吳恩達(dá)deeplearning.ai課程作業(yè)，自己寫(xiě)的答案。

補(bǔ)充說(shuō)明：
1. 評(píng)論中總有人問(wèn)為什么直接復(fù)制這些notebook運(yùn)行不了？請(qǐng)不要直接復(fù)制粘貼，不可能運(yùn)行通過(guò)的，這個(gè)只是notebook中我們要自己寫(xiě)的那部分，要正確運(yùn)行還需要其他py文件，請(qǐng)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(diǎn)一點(diǎn)寫(xiě)，如果實(shí)在卡住了再看答案。個(gè)人覺(jué)得這樣才是正確的學(xué)習(xí)方法，況且作業(yè)也不算難。
2. 關(guān)于評(píng)論中有人說(shuō)我是抄襲，注釋還沒(méi)別人詳細(xì)，復(fù)制下來(lái)還運(yùn)行不過(guò)。答復(fù)是：做伸手黨之前，請(qǐng)先搞清這個(gè)作業(yè)是干什么的。大家都是從GitHub上下載原始的作業(yè)，然后根據(jù)代碼前面的提示（通常會(huì)指定函數(shù)和公式）來(lái)編寫(xiě)代碼，而且后面還有expected output供你比對(duì)，如果程序正確，結(jié)果一般來(lái)說(shuō)是一樣的。請(qǐng)不要無(wú)腦噴，說(shuō)什么跟別人的答案一樣的。說(shuō)到底，我們要做的就是，看他的文字部分，根據(jù)提示在代碼中加入部分自己的代碼。我們自己要寫(xiě)的部分只有那么一小部分代碼。
3. 由于實(shí)在很反感無(wú)腦噴子，故禁止了下面的評(píng)論功能，請(qǐng)見(jiàn)諒。如果有問(wèn)題，請(qǐng)私信我，在力所能及的范圍內(nèi)會(huì)盡量幫忙。

注：在做這一課的第二個(gè)作業(yè)時(shí)，碰到一個(gè)坑卡了我一下午。在執(zhí)行foward propagation那部分的代碼時(shí)，有可能你的代碼都是正確的，但是你的運(yùn)行結(jié)果卻與notebook上的expected output的結(jié)果不一樣。我在同學(xué)的電腦上試圖運(yùn)行相同的代碼，結(jié)果發(fā)現(xiàn)可以正常運(yùn)行，且結(jié)果正確；但是在自己電腦上運(yùn)行的結(jié)果卻不一樣。雖然不知道原因，但是有一個(gè)解決辦法：那就是換成老版本的tensorflow。我最初使用的就是tensorflow1.4.0版本，后來(lái)?yè)Q成了1.2.0的版本就可以正確輸出結(jié)果了。
我在查找解決辦法時(shí)，看到網(wǎng)上有個(gè)人碰到了類(lèi)似的問(wèn)題：
http://mooc.study.163.com/learn/2001281004?tid=2001392030#/learn/forumdetail?pid=2001702006

Convolutional Neural Networks: Application

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

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)

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

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_placeholdersdef 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 imagen_W0 -- scalar, width of an input imagen_C0 -- scalar, number of channels of the inputn_y -- scalar, number of classesReturns: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)X = tf.placeholder(tf.float32, shape=[None, n_H0, n_W0, n_C0])Y = tf.placeholder(tf.float32, shape=[None, n_y])### END CODE HERE ###return X, Y X, Y = create_placeholders(64, 64, 3, 6) print ("X = " + str(X)) print ("Y = " + str(Y)) X = Tensor("Placeholder:0", shape=(?, 64, 64, 3), dtype=float32) Y = Tensor("Placeholder_1:0", 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 W1W1 and W2W2 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 WW of shape [1,2,3,4] in Tensorflow, use:

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

More Info.

