,6)})
        print("Z3 = " + str(a))

    Z3 = [[ 1.4416984  -0.24909666  5.450499   -0.2618962  -0.20669907  1.3654671 ]
     [ 1.4070846  -0.02573211  5.08928    -0.48669922 -0.40940708  1.2624859 ]]
    

    Expected Output:

    Z3 =	[[-0.44670227 -1.57208765 -1.53049231 -2.31013036 -1.29104376 0.46852064] [-0.17601591 -1.57972014 -1.4737016 -2.61672091 -1.00810647 0.5747785 ]]

    1.3 - Compute cost

    Implement the compute cost function below. You might find these two functions helpful:

    • tf.nn.softmax_cross_entropy_with_logits(logits = Z3, labels = Y): computes the softmax entropy loss. This function both computes the softmax activation function as well as the resulting loss. You can check the full documentation here.
    • tf.reduce_mean: computes the mean of elements across dimensions of a tensor. Use this to sum the losses over all the examples to get the overall cost. You can check the full documentation here.

    * Exercise*: Compute the cost below using the function above.

    # GRADED FUNCTION: compute_cost 
    
    def compute_cost(Z3, Y):
        """
        Computes the cost
    
        Arguments:
        Z3 -- output of forward propagation (output of the last LINEAR unit), of shape (6, number of examples)
        Y -- "true" labels vector placeholder, same shape as Z3
    
        Returns:
        cost - Tensor of the cost function
        """
    
        ### START CODE HERE ### (1 line of code)
        cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits = Z3, labels = Y))
        ### END CODE HERE ###
    
        return cost

    tf.reset_default_graph()
    
    with tf.Session() as sess:
        np.random.seed(1)
        X, Y = create_placeholders(64, 64, 3, 6)
        parameters = initialize_parameters()
        Z3 = forward_propagation(X, parameters)
        cost = compute_cost(Z3, Y)
        init = tf.global_variables_initializer()
        sess.run(init)
        a = sess.run(cost, {X: np.random.randn(4,64,64,3), Y: np.random.randn(4,6)})
        print("cost = " + str(a))
    #  这里得到的 cost 值偏大，因为是本地跑的代码，暂时没找到问题出在哪里，所以之后的训练结果都还有问题，待解决。

    cost = 4.66487
    

    这里得到的 cost 值偏大，因为是本地跑的代码，暂时没找到问题出在哪里，所以之后的训练结果都还有问题，待解决。

    Expected Output:

    cost =

    2.91034

    1.4 Model

    Finally you will merge the helper functions you implemented above to build a model. You will train it on the SIGNS dataset.

    You have implemented random_mini_batches() in the Optimization programming assignment of course 2. Remember that this function returns a list of mini-batches.

    Exercise: Complete the function below.

    The model below should:

    • create placeholders
    • initialize parameters
    • forward propagate
    • compute the cost
    • create an optimizer

    Finally you will create a session and run a for loop for num_epochs, get the mini-batches, and then for each mini-batch you will optimize the function. Hint for initializing the variables

    # GRADED FUNCTION: model
    
    def model(X_train, Y_train, X_test, Y_test, learning_rate = 0.009,
              num_epochs = 100, minibatch_size = 64, print_cost = True):
        """
        Implements a three-layer ConvNet in Tensorflow:
        CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTED
    
        Arguments:
        X_train -- training set, of shape (None, 64, 64, 3)
        Y_train -- test set, of shape (None, n_y = 6)
        X_test -- training set, of shape (None, 64, 64, 3)
        Y_test -- test set, of shape (None, n_y = 6)
        learning_rate -- learning rate of the optimization
        num_epochs -- number of epochs of the optimization loop
        minibatch_size -- size of a minibatch
        print_cost -- True to print the cost every 100 epochs
    
        Returns:
        train_accuracy -- real number, accuracy on the train set (X_train)
        test_accuracy -- real number, testing accuracy on the test set (X_test)
        parameters -- parameters learnt by the model. They can then be used to predict.
        """
    
        ops.reset_default_graph()                         # to be able to rerun the model without overwriting tf variables
        tf.set_random_seed(1)                             # to keep results consistent (tensorflow seed)
        seed = 3                                          # to keep results consistent (numpy seed)
        (m, n_H0, n_W0, n_C0) = X_train.shape             
        n_y = Y_train.shape[1]                            
        costs = []                                        # To keep track of the cost
    
        # Create Placeholders of the correct shape
        ### START CODE HERE ### (1 line)
        X, Y = create_placeholders(n_H0, n_W0, n_C0,n_y )
        ### END CODE HERE ###
    
        # Initialize parameters
        ### START CODE HERE ### (1 line)
        parameters = initialize_parameters()
        ### END CODE HERE ###
    
        # Forward propagation: Build the forward propagation in the tensorflow graph
        ### START CODE HERE ### (1 line)
        Z3 = forward_propagation(X, parameters)
        ### END CODE HERE ###
    
