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What is Convolutional Neural Network?

Convolutional neural network, also known as convnets or CNN, is a well-known method in computer vision applications. This type of architecture is dominant to recognize objects from a picture or video.

In this tutorial, you will learn how to construct a convnet and how to use TensorFlow to solve the handwritten dataset.

In this tutorial, you will learn

Architecture of a Convolutional Neural Network

Think about Facebook a few years ago, after you uploaded a picture to your profile, you were asked to add a name to the face on the picture manually. Nowadays, Facebook uses convnet to tag your friend in the picture automatically.

A convolutional neural network is not very difficult to understand. An input image is processed during the convolution phase and later attributed a label.

A typical convnet architecture can be summarized in the picture below. First of all, an image is pushed to the network; this is called the input image. Then, the input image goes through an infinite number of steps; this is the convolutional part of the network. Finally, the neural network can predict the digit on the image.

An image is composed of an array of pixels with height and width. A grayscale image has only one channel while the color image has three channels (each one for Red, Green, and Blue). A channel is stacked over each other. In this tutorial, you will use a grayscale image with only one channel. Each pixel has a value from 0 to 255 to reflect the intensity of the color. For instance, a pixel equals to 0 will show a white color while pixel with a value close to 255 will be darker.

Let's have a look of an image stored in the MNIST dataset. The picture below shows how to represent the picture of the left in a matrix format. Note that, the original matrix has been standardized to be between 0 and 1. For darker color, the value in the matrix is about 0.9 while white pixels have a value of 0.

Convolutional operation

The most critical component in the model is the convolutional layer. This part aims at reducing the size of the image for faster computations of the weights and improve its generalization.

During the convolutional part, the network keeps the essential features of the image and excludes irrelevant noise. For instance, the model is learning how to recognize an elephant from a picture with a mountain in the background. If you use a traditional neural network, the model will assign a weight to all the pixels, including those from the mountain which is not essential and can mislead the network.

Instead, a convolutional neural network will use a mathematical technique to extract only the most relevant pixels. This mathematical operation is called convolution. This technique allows the network to learn increasingly complex features at each layer. The convolution divides the matrix into small pieces to learn to most essential elements within each piece.

Components of Convnets

There are four components of a Convnets

  1. Convolution
  2. Non Linearity (ReLU)
  3. Pooling or Sub Sampling
  4. Classification (Fully Connected Layer)
  • Convolution

The purpose of the convolution is to extract the features of the object on the image locally. It means the network will learn specific patterns within the picture and will be able to recognize it everywhere in the picture.

Convolution is an element-wise multiplication. The concept is easy to understand. The computer will scan a part of the image, usually with a dimension of 3x3 and multiplies it to a filter. The output of the element-wise multiplication is called a feature map. This step is repeated until all the image is scanned. Note that, after the convolution, the size of the image is reduced.

Below, there is a URL to see in action how convolution works.

There are numerous channels available. Below, we listed some of the channels. You can see that each filter has a specific purpose. Note, in the picture below; the Kernel is a synonym of the filter.

Source

Arithmetic behind the convolution

The convolutional phase will apply the filter on a small array of pixels within the picture. The filter will move along the input image with a general shape of 3x3 or 5x5. It means the network will slide these windows across all the input image and compute the convolution. The image below shows how the convolution operates. The size of the patch is 3x3, and the output matrix is the result of the element-wise operation between the image matrix and the filter.

Source

You notice that the width and height of the output can be different from the width and height of the input. It happens because of the border effect.

Border effect

Image has a 5x5 features map and a 3x3 filter. There is only one window in the center where the filter can screen an 3x3 grid. The output feature map will shrink by two tiles alongside with a 3x3 dimension.

To get the same output dimension as the input dimension, you need to add padding. Padding consists of adding the right number of rows and columns on each side of the matrix. It will allow the convolution to center fit every input tile. In the image below, the input/output matrix have the same dimension 5x5

When you define the network, the convolved features are controlled by three parameters:

  1. Depth: It defines the number of filters to apply during the convolution. In the previous example, you saw a depth of 1, meaning only one filter is used. In most of the case, there is more than one filter. The picture below shows the operations done in a situation with three filters

  1. Stride: It defines the number of "pixel's jump" between two slices. If the stride is equal to 1, the windows will move with a pixel's spread of one. If the stride is equal to two, the windows will jump by 2 pixels. If you increase the stride, you will have smaller feature maps.

