forward

Load Training Data

Load the digits data as an image datastore using the imageDatastore function and specify the folder containing the image data.

unzip("DigitsData.zip")

imds = imageDatastore("DigitsData", ...
    IncludeSubfolders=true, ...
    LabelSource="foldernames");

Partition the data into training and test sets. Set aside 10% of the data for testing using the splitEachLabel function.

[imdsTrain,imdsTest] = splitEachLabel(imds,0.9,"randomize");

The network used in this example requires input images of size 28-by-28-by-1. To automatically resize the training images, use an augmented image datastore. Specify additional augmentation operations to perform on the training images: randomly translate the images up to 5 pixels in the horizontal and vertical axes. Data augmentation helps prevent the network from overfitting and memorizing the exact details of the training images.

inputSize = [28 28 1];
pixelRange = [-5 5];

imageAugmenter = imageDataAugmenter( ...
    RandXTranslation=pixelRange, ...
    RandYTranslation=pixelRange);

augimdsTrain = augmentedImageDatastore(inputSize(1:2),imdsTrain,DataAugmentation=imageAugmenter);

To automatically resize the test images without performing further data augmentation, use an augmented image datastore without specifying any additional preprocessing operations.

augimdsTest = augmentedImageDatastore(inputSize(1:2),imdsTest);

Determine the number of classes in the training data.

classes = categories(imdsTrain.Labels);
numClasses = numel(classes);

Define Network

Define the network for image classification.

When training a network using a custom training loop, do not include an output layer.

layers = [
    imageInputLayer(inputSize,Normalization="none")
    convolution2dLayer(5,20,Padding="same")
    batchNormalizationLayer
    reluLayer
    convolution2dLayer(3,20,Padding="same")
    batchNormalizationLayer
    reluLayer
    convolution2dLayer(3,20,Padding="same")
    batchNormalizationLayer
    reluLayer
    fullyConnectedLayer(numClasses)
    softmaxLayer];

Create a dlnetwork object from the layer array.

net = dlnetwork(layers)

net = 
  dlnetwork with properties:

         Layers: [12×1 nnet.cnn.layer.Layer]
    Connections: [11×2 table]
     Learnables: [14×3 table]
          State: [6×3 table]
     InputNames: {'imageinput'}
    OutputNames: {'softmax'}
    Initialized: 1

  View summary with summary.

Define Model Loss Function

Training a deep neural network is an optimization task. By considering a neural network as a function $$f(X;\theta )$$, where $$X$$ is the network input, and $$\theta$$ is the set of learnable parameters, you can optimize $$\theta$$ so that it minimizes some loss value based on the training data. For example, optimize the learnable parameters $$\theta$$ such that for a given inputs $$X$$ with a corresponding targets $$T$$, they minimize the error between the predictions $$Y=f(X;\theta )$$ and $$T$$.

Define the modelLoss function. The modelLoss function takes a dlnetwork object net, a mini-batch of input data X with corresponding targets T and returns the loss, the gradients of the loss with respect to the learnable parameters in net, and the network state. To compute the gradients automatically, use the dlgradient function.

function [loss,gradients,state] = modelLoss(net,X,T)

% Forward data through network.
[Y,state] = forward(net,X);

% Calculate cross-entropy loss.
loss = crossentropy(Y,T);

% Calculate gradients of loss with respect to learnable parameters.
gradients = dlgradient(loss,net.Learnables);

end

Define SGD Function

Create the function sgdStep that takes the parameters and the gradients of the loss with respect to the parameters, and returns the updated parameters using the stochastic gradient descent algorithm, expressed as $${\theta }_{t+1}={\theta }_t-\rho \nabla L$$, where $$t$$ is the iteration number, $$\rho$$ is the learning rate, and $$\nabla L$$ denotes the gradients (the derivatives of the loss with respect to the learnable parameters).

function parameters = sgdStep(parameters,gradients,learnRate)

parameters = parameters - learnRate .* gradients;

end

Defining a custom update function is not a necessary step for custom training loops. Alternatively, you can use built in update functions like sgdmupdate, adamupdate, and rmspropupdate.

