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Define a Custom Classification Output Layer

To construct a classification output layer with cross entropy loss for k mutually exclusive classes, use `classificationLayer`. If you want to use a different loss function for your classification problems, then you can define a custom classification output layer using this example as a guide. This example shows how to define a custom classification output layer with the sum of squares error (SSE) loss and use it in a convolutional neural network.

To define a custom classification output layer, you can use the template provided in this example, which takes you through the following steps:

1. Name the layer – Give the layer a name so it can be used in MATLAB®.

2. Declare the layer properties – Specify the properties of the layer.

3. Create a constructor function (optional) – Specify how to construct the layer and initialize its properties. If you do not specify a constructor function, then the software initializes the properties with `[]` at creation.

4. Create a forward loss function – Specify the loss between the predictions and the training targets.

5. Create a backward loss function – Specify the derivative of the loss with respect to the predictions.

SSE is an error measure between two continuous random variables. For predictions Y and training targets T, the SSE loss between Y and T is given by

`$L=\sum _{i=1}^{K}{\left({Y}_{i}-{T}_{i}\right)}^{2}$`

where K is the number of observations.

Classification Output Layer Template

Copy the classification output layer template into a new file in MATLAB. This template outlines the structure of a classification output layer and includes the functions that define the layer behavior.

```classdef myClassificationLayer < nnet.layer.ClassificationLayer properties % (Optional) Layer properties % Layer properties go here end methods function layer = myClassificationLayer() % (Optional) Create a myClassificationLayer % Layer constructor function goes here end function loss = forwardLoss(layer, Y, T) % Return the loss between the predictions Y and the % training targets T % % Inputs: % layer - Output layer % Y – Predictions made by network % T – Training targets % % Output: % loss - Loss between Y and T % Layer forward loss function goes here end function dLdY = backwardLoss(layer, Y, T) % Backward propagate the derivative of the loss function % % Inputs: % layer - Output layer % Y – Predictions made by network % T – Training targets % % Output: % dLdY - Derivative of the loss with respect to the predictions Y % Layer backward loss function goes here end end end ```

Name the Layer

First, give the layer a name. In the first line of the class file, replace the existing name `myClassificationLayer` with `exampleClassificationSSELayer`.

```classdef exampleClassificationSSELayer < nnet.layer.ClassificationLayer ... end```

Next, rename the `myClassificationLayer` constructor function (the first function in the `methods` section) to have the same name, and update the header comment.

``` methods function layer = exampleClassificationSSELayer() % Create an exampleClassificationSSELayer % Layer constructor function goes here end ... end```

Save the Layer

Save the layer class file in a new file named `exampleClassificationSSELayer.m`. The file name must match the layer name. To use the layer, you must save the file in the current folder or in a folder on the MATLAB path.

Declare Layer Properties

Declare the layer properties in the `properties` section.

By default, user-defined layers have three properties:

• `Name` – Name of the layer, specified as a character vector. Use the `Name` property to identify and index layers in a network. If you do not set the layer name, then the software automatically assigns one at training time.

• `Description` – One-line description of the layer, specified as a character vector. This description appears when the layer is displayed in a `Layer` array. The default value is the layer class name.

• `Type` – Type of the layer, specified as a character vector. The value of `Type` appears when the layer is displayed in a `Layer` array. The default value is the layer class name.

If the layer has no other properties, then you can omit the `properties` section.

In this example, the layer does not require any additional properties, so you can remove the `properties` section.

Create Constructor Function

Create the function that constructs the layer and initializes the layer properties. Specify any variables required to create the layer as inputs to the constructor function.

Specify an optional input argument `name` to assign to the `Name` property at creation.

```function layer = exampleClassificationSSELayer(name) % Create an exampleClassificationSSELayer % Layer constructor function goes here end```

Initialize Layer Properties

Replace the comment `% Layer constructor function goes here` with code that initializes the layer properties.

Give the layer a one-line description by setting the `Description` property of the layer. Set the `Name` property to the optional input argument `name`.