Example stride 1

Image stride 2

  1. Zero-padding: A padding is an operation of adding a corresponding number of rows and column on each side of the input features maps. In this case, the output has the same dimension as the input.
  2. Non Linearity (ReLU)

At the end of the convolution operation, the output is subject to an activation function to allow non-linearity. The usual activation function for convnet is the Relu. All the pixel with a negative value will be replaced by zero.

  • Max-pooling operation

This step is easy to understand. The purpose of the pooling is to reduce the dimensionality of the input image. The steps are done to reduce the computational complexity of the operation. By diminishing the dimensionality, the network has lower weights to compute, so it prevents overfitting.

In this stage, you need to define the size and the stride. A standard way to pool the input image is to use the maximum value of the feature map. Look at the picture below. The "pooling" will screen a four submatrix of the 4x4 feature map and return the maximum value. The pooling takes the maximum value of a 2x2 array and then move this windows by two pixels. For instance, the first sub-matrix is [3,1,3,2], the pooling will return the maximum, which is 3.

There is another pooling operation such as the mean.

This operation aggressively reduces the size of the feature map

  • Fully connected layers

The last step consists of building a traditional artificial neural network as you did in the previous tutorial. You connect all neurons from the previous layer to the next layer. You use a softmax activation function to classify the number on the input image.

Recap:

Convolutional Neural network compiles different layers before making a prediction. A neural network has:

  • A convolutional layer
  • Relu Activation function
  • Pooling layer
  • Densely connected layer

The convolutional layers apply different filters on a subregion of the picture. The Relu activation function adds non-linearity, and the pooling layers reduce the dimensionality of the features maps.

All these layers extract essential information from the images. At last, the features map are feed to a primary fully connected layer with a softmax function to make a prediction.

Train CNN with TensorFlow

Now that you are familiar with the building block of a convnets, you are ready to build one with TensorFlow. We will use the MNIST dataset for image classification.

The data preparation is the same as the previous tutorial. You can run the codes and jump directly to the architecture of the CNN.

You will follow the steps below:

Step 1: Upload Dataset

Step 2: Input layer

Step 3: Convolutional layer

Step 4: Pooling layer

Step 5: Second Convolutional Layer and Pooling Layer

Step 6: Dense layer

Step 7: Logit Layer

Step 1: Upload Dataset

The MNIST dataset is available with scikit to learn at this URL. Please download it and store it in Downloads. You can upload it with fetch_mldata('MNIST original').

Create a train/test set

You need to split the dataset with train_test_split

Scale the features

Finally, you can scale the feature with MinMaxScaler

import numpy as np
import tensorflow as tf
from sklearn.datasets import fetch_mldata

#Change USERNAME by the username of your machine
## Windows USER
mnist = fetch_mldata('C:\\Users\\USERNAME\\Downloads\\MNIST original')
## Mac User
mnist = fetch_mldata('/Users/USERNAME/Downloads/MNIST original')

print(mnist.data.shape)
print(mnist.target.shape)
from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(mnist.data, mnist.target, test_size=0.2, random_state=42)
y_train  = y_train.astype(int)
y_test  = y_test.astype(int)
batch_size =len(X_train)

print(X_train.shape, y_train.shape,y_test.shape )
## resclae
from sklearn.preprocessing import MinMaxScaler
scaler = MinMaxScaler()
# Train
X_train_scaled = scaler.fit_transform(X_train.astype(np.float64))
# test
X_test_scaled = scaler.fit_transform(X_test.astype(np.float64))
feature_columns = [tf.feature_column.numeric_column('x', shape=X_train_scaled.shape[1:])]
X_train_scaled.shape[1:]

Define the CNN

A CNN uses filters on the raw pixel of an image to learn details pattern compare to global pattern with a traditional neural net. To construct a CNN, you need to define:

  1. A convolutional layer: Apply n number of filters to the feature map. After the convolution, you need to use a Relu activation function to add non-linearity to the network.
  2. Pooling layer: The next step after the convolution is to downsample the feature max. The purpose is to reduce the dimensionality of the feature map to prevent overfitting and improve the computation speed. Max pooling is the conventional technique, which divides the feature maps into subregions (usually with a 2x2 size) and keeps only the maximum values.
  3. Fully connected layers: All neurons from the previous layers are connected to the next layers. The CNN will classify the label according to the features from the convolutional layers and reduced with the pooling layer.