# GRADED FUNCTION: initialize_parametersdef 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", [4, 4, 3, 8], initializer=tf.contrib.layers.xavier_initializer(seed=0))W2 = tf.get_variable("W2", [2, 2, 8, 16], initializer=tf.contrib.layers.xavier_initializer(seed=0))### END CODE HERE ###parameters = {"W1": W1,"W2": W2}return parameterstf.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 0.14176141 -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]

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

In TensorFlow, there are built-in functions that carry out the convolution steps for you.

• tf.nn.conv2d(X,W1, strides = [1,s,s,1], padding = ‘SAME’): given an input XX and a group of filters W1W1, this function convolves W1W1’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

  • 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

  • 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.

  • 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.

  • 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.

    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.

    # GRADED FUNCTION: forward_propagationdef forward_propagation(X, parameters):"""Implements the forward propagation for the model:CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTEDArguments: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_parametersReturns: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(X, W1, strides=[1, 1, 1, 1], padding='SAME')# RELUA1 = tf.nn.relu(Z1)# MAXPOOL: window 8x8, sride 8, padding 'SAME'P1 = tf.nn.max_pool(A1, ksize=[1, 8, 8, 1], strides=[1, 8, 8, 1], padding='SAME')# CONV2D: filters W2, stride 1, padding 'SAME'Z2 = tf.nn.conv2d(P1, W2, strides=[1, 1, 1, 1], padding='SAME')# RELUA2 = tf.nn.relu(Z2)# MAXPOOL: window 4x4, stride 4, padding 'SAME'P2 = tf.nn.max_pool(A2, ksize=[1, 4, 4, 1], strides=[1, 4, 4, 1], padding='SAME')# FLATTENP2 = 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(P2, 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 = [[-0.44670227 -1.57208765 -1.53049231 -2.31013036 -1.29104376 0.46852064][-0.17601591 -1.57972014 -1.4737016 -2.61672091 -1.00810647 0.5747785 ]]

    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 costArguments: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 Z3Returns: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)) cost = 2.91034

    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: modeldef 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 -> FULLYCONNECTEDArguments: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 optimizationnum_epochs -- number of epochs of the optimization loopminibatch_size -- size of a minibatchprint_cost -- True to print the cost every 100 epochsReturns: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 variablestf.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 globallyinit = tf.global_variables_initializer()# Start the session to compute the tensorflow graphwith tf.Session() as sess:# Run the initializationsess.run(init)# Do the training loopfor epoch in range(num_epochs):minibatch_cost = 0.num_minibatches = int(m / minibatch_size) # number of minibatches of size minibatch_size in the train setseed = seed + 1minibatches = 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 epochif 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 costplt.plot(np.squeeze(costs))plt.ylabel('cost')plt.xlabel('iterations (per tens)')plt.title("Learning rate =" + str(learning_rate))plt.show()# Calculate the correct predictionspredict_op = tf.argmax(Z3, 1)correct_prediction = tf.equal(predict_op, tf.argmax(Y, 1))# Calculate accuracy on the test setaccuracy = 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: 1.917929 Cost after epoch 5: 1.506757 Cost after epoch 10: 0.955359 Cost after epoch 15: 0.845802 Cost after epoch 20: 0.701174 Cost after epoch 25: 0.571977 Cost after epoch 30: 0.518435 Cost after epoch 35: 0.495806 Cost after epoch 40: 0.429827 Cost after epoch 45: 0.407291 Cost after epoch 50: 0.366394 Cost after epoch 55: 0.376922 Cost after epoch 60: 0.299491 Cost after epoch 65: 0.338870 Cost after epoch 70: 0.316400 Cost after epoch 75: 0.310413 Cost after epoch 80: 0.249549 Cost after epoch 85: 0.243457 Cost after epoch 90: 0.200031 Cost after epoch 95: 0.175452
    Tensor("Mean_1:0", shape=(), dtype=float32) Train Accuracy: 0.940741 Test Accuracy: 0.783333

    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) <matplotlib.image.AxesImage at 0x7f5de5415eb8>

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