Set the description to describe the type of layer and its size.

``` function layer = exampleClassificationSSELayer(name) % Create an exampleClassificationSSELayer % Set layer name if nargin == 1 layer.Name = name; end % Set layer description layer.Description = 'Example classification layer with SSE loss'; end```

Create Forward Loss Function

Create a function named `forwardLoss` that returns the SSE loss between the predictions made by the network and the training targets. The syntax for `forwardLoss` is ```loss = forwardLoss(layer, Y, T)```, where `Y` is the output of the previous layer and `T` represents the training targets.

For classification problems, the dimensions of `T` depend on the type of problem. The following table describes the dimensions of `T`.

TaskDimensions of `T`
Image classification4-D array of size 1-by-1-by-K-by-N, where K is the number of classes, and N is the mini-batch size.
Sequence-to-label classificationMatrix of size K-by-N, where K is the number of classes, and N is the mini-batch size.
Sequence-to-sequence classification3-D array of size K-by-N-by-S, where K is the number of classes, N is the mini-batch size, and S is the sequence length.

The size of `Y` depends on the output of the previous layer. To ensure that `Y` is the same size as `T`, you must include a layer that outputs the correct size before the output layer. For example, to ensure that `Y` is a 4-D array of prediction scores for K classes, you can include a fully connected layer of size K followed by a softmax layer before the output layer.

For prediction scores Y and training targets T, the SSE loss between Y and T is given by

`$L=\sum _{i=1}^{K}{\left({Y}_{i}-{T}_{i}\right)}^{2}$`

where K is the number of classes.

The inputs `Y` and `T` correspond to Y and T in the equation, respectively. The output `loss` corresponds to L. To ensure that `loss` is scalar, output the mean loss over the mini-batch.

``` function loss = forwardLoss(layer, Y, T) % Returns the SSE loss between the predictions Y and the % training targets T % Calculate sum of squares sumSquares = sum((Y-T).^2); % Take mean over mini-batch N = size(Y,4); loss = sum(sumSquares)/N; end```

Create Backward Loss Function

Create the backward loss function.

Create a function named `backwardLoss` that returns the derivatives of the SSE loss with respect to the predictions `Y`. The syntax for `backwardLoss` is ```loss = backwardLoss(layer, Y, T)```, where `Y` is the output of the previous layer and `T` represents the training targets.

The dimensions of `Y` and `T` are the same as the inputs in `forwardLoss`.

The derivative of the SSE loss with respect to the predictions Y is given by

`$\frac{\delta L}{\delta {Y}_{i}}=\frac{2}{N}\left({Y}_{i}-{T}_{i}\right)$`

where N is the size of the mini-batch.

``` function dLdY = backwardLoss(layer, Y, T) % Returns the derivatives of the SSE loss with respect to the predictions Y N = size(Y,4); dLdY = 2*(Y-T)/N; end```

Completed Layer

View the completed classification output layer class file.

```classdef exampleClassificationSSELayer < nnet.layer.ClassificationLayer methods function layer = exampleClassificationSSELayer(name) % Create an exampleClassificationSSELayer % Set layer name if nargin == 1 layer.Name = name; end % Set layer description layer.Description = 'Example classification layer with SSE loss'; end function loss = forwardLoss(layer, Y, T) % Returns the SSE loss between the predictions Y and the % training targets T % Calculate sum of squares sumSquares = sum((Y-T).^2); % Take mean over mini-batch N = size(Y,4); loss = sum(sumSquares)/N; end function dLdY = backwardLoss(layer, Y, T) % Returns the derivatives of the SSE loss with respect to the predictions Y N = size(Y,4); dLdY = 2*(Y-T)/N; end end end```

GPU Compatibility

For GPU compatibility, the layer functions must support inputs and return outputs of type `gpuArray`. Any other functions used by the layer must do the same. Many MATLAB built-in functions support `gpuArray` input arguments. If you call any of these functions with at least one `gpuArray` as an input, then the function executes on the GPU and returns a `gpuArray`. For a list of functions that execute on a GPU, see Run Built-In Functions on a GPU (Parallel Computing Toolbox). To use a GPU for deep learning, you must also have a CUDA® enabled NVIDIA® GPU with compute capability 3.0 or higher. For more information on working with GPUs in MATLAB, see GPU Computing in MATLAB (Parallel Computing Toolbox).