        # Cost function: Add cost function to tensorflow graph
        ### START CODE HERE ### (1 line)
        cost = compute_cost(Z3, Y)
        ### END CODE HERE ###
    
        # Backpropagation: Define the tensorflow optimizer. Use an AdamOptimizer that minimizes the cost.
        ### START CODE HERE ### (1 line)
        optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost)
        ### END CODE HERE ###
    
        # Initialize all the variables globally
        init = tf.global_variables_initializer()
    
        # Start the session to compute the tensorflow graph
        with tf.Session() as sess:
    
            # Run the initialization
            sess.run(init)
    
            # Do the training loop
            for epoch in range(num_epochs):
    
                minibatch_cost = 0.
                num_minibatches = int(m / minibatch_size) # number of minibatches of size minibatch_size in the train set
                seed = seed + 1
                minibatches = random_mini_batches(X_train, Y_train, minibatch_size, seed)
    
                for minibatch in minibatches:
    
                    # Select a minibatch
                    (minibatch_X, minibatch_Y) = minibatch
                    # IMPORTANT: The line that runs the graph on a minibatch.
                    # Run the session to execute the optimizer and the cost, the feedict should contain a minibatch for (X,Y).
                    ### START CODE HERE ### (1 line)
                    _ , temp_cost = sess.run([optimizer, cost], feed_dict = {X: minibatch_X, Y:minibatch_Y})
                    ### END CODE HERE ###
    
                    minibatch_cost += temp_cost / num_minibatches
    
    
                # Print the cost every epoch
                if print_cost == True and epoch % 5 == 0:
                    print ("Cost after epoch %i: %f" % (epoch, minibatch_cost))
                if print_cost == True and epoch % 1 == 0:
                    costs.append(minibatch_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()
    
            # Calculate the correct predictions
            predict_op = tf.argmax(Z3, 1)
            correct_prediction = tf.equal(predict_op, tf.argmax(Y, 1))
    
            # Calculate accuracy on the test set
            accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
            print(accuracy)
            train_accuracy = accuracy.eval({X: X_train, Y: Y_train})
            test_accuracy = accuracy.eval({X: X_test, Y: Y_test})
            print("Train Accuracy:", train_accuracy)
            print("Test Accuracy:", test_accuracy)
    
            return train_accuracy, test_accuracy, parameters

    Run the following cell to train your model for 100 epochs. Check if your cost after epoch 0 and 5 matches our output. If not, stop the cell and go back to your code!

    _, _, parameters = model(X_train, Y_train, X_test, Y_test)

    Cost after epoch 0: 1.921332
    Cost after epoch 5: 1.904156
    Cost after epoch 10: 1.904309
    Cost after epoch 15: 1.904477
    Cost after epoch 20: 1.901876
    Cost after epoch 25: 1.784078
    Cost after epoch 30: 1.681051
    Cost after epoch 35: 1.618207
    Cost after epoch 40: 1.597971
    Cost after epoch 45: 1.566707
    Cost after epoch 50: 1.554487
    Cost after epoch 55: 1.502188
    Cost after epoch 60: 1.461036
    Cost after epoch 65: 1.304479
    Cost after epoch 70: 1.201502
    Cost after epoch 75: 1.144233
    Cost after epoch 80: 1.096785
    Cost after epoch 85: 1.081992
    Cost after epoch 90: 1.054077
    Cost after epoch 95: 1.025999
    

    

    Tensor("Mean_1:0", shape=(), dtype=float32)
    Train Accuracy: 0.65833336
    Test Accuracy: 0.5416667
    

    Expected output: although it may not match perfectly, your expected output should be close to ours and your cost value should decrease.

    **Cost after epoch 0 =**	1.917929
    **Cost after epoch 5 =**	1.506757
    **Train Accuracy =**	0.940741
    **Test Accuracy =**	0.783333

    Congratulations! You have finised the assignment and built a model that recognizes SIGN language with almost 80% accuracy on the test set. If you wish, feel free to play around with this dataset further. You can actually improve its accuracy by spending more time tuning the hyperparameters, or using regularization (as this model clearly has a high variance).

    Once again, here’s a thumbs up for your work!

    fname = "images/thumbs_up.jpg"
    image = np.array(ndimage.imread(fname, flatten=False))
    my_image = scipy.misc.imresize(image, size=(64,64))
    plt.imshow(my_image)

    d:\program files\python36\lib\site-packages\ipykernel_launcher.py:2: DeprecationWarning: `imread` is deprecated!
    `imread` is deprecated in SciPy 1.0.0.
    Use ``matplotlib.pyplot.imread`` instead.
    
    d:\program files\python36\lib\site-packages\ipykernel_launcher.py:3: DeprecationWarning: `imresize` is deprecated!
    `imresize` is deprecated in SciPy 1.0.0, and will be removed in 1.2.0.
    Use ``skimage.transform.resize`` instead.
      This is separate from the ipykernel package so we can avoid doing imports until
    
    
    
    
    
    
    

    

    ---

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