Tuesday 7 May 2024

Handwritten Digit Recognition Using Convolutional Neural Networks in Python with Keras

 A popular demonstration of the capability of deep learning techniques is object recognition in image data.

The “hello world” of object recognition for machine learning and deep learning is the MNIST dataset for handwritten digit recognition.

In this post, you will discover how to develop a deep learning model to achieve near state-of-the-art performance on the MNIST handwritten digit recognition task in Python using the Keras deep learning library.

After completing this tutorial, you will know:

  • How to load the MNIST dataset in Keras
  • How to develop and evaluate a baseline neural network model for the MNIST problem
  • How to implement and evaluate a simple Convolutional Neural Network for MNIST
  • How to implement a close to state-of-the-art deep learning model for MNIST

    Description of the MNIST Handwritten Digit Recognition Problem

    The MNIST problem is a dataset developed by Yann LeCun, Corinna Cortes, and Christopher Burges for evaluating machine learning models on the handwritten digit classification problem.

    The dataset was constructed from a number of scanned document datasets available from the National Institute of Standards and Technology (NIST). This is where the name for the dataset comes from, the Modified NIST or MNIST dataset.

    Images of digits were taken from a variety of scanned documents, normalized in size, and centered. This makes it an excellent dataset for evaluating models, allowing the developer to focus on machine learning with minimal data cleaning or preparation required.

    Each image is a 28×28-pixel square (784 pixels total). A standard split of the dataset is used to evaluate and compare models, where 60,000 images are used to train a model, and a separate set of 10,000 images are used to test it.

    It is a digit recognition task. As such, there are ten digits (0 to 9) or ten classes to predict. Results are reported using prediction error, which is nothing more than the inverted classification accuracy.

    Excellent results achieve a prediction error of less than 1%. A state-of-the-art prediction error of approximately 0.2% can be achieved with large convolutional neural networks. There is a listing of the state-of-the-art results and links to the relevant papers on the MNIST and other datasets on Rodrigo Benenson’s webpage.

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    Loading the MNIST Dataset in Keras

    The Keras deep learning library provides a convenient method for loading the MNIST dataset.

    The dataset is downloaded automatically the first time this function is called and stored in your home directory in ~/.keras/datasets/mnist.npz as an 11MB file.

    This is very handy for developing and testing deep learning models.

    To demonstrate how easy it is to load the MNIST dataset, first, write a little script to download and visualize the first four images in the training dataset.

    You can see that downloading and loading the MNIST dataset is as easy as calling the mnist.load_data() function. Running the above example, you should see the image below.

    Examples from the MNIST dataset

    Examples from the MNIST dataset

    Baseline Model with Multi-Layer Perceptrons

    Do you really need a complex model like a convolutional neural network to get the best results with MNIST?

    You can get very good results using a very simple neural network model with a single hidden layer. In this section, you will create a simple multi-layer perceptron model that achieves an error rate of 1.74%. You will use this as a baseline for comparing more complex convolutional neural network models.

    Let’s start by importing the classes and functions you will need.

    Now, you can load the MNIST dataset using the Keras helper function.

    The training dataset is structured as a 3-dimensional array of instance, image width, and image height. For a multi-layer perceptron model, you must reduce the images down into a vector of pixels. In this case, the 28×28-sized images will be 784 pixel input values.

    You can do this transform easily using the reshape() function on the NumPy array. You can also reduce your memory requirements by forcing the precision of the pixel values to be 32-bit, the default precision used by Keras anyway.

    The pixel values are grayscale between 0 and 255. It is almost always a good idea to perform some scaling of input values when using neural network models. Because the scale is well known and well behaved, you can very quickly normalize the pixel values to the range 0 and 1 by dividing each value by the maximum of 255.

    Finally, the output variable is an integer from 0 to 9. This is a multi-class classification problem. As such, it is good practice to use a one-hot encoding of the class values, transforming the vector of class integers into a binary matrix.

    You can easily do this using the built-in tf.keras.utils.to_categorical() helper function in Keras.

    You are now ready to create your simple neural network model. You will define your model in a function. This is handy if you want to extend the example later and try and get a better score.

    The model is a simple neural network with one hidden layer with the same number of neurons as there are inputs (784). A rectifier activation function is used for the neurons in the hidden layer.

    A softmax activation function is used on the output layer to turn the outputs into probability-like values and allow one class of the ten to be selected as the model’s output prediction. Logarithmic loss is used as the loss function (called categorical_crossentropy in Keras), and the efficient ADAM gradient descent algorithm is used to learn the weights.

    You can now fit and evaluate the model. The model is fit over ten epochs with updates every 200 images. The test data is used as the validation dataset, allowing you to see the skill of the model as it trains. A verbose value of 2 is used to reduce the output to one line for each training epoch.

    Finally, the test dataset is used to evaluate the model, and a classification error rate is printed.

    After tying this all together, the complete code listing is provided below.

    Running the example might take a few minutes when you run it on a CPU.

    Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

    You should see the output below. This very simple network defined in very few lines of code achieves a respectable error rate of 2.3%.

    Simple Convolutional Neural Network for MNIST

    Now that you have seen how to load the MNIST dataset and train a simple multi-layer perceptron model on it, it is time to develop a more sophisticated convolutional neural network or CNN model.

    Keras does provide a lot of capability for creating convolutional neural networks.

    In this section, you will create a simple CNN for MNIST that demonstrates how to use all the aspects of a modern CNN implementation, including Convolutional layers, Pooling layers, and Dropout layers.

    The first step is to import the classes and functions needed.

    Next, you need to load the MNIST dataset and reshape it to be suitable for training a CNN. In Keras, the layers used for two-dimensional convolutions expect pixel values with the dimensions [pixels][width][height][channels].

    Note that you are forcing so-called channels-last ordering for consistency in this example.

    In the case of RGB, the last dimension pixels would be 3 for the red, green, and blue components, and it would be like having three image inputs for every color image. In the case of MNIST, where the pixel values are grayscale, the pixel dimension is set to 1.

    As before, it is a good idea to normalize the pixel values to the range 0 and 1 and one-hot encode the output variables.

    Next, define your neural network model.

    Convolutional neural networks are more complex than standard multi-layer perceptrons, so you will start by using a simple structure that uses all the elements for state-of-the-art results. Below summarizes the network architecture.

    1. The first hidden layer is a convolutional layer called a Convolution2D. The layer has 32 feature maps, with the size of 5×5 and a rectifier activation function. This is the input layer that expects images with the structure outlined above: [pixels][width][height].
    2. Next, define a pooling layer that takes the max called MaxPooling2D. It is configured with a pool size of 2×2.
    3. The next layer is a regularization layer using dropout called Dropout. It is configured to randomly exclude 20% of neurons in the layer in order to reduce overfitting.
    4. Next is a layer that converts the 2D matrix data to a vector called Flatten. It allows the output to be processed by standard, fully connected layers.
    5. Next is a fully connected layer with 128 neurons and a rectifier activation function.
    6. Finally, the output layer has ten neurons for the ten classes and a softmax activation function to output probability-like predictions for each class.

    As before, the model is trained using logarithmic loss and the ADAM gradient descent algorithm.

    You evaluate the model the same way as before with the multi-layer perceptron. The CNN is fit over ten epochs with a batch size of 200.

    After tying this all together, the complete example is listed below.

    After running the example, the accuracy of the training and validation test is printed for each epoch, and at the end, the classification error rate is printed.

    Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

    Epochs may take about 45 seconds to run on the GPU (e.g., on AWS). You can see that the network achieves an error rate of 1.19%, which is better than our simple multi-layer perceptron model above.

    Larger Convolutional Neural Network for MNIST

    Now that you have seen how to create a simple CNN, let’s take a look at a model capable of close to state-of-the-art results.

    You will import the classes and functions, then load and prepare the data the same as in the previous CNN example.

    This time you will define a large CNN architecture with additional convolutional, max pooling layers, and fully connected layers. The network topology can be summarized as follows:

    1. Convolutional layer with 30 feature maps of size 5×5
    2. Pooling layer taking the max over 2*2 patches
    3. Convolutional layer with 15 feature maps of size 3×3
    4. Pooling layer taking the max over 2*2 patches
    5. Dropout layer with a probability of 20%
    6. Flatten layer
    7. Fully connected layer with 128 neurons and rectifier activation
    8. Fully connected layer with 50 neurons and rectifier activation
    9. Output layer

    Like the previous two experiments, the model is fit over ten epochs with a batch size of 200.

    After tying this all together, the complete example is listed below.

    Running the example prints accuracy on the training and validation datasets of each epoch and a final classification error rate.

    Note: Your results may vary given the stochastic nature of the algorithm or evaluation procedure, or differences in numerical precision. Consider running the example a few times and compare the average outcome.

    The model takes about 100 seconds to run per epoch. This slightly larger model achieves a respectable classification error rate of 0.83%.

    This is not an optimized network topology. Nor is it a reproduction of a network topology from a recent paper. There is a lot of opportunity for you to tune and improve upon this model.

    What is the best error rate score you can achieve?

    Post your configuration and best score in the comments.

    Resources on MNIST

    The MNIST dataset is very well studied. Below are some additional resources you might want to look into.

    Summary

    In this post, you discovered the MNIST handwritten digit recognition problem and deep learning models developed in Python using the Keras library that are capable of achieving excellent results.

    Working through this tutorial, you learned:

    • How to load the MNIST dataset in Keras and generate plots of the dataset
    • How to reshape the MNIST dataset and develop a simple but well-performing multi-layer perceptron model on the problem
    • How to use Keras to create convolutional neural network models for MNIST
    • How to develop and evaluate larger CNN models for MNIST capable of near world-class results.

    Do you have any questions about handwriting recognition with deep learning or this post? Ask your question in the comments, and I will do my best to answer.

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