Include Custom Classification Output Layer in Network

You can use a custom output layer in the same way as any other output layer in Neural Network Toolbox. This section shows how to create and train a network for classification using the custom classification output layer you created earlier.

`[XTrain, YTrain] = digitTrain4DArrayData;`

Create a layer array including the custom classification output layer `exampleClassificationSSELayer`.

```layers = [ ... imageInputLayer([28 28 1]) convolution2dLayer(5,20) batchNormalizationLayer reluLayer fullyConnectedLayer(10) softmaxLayer exampleClassificationSSELayer]```
```layers = 7x1 Layer array with layers: 1 '' Image Input 28x28x1 images with 'zerocenter' normalization 2 '' Convolution 20 5x5 convolutions with stride [1 1] and padding [0 0 0 0] 3 '' Batch Normalization Batch normalization 4 '' ReLU ReLU 5 '' Fully Connected 10 fully connected layer 6 '' Softmax softmax 7 '' Classification layer Example classification layer with SSE loss ```

Set the training options and train the network.

```options = trainingOptions('sgdm'); net = trainNetwork(XTrain,YTrain,layers,options);```
```Training on single CPU. Initializing image normalization. |========================================================================================| | Epoch | Iteration | Time Elapsed | Mini-batch | Mini-batch | Base Learning | | | | (hh:mm:ss) | Accuracy | Loss | Rate | |========================================================================================| | 1 | 1 | 00:00:00 | 14.84% | 0.8972 | 0.0100 | | 2 | 50 | 00:00:05 | 75.00% | 0.3219 | 0.0100 | | 3 | 100 | 00:00:10 | 92.97% | 0.1306 | 0.0100 | | 4 | 150 | 00:00:16 | 94.53% | 0.0919 | 0.0100 | | 6 | 200 | 00:00:23 | 97.66% | 0.0606 | 0.0100 | | 7 | 250 | 00:00:30 | 97.66% | 0.0493 | 0.0100 | | 8 | 300 | 00:00:37 | 100.00% | 0.0083 | 0.0100 | | 9 | 350 | 00:00:44 | 100.00% | 0.0136 | 0.0100 | | 11 | 400 | 00:00:51 | 99.22% | 0.0187 | 0.0100 | | 12 | 450 | 00:00:58 | 100.00% | 0.0060 | 0.0100 | | 13 | 500 | 00:01:04 | 99.22% | 0.0130 | 0.0100 | | 15 | 550 | 00:01:10 | 100.00% | 0.0046 | 0.0100 | | 16 | 600 | 00:01:16 | 99.22% | 0.0132 | 0.0100 | | 17 | 650 | 00:01:23 | 100.00% | 0.0032 | 0.0100 | | 18 | 700 | 00:01:30 | 99.22% | 0.0136 | 0.0100 | | 20 | 750 | 00:01:37 | 99.22% | 0.0131 | 0.0100 | | 21 | 800 | 00:01:45 | 99.22% | 0.0104 | 0.0100 | | 22 | 850 | 00:01:52 | 100.00% | 0.0018 | 0.0100 | | 24 | 900 | 00:02:00 | 100.00% | 0.0017 | 0.0100 | | 25 | 950 | 00:02:08 | 100.00% | 0.0016 | 0.0100 | | 26 | 1000 | 00:02:17 | 100.00% | 0.0008 | 0.0100 | | 27 | 1050 | 00:02:25 | 100.00% | 0.0010 | 0.0100 | | 29 | 1100 | 00:02:33 | 100.00% | 0.0012 | 0.0100 | | 30 | 1150 | 00:02:41 | 100.00% | 0.0010 | 0.0100 | | 30 | 1170 | 00:02:44 | 100.00% | 0.0009 | 0.0100 | |========================================================================================| ```

Evaluate the network performance by making predictions on new data and calculating the accuracy.

```[XTest, YTest] = digitTest4DArrayData; YPred = classify(net, XTest); accuracy = sum(YTest == YPred)/numel(YTest)```
```accuracy = 0.9856 ```