CNN architecture

  • Convolutional Layer: Applies 14 5x5 filters (extracting 5x5-pixel subregions), with ReLU activation function
  • Pooling Layer: Performs max pooling with a 2x2 filter and stride of 2 (which specifies that pooled regions do not overlap)
  • Convolutional Layer: Applies 36 5x5 filters, with ReLU activation function
  • Pooling Layer #2: Again, performs max pooling with a 2x2 filter and stride of 2
  • 1,764 neurons, with dropout regularization rate of 0.4 (probability of 0.4 that any given element will be dropped during training)
  • Dense Layer (Logits Layer): 10 neurons, one for each digit target class (0–9).

There are three important modules to use to create a CNN:

  • conv2d(). Constructs a two-dimensional convolutional layer with the number of filters, filter kernel size, padding, and activation function as arguments.
  • max_pooling2d(). Constructs a two-dimensional pooling layer using the max-pooling algorithm.
  • dense(). Constructs a dense layer with the hidden layers and units

You will define a function to build the CNN. Let's see in detail how to construct each building block before to wrap everything together in the function.

Step 2: Input layer

def cnn_model_fn(features, labels, mode):
    input_layer = tf.reshape(tensor = features["x"],shape =[-1, 28, 28, 1])

You need to define a tensor with the shape of the data. For that, you can use the module tf.reshape. In this module, you need to declare the tensor to reshape and the shape of the tensor. The first argument is the features of the data, which is defined in the argument of the function.

A picture has a height, a width, and a channel. The MNIST dataset is a monochronic picture with a 28x28 size. We set the batch size to -1 in the shape argument so that it takes the shape of the features["x"]. The advantage is to make the batch size hyperparameters to tune. If the batch size is set to 7, then the tensor will feed 5,488 values (28*28*7).

Step 3: Convolutional layer
# first Convolutional Layer
  conv1 = tf.layers.conv2d(
      inputs=input_layer,
      filters=14,
      kernel_size=[5, 5],
      padding="same",
      activation=tf.nn.relu)

The first convolutional layer has 14 filters with a kernel size of 5x5 with the same padding. The same padding means both the output tensor and input tensor should have the same height and width. Tensorflow will add zeros to the rows and columns to ensure the same size.

You use the Relu activation function. The output size will be [28, 28, 14].

Step 4: Pooling layer

The next step after the convolution is the pooling computation. The pooling computation will reduce the dimensionality of the data. You can use the module max_pooling2d with a size of 2x2 and stride of 2. You use the previous layer as input. The output size will be [batch_size, 14, 14, 14]

# first Pooling Layer 
pool1 = tf.layers.max_pooling2d(inputs=conv1, pool_size=[2, 2], strides=2)

Step 5: Second Convolutional Layer and Pooling Layer

The second convolutional layer has 32 filters, with an output size of [batch_size, 14, 14, 32]. The pooling layer has the same size as before and the output shape is [batch_size, 14, 14, 18].

conv2 = tf.layers.conv2d(
      inputs=pool1,
      filters=36,
      kernel_size=[5, 5],
      padding="same",
      activation=tf.nn.relu)
pool2 = tf.layers.max_pooling2d(inputs=conv2, pool_size=[2, 2], strides=2)

Step 6: Dense layer

Then, you need to define the fully-connected layer. The feature map has to be flatten before to be connected with the dense layer. You can use the module reshape with a size of 7*7*36.

The dense layer will connect 1764 neurons. You add a Relu activation function. Besides, you add a dropout regularization term with a rate of 0.3, meaning 30 percents of the weights will be set to 0. Note that, the dropout takes place only during the training phase. The function cnn_model_fn has an argument mode to declare if the model needs to be trained or to evaluate.

pool2_flat = tf.reshape(pool2, [-1, 7 * 7 * 36])

dense = tf.layers.dense(inputs=pool2_flat, units=7 * 7 * 36, activation=tf.nn.relu)
dropout = tf.layers.dropout(
      inputs=dense, rate=0.3, training=mode == tf.estimator.ModeKeys.TRAIN)

Step 7: Logit Layer

Finally, you can define the last layer with the prediction of the model. The output shape is equal to the batch size and 10, the total number of images.

