Crash Course in Convolutional Neural Networks for Machine Learning

Convolutional neural networks are a powerful artificial neural network technique.

These networks preserve the spatial structure of the problem and were developed for object recognition tasks such as handwritten digit recognition. They are popular because people can achieve state-of-the-art results on challenging computer vision and natural language processing tasks.

In this post, you will discover convolutional neural networks for deep learning, also called ConvNets or CNNs. After completing this crash course, you will know:

• The building blocks used in CNNs, such as convolutional layers and pool layers
• How the building blocks fit together with a short worked example
• Best practices for configuring CNNs on your object recognition tasks
• References for state-of-the-art networks applied to complex machine learning problems

Kick-start your project with my new book Deep Learning With Python, including step-by-step tutorials and the Python source code files for all examples.

Let’s get started.

Crash course in convolutional neural networks for machine learning
Photo by Bryan Ledgard, some rights reserved.

The Case for Convolutional Neural Networks

Given a dataset of grayscale images with the standardized size of 32×32 pixels each, a traditional feed-forward neural network would require 1024 input weights (plus one bias).

This is fair enough, but the flattening of the image matrix of pixels to a long vector of pixel values loses all the spatial structure in the image. Unless all the images are perfectly resized, the neural network will have great difficulty with the problem.

Convolutional neural networks expect and preserve the spatial relationship between pixels by learning internal feature representations using small squares of input data. Features are learned and used across the whole image, allowing the objects in the images to be shifted or translated in the scene but still detectable by the network.

This is why the network is so useful for object recognition in photographs, picking out digits, faces, objects, and so on with varying orientations.

In summary, below are some benefits of using convolutional neural networks:

• They use fewer parameters (weights) to learn than a fully connected network
• They are designed to be invariant to object position and distortion in the scene
• They automatically learn and generalize features from the input domain

Building Blocks of Convolutional Neural Networks

There are three types of layers in a convolutional neural network:

1. Convolutional Layers
2. Pooling Layers
3. Fully-Connected Layers

1. Convolutional Layers

Convolutional layers are comprised of filters and feature maps.

Filters

The filters are the “neurons” of the layer. They take weighted inputs and output a value. The input size is a fixed square called a patch or a receptive field.

If the convolutional layer is an input layer, then the input patch will be the pixel values. If deeper in the network architecture, then the convolutional layer will take input from a feature map from the previous layer.

Feature Maps

The feature map is the output of one filter applied to the previous layer.

A given filter is drawn across the entire previous layer, moved one pixel at a time. Each position results in the activation of the neuron, and the output is collected in the feature map. You can see that if the receptive field is moved one pixel from activation to activation, then the field will overlap with the previous activation by (field width – 1) input values.

Zero Padding

The distance that a filter is moved across the input from the previous layer for each activation is referred to as the stride.

If the size of the previous layer is not cleanly divisible by the size of the filter’s receptive field and the size of the stride, then it is possible for the receptive field to attempt to read off the edge of the input feature map. In this case, techniques like zero padding can be used to invent mock inputs for the receptive field to read.

2. Pooling Layers

The pooling layers down-sample the previous layer’s feature map.

Pooling layers follow a sequence of one or more convolutional layers and are intended to consolidate the features learned and expressed in the previous layer’s feature map. As such, pooling may be considered a technique to compress or generalize feature representations and generally reduce the overfitting of the training data by the model.

They, too, have a receptive field, often much smaller than the convolutional layer. Also, the stride or number of inputs that the receptive field is moved for each activation is often equal to the size of the receptive field to avoid any overlap.

Pooling layers are often very simple, taking the average or the maximum of the input value in order to create its own feature map.

For more about pooling layers, see the post:

• A Gentle Introduction to Pooling Layers for Convolutional Neural Networks

3. Fully Connected Layers

Fully connected layers are the normal flat feed-forward neural network layer.

These layers may have a nonlinear activation function or a softmax activation in order to output probabilities of class predictions.

Fully connected layers are used at the end of the network after feature extraction and consolidation have been performed by the convolutional and pooling layers. They are used to create final nonlinear combinations of features and for making predictions by the network.

Worked Example of a Convolutional Neural Network

You now know about convolutional, pooling, and fully connected layers. Let’s make this more concrete by working through how these three layers may be connected together.

1. Image Input Data

Let’s assume you have a dataset of grayscale images. Each image has the same size of 32 pixels wide and 32 pixels high, and pixel values are between 0 and 255, e.g., a matrix of 32x32x1 or 1024 pixel values.

Image input data is expressed as a 3-dimensional matrix of width * height * channels. If you were using color images in the example, you would have three channels for the red, green, and blue pixel values, e.g., 32x32x3.

2. Convolutional Layer

Define a convolutional layer with ten filters, a receptive field 5 pixels wide and 5 pixels high, and a stride length of 1.