Specify Training Options

Train for fifteen epochs with a mini-batch size of 128 and a learning rate of 0.01.

numEpochs = 15;
miniBatchSize = 128;
learnRate = 0.01;

Train Model

Create a minibatchqueue object that processes and manages mini-batches of images during training. For each mini-batch:

mbq = minibatchqueue(augimdsTrain,...
    MiniBatchSize=miniBatchSize,...
    MiniBatchFcn=@preprocessMiniBatch,...
    MiniBatchFormat=["SSCB" ""], ...
    PartialMiniBatch="discard");

Calculate the total number of iterations for the training progress monitor.

numObservationsTrain = numel(imdsTrain.Files);
numIterationsPerEpoch = floor(numObservationsTrain / miniBatchSize);
numIterations = numEpochs * numIterationsPerEpoch;

Initialize the TrainingProgressMonitor object. Because the timer starts when you create the monitor object, make sure that you create the object close to the training loop.

monitor = trainingProgressMonitor( ...
    Metrics="Loss", ...
    Info="Epoch", ...
    XLabel="Iteration");

Train the network using a custom training loop. For each epoch, shuffle the data and loop over mini-batches of data. For each mini-batch:

epoch = 0;
iteration = 0;

% Loop over epochs.
while epoch < numEpochs && ~monitor.Stop
    
    epoch = epoch + 1;

    % Shuffle data.
    shuffle(mbq);
    
    % Loop over mini-batches.
    while hasdata(mbq) && ~monitor.Stop

        iteration = iteration + 1;
        
        % Read mini-batch of data.
        [X,T] = next(mbq);
        
        % Evaluate the model gradients, state, and loss using dlfeval and the
        % modelLoss function and update the network state.
        [loss,gradients,state] = dlfeval(@modelLoss,net,X,T);
        net.State = state;
        
        % Update the network parameters using SGD.
        updateFcn = @(parameters,gradients) sgdStep(parameters,gradients,learnRate);
        net = dlupdate(updateFcn,net,gradients);
        
        % Update the training progress monitor.
        recordMetrics(monitor,iteration,Loss=loss);
        updateInfo(monitor,Epoch=epoch);
        monitor.Progress = 100 * iteration/numIterations;
    end
end

Test Model

Test the neural network using the testnet function. For single-label classification, evaluate the accuracy. The accuracy is the percentage of correct predictions. By default, the testnet function uses a GPU if one is available. To select the execution environment manually, use the ExecutionEnvironment argument of the testnet function.

accuracy = testnet(net,augimdsTest,"accuracy")

accuracy = 
96.3000

Visualize the predictions in a confusion chart. Make predictions using the minibatchpredict function, and convert the classification scores to labels using the scores2label function. By default, the minibatchpredict function uses a GPU if one is available. To select the execution environment manually, use the ExecutionEnvironment argument of the minibatchpredict function.

scores = minibatchpredict(net,augimdsTest);
YTest = scores2label(scores,classes);

Visualize the predictions in a confusion chart.

TTest = imdsTest.Labels;
figure
confusionchart(TTest,YTest)

Large values on the diagonal indicate accurate predictions for the corresponding class. Large values on the off-diagonal indicate strong confusion between the corresponding classes.

Supporting Functions

Mini Batch Preprocessing Function

The preprocessMiniBatch function preprocesses a mini-batch of predictors and labels using the following steps:

function [X,T] = preprocessMiniBatch(dataX,dataT)

% Preprocess predictors.
X = preprocessMiniBatchPredictors(dataX);

% Extract label data from cell and concatenate.
T = cat(2,dataT{:});

% One-hot encode labels.
T = onehotencode(T,1);

end

Mini-Batch Predictors Preprocessing Function

The preprocessMiniBatchPredictors function preprocesses a mini-batch of predictors by extracting the image data from the input cell array and concatenate into a numeric array. For grayscale input, concatenating over the fourth dimension adds a third dimension to each image, to use as a singleton channel dimension.

function X = preprocessMiniBatchPredictors(dataX)

% Concatenate.
X = cat(4,dataX{:});

end