# Logits Layer
logits = tf.layers.dense(inputs=dropout, units=10)			

You can create a dictionary containing the classes and the probability of each class. The module tf.argmax() with returns the highest value if the logit layers. The softmax function returns the probability of each class.

predictions = {				
	# Generate predictions				
    "classes": tf.argmax(input=logits, axis=1),				
    "probabilities": tf.nn.softmax(logits, name="softmax_tensor")  }			

You only want to return the dictionnary prediction when mode is set to prediction. You add this codes to dispay the predictions

if mode == tf.estimator.ModeKeys.PREDICT:
    return tf.estimator.EstimatorSpec(mode=mode, predictions=predictions)

The next step consists to compute the loss of the model. In the last tutorial, you learnt that the loss function for a multiclass model is cross entropy. The loss is easily computed with the following code:

# Calculate Loss (for both TRAIN and EVAL modes)
loss = tf.losses.sparse_softmax_cross_entropy(labels=labels, logits=logits)

The final step is to optimize the model, that is to find the best values of the weights. For that, you use a Gradient descent optimizer with a learning rate of 0.001. The objective is to minimize the loss

optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.001)
train_op = optimizer.minimize(
        loss=loss,
        global_step=tf.train.get_global_step())

You are done with the CNN. However, you want to display the performance metrics during the evaluation mode. The performance metrics for a multiclass model is the accuracy metrics. Tensorflow is equipped with a module accuracy with two arguments, the labels, and the predicted values.

eval_metric_ops = {
      "accuracy": tf.metrics.accuracy(labels=labels, predictions=predictions["classes"])}
return tf.estimator.EstimatorSpec(mode=mode, loss=loss, eval_metric_ops=eval_metric_ops)

That's it. You created your first CNN and you are ready to wrap everything into a function in order to use it to train and evaluate the model.

def cnn_model_fn(features, labels, mode):
  """Model function for CNN."""
  # Input Layer
  input_layer = tf.reshape(features["x"], [-1, 28, 28, 1])

  # Convolutional Layer
  conv1 = tf.layers.conv2d(
      inputs=input_layer,
      filters=32,
      kernel_size=[5, 5],
      padding="same",
      activation=tf.nn.relu)

  # Pooling Layer
  pool1 = tf.layers.max_pooling2d(inputs=conv1, pool_size=[2, 2], strides=2)

  # Convolutional Layer #2 and Pooling Layer
  conv2 = tf.layers.conv2d(
      inputs=pool1,
      filters=36,
      kernel_size=[5, 5],
      padding="same",
      activation=tf.nn.relu)
  pool2 = tf.layers.max_pooling2d(inputs=conv2, pool_size=[2, 2], strides=2)

  # Dense Layer
  pool2_flat = tf.reshape(pool2, [-1, 7 * 7 * 36])
  dense = tf.layers.dense(inputs=pool2_flat, units=7 * 7 * 36, activation=tf.nn.relu)
  dropout = tf.layers.dropout(
      inputs=dense, rate=0.4, training=mode == tf.estimator.ModeKeys.TRAIN)

  # Logits Layer
  logits = tf.layers.dense(inputs=dropout, units=10)

  predictions = {
      # Generate predictions (for PREDICT and EVAL mode)
      "classes": tf.argmax(input=logits, axis=1),
      "probabilities": tf.nn.softmax(logits, name="softmax_tensor")
  }

  if mode == tf.estimator.ModeKeys.PREDICT:
    return tf.estimator.EstimatorSpec(mode=mode, predictions=predictions)

  # Calculate Loss
  loss = tf.losses.sparse_softmax_cross_entropy(labels=labels, logits=logits)

  # Configure the Training Op (for TRAIN mode)
  if mode == tf.estimator.ModeKeys.TRAIN:
    optimizer = tf.train.GradientDescentOptimizer(learning_rate=0.001)
    train_op = optimizer.minimize(
        loss=loss,
        global_step=tf.train.get_global_step())
    return tf.estimator.EstimatorSpec(mode=mode, loss=loss, train_op=train_op)

  # Add evaluation metrics Evaluation mode
  eval_metric_ops = {
      "accuracy": tf.metrics.accuracy(
          labels=labels, predictions=predictions["classes"])}
  return tf.estimator.EstimatorSpec(
      mode=mode, loss=loss, eval_metric_ops=eval_metric_ops)

The steps below are the same as the previous tutorials.

First of all, you define an estimator with the CNN model.

