Convolutional Neural Networks:Application

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Welcome to Convolutional Neural Networks’s second article! In this article,I will:

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

After this article you will be able to:

  • Build and train a ConvNet in TensorFlow for a classification problem

I assume here that you are already familiar with TensorFlow. If you are not, please refer the TensorFlow Tutorial .

TensorFlow model

In the previous article, I 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, I will start by loading in the packages. 

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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 *

np.random.seed(1)

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

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# 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.

SIGNS

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. 

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

Output:

y = 2

6-1

In previous article, I 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 out data. 

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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 = {}

Output:

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)

Create placeholders

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

I implemented the function below to create placeholders for the input image X and the output Y. We should not define the number of training examples for the moment. To do so, we 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.

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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"
    """

    X = tf.placeholder(shape=[None, n_H0, n_W0, n_C0], dtype=tf.float32)
    Y = tf.placeholder(shape=[None, n_y], dtype=tf.float32)

    return X, Y

Initialize parameters

I will initialize weights/filters $W1$ and $W2$ 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 we 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.

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

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

More Info.

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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

    W1 = tf.get_variable("W1", [4, 4, 3, 8], initializer=tf.contrib.layers.xavier_initializer(seed=0), dtype=tf.float32)
    W2 = tf.get_variable("W2", [2, 2, 8, 16], initializer=tf.contrib.layers.xavier_initializer(seed=0),
                         dtype=tf.float32)

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

    return parameters

Forward propagation

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

  • tf.nn.conv2d(X,W1, strides = [1,s,s,1], padding = ‘SAME’): given an input $X$ and a group of filters $W1$, this function convolves $W1$’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 we train the model. Hence, we did not need to initialize those weights when initializing the parameters.

I implemented the forward_propagation function below to build the following model: CONV2D -> RELU -> MAXPOOL -> CONV2D -> RELU -> MAXPOOL -> FLATTEN -> FULLYCONNECTED. I will 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. 

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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']

    # CONV2D: stride of 1, padding 'SAME'
    Z1 = tf.nn.conv2d(X, W1, [1, 1, 1, 1], padding='SAME')
    # RELU
    A1 = tf.nn.relu(Z1)
    # MAXPOOL: window 8x8, sride 8, padding 'SAME'
    P1 = tf.nn.max_pool(A1, [1, 8, 8, 1], [1, 8, 8, 1], padding='SAME')
    # CONV2D: filters W2, stride 1, padding 'SAME'
    Z2 = tf.nn.conv2d(P1, W2, [1, 1, 1, 1], padding='SAME')
    # RELU
    A2 = tf.nn.relu(Z2)
    # MAXPOOL: window 4x4, stride 4, padding 'SAME'
    P2 = tf.nn.max_pool(A2, [1, 4, 4, 1], [1, 4, 4, 1], padding='SAME')
    # FLATTEN
    P2 = 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)

    return Z3

Compute cost

I will 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.
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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
    """

    cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=Z3, labels=Y))

    return cost

Model

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

I have implemented random_mini_batches() in the Optimization programming article. Remember that this function returns a list of mini-batches.

The model below should:

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

Finally I 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

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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
    X, Y = create_placeholders(64, 64, 3, 6)

    # Initialize parameters
    parameters = initialize_parameters()

    # Forward propagation: Build the forward propagation in the tensorflow graph
    Z3 = forward_propagation(X, parameters)

    # Cost function: Add cost function to tensorflow graph
    cost = compute_cost(Z3, Y)

    # Backpropagation: Define the tensorflow optimizer. Use an AdamOptimizer that minimizes the cost.
    optimizer = tf.train.AdamOptimizer().minimize(cost)

    # 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).
                _, temp_cost = sess.run([optimizer, cost], feed_dict={X: minibatch_X, Y: minibatch_Y})

                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 our model for 100 epochs.:

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

Output:

Cost after epoch 0: 1.920183
Cost after epoch 5: 1.885439
Cost after epoch 10: 1.849110
Cost after epoch 15: 1.730203
Cost after epoch 20: 1.503597
Cost after epoch 25: 1.264177
Cost after epoch 30: 1.095219
Cost after epoch 35: 0.985675
Cost after epoch 40: 0.902660
Cost after epoch 45: 0.831738
Cost after epoch 50: 0.776374
Cost after epoch 55: 0.730666
Cost after epoch 60: 0.678335
Cost after epoch 65: 0.643941
Cost after epoch 70: 0.621297
Cost after epoch 75: 0.594998
Cost after epoch 80: 0.568649
Cost after epoch 85: 0.539469
Cost after epoch 90: 0.514542
Cost after epoch 95: 0.490415

acc

Tensor("Mean_1:0", shape=(), dtype=float32)
Train Accuracy: 0.860185
Test Accuracy: 0.75

Github

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