Because each filter can only get input from (i.e., “see”) 5×5 or 25 pixels at a time, you can calculate that each will require 25 + 1 input weights (plus 1 for the bias input).

Dragging the 5×5 receptive field across the input image data with a stride width of 1 will result in a feature map of 28×28 output values or 784 distinct activations per image.

You have ten filters, so ten different 28×28 feature maps or 7,840 outputs will be created for one image.

Finally, you know you have 26 inputs per filter, ten filters, and 28×28 output values to calculate per filter. Therefore, you have a total of 26x10x28x28 or 203,840 “connections” in your convolutional layer if you want to phrase it using traditional neural network nomenclature.

Convolutional layers also make use of a nonlinear transfer function as part of the activation, and the rectifier activation function is the popular default to use.

3. Pool Layer

You can define a pooling layer with a receptive field with a width of 2 inputs and a height of 2 inputs. You can also use a stride of 2 to ensure that there is no overlap.

This results in feature maps that are one-half the size of the input feature maps, from ten different 28×28 feature maps as input to ten different 14×14 feature maps as output.

You will use a max() operation for each receptive field so that the activation is the maximum input value.

4. Fully Connected Layer

Finally, you can flatten out the square feature maps into a traditional flat, fully connected layer.

You can define the fully connected layer with 200 hidden neurons, each with 10x14x14 input connections, or 1960 + 1 weights per neuron. That is a total of 392,200 connections and weights to learn in this layer.

You can use a sigmoid or softmax transfer function to output probabilities of class values directly.

Convolutional Neural Networks Best Practices

Now that you know about the building blocks for a convolutional neural network and how the layers hang together, you can review some best practices to consider when applying them.

• Input Receptive Field Dimensions: The default is 2D for images but could be 1D for words in a sentence or 3D for a video that adds a time dimension.
• Receptive Field Size: The patch should be as small as possible but large enough to “see” features in the input data. It is common to use 3×3 on small images and 5×5 or 7×7 and more on larger image sizes.
• Stride Width: Use the default stride of 1. It is easy to understand, and you don’t need padding to handle the receptive field falling off the edge of your images. This could be increased to 2 or larger for larger images.
• Number of Filters: Filters are the feature detectors. Generally, fewer filters are used at the input layer, and increasingly more filters are used at deeper layers.
• Padding: Set to zero and called zero padding when reading non-input data. This is useful when you cannot or do not want to standardize input image sizes or when you want to use receptive field and stride sizes that do not neatly divide up the input image size.
• Pooling: Pooling is a destructive or generalization process to reduce overfitting. The receptive field is almost always set to 2×2 with a stride of 2 to discard 75% of the activations from the output of the previous layer.
• Data Preparation: Consider standardizing input data, both the dimensions of the images and pixel values.
• Pattern Architecture: It is common to pattern the layers in your network architecture. This might be one, two, or some number of convolutional layers followed by a pooling layer. This structure can then be repeated one or more times. Finally, fully connected layers are often only used at the output end and may be stacked one, two, or more deep.
• Dropout: CNNs have a habit of overfitting, even with pooling layers. Dropout should be used, such as between fully connected layers and perhaps after pooling layers.

Do you know about some more best practices for using CNNs?

Let me know in the comments.

Further Reading on Convolutional Neural Networks

You have only scratched the surface on convolutional neural networks. The field is moving very fast, and new and interesting architectures and techniques are being discussed and used all the time.

If you are looking for a deeper understanding of the technique, take a look at LeCun et al.’s seminal paper titled “Gradient-Based Learning Applied to Document Recognition” [PDF]. In it, they introduce LeNet applied to handwritten digit recognition and carefully explain the layers and how the network is connected.

There are a lot of tutorials and discussions of CNNs around the web. A few choice examples are listed below. Personally, I find the explanatory pictures in the posts useful only after understanding how the network hangs together. Many of the explanations are confusing and defer you to LeCun’s paper if in doubt.

• Convolutional Networks in DeepLearning4J
• Convolutional Networks model in the Stanford CS231n course
• Convolutional Networks and Applications in Vision [PDF]
• Chapter 6 in Michael Nielsen’s open Deep Learning book
• VGG Convolutional Neural Networks Practical from Oxford
• Understanding Convolutional Neural Networks for NLP by Denny Britz

Summary

In this post, you discovered convolutional neural networks. You learned about:

• Why CNNs are needed to preserve spatial structure in your input data and the benefits they provide
• The building blocks of CNN include convolutional, pooling, and fully connected layers.
• How the layers in a CNN hang together
• Best practices when applying a CNN to your own problems

Do you have any questions about convolutional neural networks or this post? Ask your questions in the comments, and I will do my best to answer.