# Create the Estimator
mnist_classifier = tf.estimator.Estimator(
    model_fn=cnn_model_fn, model_dir="train/mnist_convnet_model")

A CNN takes many times to train, therefore, you create a Logging hook to store the values of the softmax layers every 50 iterations.

# Set up logging for predictions
tensors_to_log = {"probabilities": "softmax_tensor"}
logging_hook = tf.train.LoggingTensorHook(tensors=tensors_to_log, every_n_iter=50)

You are ready to estimate the model. You set a batch size of 100 and shuffle the data. Note that we set training steps of 16.000, it can take lots of time to train. Be patient.

# Train the model
train_input_fn = tf.estimator.inputs.numpy_input_fn(
    x={"x": X_train_scaled},
    y=y_train,
    batch_size=100,
    num_epochs=None,
    shuffle=True)
mnist_classifier.train(
    input_fn=train_input_fn,
    steps=16000,
    hooks=[logging_hook])

Now that the model is train, you can evaluate it and print the results

# Evaluate the model and print results
eval_input_fn = tf.estimator.inputs.numpy_input_fn(
    x={"x": X_test_scaled},
    y=y_test,
    num_epochs=1,
    shuffle=False)
eval_results = mnist_classifier.evaluate(input_fn=eval_input_fn)
print(eval_results)
INFO:tensorflow:Calling model_fn.
INFO:tensorflow:Done calling model_fn.
INFO:tensorflow:Starting evaluation at 2018-08-05-12:52:41
INFO:tensorflow:Graph was finalized.
INFO:tensorflow:Restoring parameters from train/mnist_convnet_model/model.ckpt-15652
INFO:tensorflow:Running local_init_op.
INFO:tensorflow:Done running local_init_op.
INFO:tensorflow:Finished evaluation at 2018-08-05-12:52:56
INFO:tensorflow:Saving dict for global step 15652: accuracy = 0.9589286, global_step = 15652, loss = 0.13894269
{'accuracy': 0.9689286, 'loss': 0.13894269, 'global_step': 15652}

With the current architecture, you get an accuracy of 97%. You can change the architecture, the batch size and the number of iteration to improve the accuracy. The CNN neural network has performed far better than ANN or logistic regression. In the tutorial on artificial neural network, you had an accuracy of 96%, which is lower the CNN. The performances of the CNN are impressive with a larger image set, both in term of speed computation and accuracy.

Summary

A convolutional neural network works very well to evaluate picture. This type of architecture is dominant to recognize objects from a picture or video.

To build a CNN, you need to follow six steps:

Step 1: Input layer:

This step reshapes the data. The shape is equal to the square root of the number of pixels. For instance, if a picture has 156 pixels, then the shape is 26x26. You need to specify if the picture has colour or not. If yes, then you had 3 to the shape- 3 for RGB-, otherwise 1.

input_layer = tf.reshape(tensor = features["x"],shape =[-1, 28, 28, 1])	

Step 2: Convolutional layer

Next, you need to create the convolutional layers. You apply different filters to allow the network to learn important feature. You specify the size of the kernel and the amount of filters.

conv1 = tf.layers.conv2d(
      inputs=input_layer,
      filters=14,
      kernel_size=[5, 5],
      padding="same",
      activation=tf.nn.relu)

Step 3: Pooling layer

In the third step, you add a pooling layer. This layer decreases the size of the input. It does so by taking the maximum value of the a sub-matrix. For instance, if the sub-matrix is [3,1,3,2], the pooling will return the maximum, which is 3.

pool1 = tf.layers.max_pooling2d(inputs=conv1, pool_size=[2, 2], strides=2)	

Step 4: Add Convolutional Layer and Pooling Layer

In this step, you can add as much as you want conv layers and pooling layers. Google uses architecture with more than 20 conv layers.

Step 5: Dense layer

The step 5 flatten the previous to create a fully connected layers. In this step, you can use different activation function and add a dropout effect.

pool2_flat = tf.reshape(pool2, [-1, 7 * 7 * 36])

dense = tf.layers.dense(inputs=pool2_flat, units=7 * 7 * 36, activation=tf.nn.relu)
dropout = tf.layers.dropout(
      inputs=dense, rate=0.3, training=mode == tf.estimator.ModeKeys.TRAIN)

Step 6: Logit Layer

The final step is the prediction.

logits = tf.layers.dense(inputs=dropout, units=10)			

 

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