## Define Custom Weighted Classification Layer

### Tip

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 and create a custom weighted classification output layer with weighted cross entropy loss. Use a weighted classification layer for classification problems with an imbalanced distribution of classes. For an example showing how to use a weighted classification layer in a network, see Speech Command Recognition Using Deep Learning.

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 (optional) – Specify the derivative of the loss with respect to the predictions. If you do not specify a backward loss function, then the forward loss function must support dlarray objects.

A weighted classification layer computes the weighted cross entropy loss for classification problems. Weighted cross entropy is an error measure between two continuous random variables. For prediction scores Y and training targets T, the weighted cross entropy loss between Y and T is given by

$L=-\frac{1}{N}\sum _{n=1}^{N}\sum _{i=1}^{K}\text{​}{w}_{i}{T}_{ni}\mathrm{log}\left({Y}_{ni}\right),$

where N is the number of observations, K is the number of classes, and w is a vector of weights for each class.

### 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)
% (Optional) 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 weightedClassificationLayer.

classdef weightedClassificationLayer < nnet.layer.ClassificationLayer
...
end

Next, rename the myClassificationLayer constructor function (the first function in the methods section) so that it has the same name as the layer.

methods
function layer = weightedClassificationLayer()
...
end

...
end

#### Save the Layer

Save the layer class file in a new file named weightedClassificationLayer.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, custom output layers have the following properties:

• NameLayer name, specified as a character vector or a string scalar. To include a layer in a layer graph, you must specify a nonempty unique layer name. If you train a series network with the layer and Name is set to '', then the software automatically assigns a name to the layer at training time.

• Description – One-line description of the layer, specified as a character vector or a string scalar. This description appears when the layer is displayed in a Layer array. If you do not specify a layer description, then the software displays "Classification Output" or "Regression Output".

• Type – Type of the layer, specified as a character vector or a string scalar. The value of Type appears when the layer is displayed in a Layer array. If you do not specify a layer type, then the software displays the layer class name.

Custom classification layers also have the following property:

• ClassesClasses of the output layer, specified as a categorical vector, string array, cell array of character vectors, or 'auto'. If Classes is 'auto', then the software automatically sets the classes at training time. If you specify the string array or cell array of character vectors str, then the software sets the classes of the output layer to categorical(str,str). The default value is 'auto'.

Custom regression layers also have the following property:

• ResponseNamesNames of the responses, specified a cell array of character vectors or a string array. At training time, the software automatically sets the response names according to the training data. The default is {}.

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

In this example, the layer requires an additional property to save the class weights. Specify the property ClassWeights in the properties section.

properties
% Vector of weights corresponding to the classes in the training
% data
ClassWeights
end

### 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 input argument classWeights to assign to the ClassWeights property. Also specify an optional input argument name to assign to the Name property at creation. Add a comment to the top of the function that explains the syntaxes of the function.

function layer = weightedClassificationLayer(classWeights, name)
% layer = weightedClassificationLayer(classWeights) creates a
% weighted cross entropy loss layer. classWeights is a row
% vector of weights corresponding to the classes in the order
% that they appear in the training data.
%
% layer = weightedClassificationLayer(classWeights, name)
% additionally specifies the layer name.

...
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.

function layer = weightedClassificationLayer(classWeights, name)
% layer = weightedClassificationLayer(classWeights) creates a
% weighted cross entropy loss layer. classWeights is a row
% vector of weights corresponding to the classes in the order
% that they appear in the training data.
%
% layer = weightedClassificationLayer(classWeights, name)
% additionally specifies the layer name.

% Set class weights
layer.ClassWeights = classWeights;

% Set layer name
if nargin == 2
layer.Name = name;
end

% Set layer description
layer.Description = 'Weighted cross entropy';
end

### Create Forward Loss Function

Create a function named forwardLoss that returns the weighted cross entropy 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.

2-D image classification1-by-1-by-K-by-N, where K is the number of classes and N is the number of observations.4
3-D image classification1-by-1-by-1-by-K-by-N, where K is the number of classes and N is the number of observations.5
Sequence-to-label classificationK-by-N, where K is the number of classes and N is the number of observations.2
Sequence-to-sequence classificationK-by-N-by-S, where K is the number of classes, N is the number of observations, and S is the sequence length.2

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.

A weighted classification layer computes the weighted cross entropy loss for classification problems. Weighted cross entropy is an error measure between two continuous random variables. For prediction scores Y and training targets T, the weighted cross entropy loss between Y and T is given by

$L=-\frac{1}{N}\sum _{n=1}^{N}\sum _{i=1}^{K}\text{​}{w}_{i}{T}_{ni}\mathrm{log}\left({Y}_{ni}\right),$

where N is the number of observations, K is the number of classes, and w is a vector of weights for each class.

The inputs Y and T correspond to Y and T in the equation, respectively. The output loss corresponds to L. Add a comment to the top of the function that explains the syntaxes of the function.

function loss = forwardLoss(layer, Y, T)
% loss = forwardLoss(layer, Y, T) returns the weighted cross
% entropy loss between the predictions Y and the training
% targets T.

N = size(Y,4);
Y = squeeze(Y);
T = squeeze(T);
W = layer.ClassWeights;

loss = -sum(W*(T.*log(Y)))/N;
end

Because the forwardLoss function only uses functions that support dlarray objects, defining the backwardLoss function is optional. For a list of functions that support dlarray objects, see List of Functions with dlarray Support.

### Completed Layer

View the completed classification output layer class file.

classdef weightedClassificationLayer < nnet.layer.ClassificationLayer

properties
% Vector of weights corresponding to the classes in the training
% data
ClassWeights
end

methods
function layer = weightedClassificationLayer(classWeights, name)
% layer = weightedClassificationLayer(classWeights) creates a
% weighted cross entropy loss layer. classWeights is a row
% vector of weights corresponding to the classes in the order
% that they appear in the training data.
%
% layer = weightedClassificationLayer(classWeights, name)
% additionally specifies the layer name.

% Set class weights
layer.ClassWeights = classWeights;

% Set layer name
if nargin == 2
layer.Name = name;
end

% Set layer description
layer.Description = 'Weighted cross entropy';
end

function loss = forwardLoss(layer, Y, T)
% loss = forwardLoss(layer, Y, T) returns the weighted cross
% entropy loss between the predictions Y and the training
% targets T.

N = size(Y,4);
Y = squeeze(Y);
T = squeeze(T);
W = layer.ClassWeights;

loss = -sum(W*(T.*log(Y)))/N;
end
end
end

### GPU Compatibility

If the layer forward functions fully support dlarray objects, then the layer is GPU compatible. Otherwise, to be GPU compatible, the layer functions must support inputs and return outputs of type gpuArray.

Many MATLAB built-in functions support gpuArray and dlarray input arguments. For a list of functions that support dlarray objects, see List of Functions with dlarray Support. For a list of functions that execute on a GPU, see Run MATLAB 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).

The MATLAB functions used in forwardLoss in weightedClassificationLayer all support dlarray objects, so the layer is GPU compatible.

### Check Output Layer Validity

Check the validity of the custom classification output layer weightedClassificationLayer.

Define a custom weighted classification layer. To create this layer, save the file weightedClassificationLayer.m in the current folder.

Create an instance of the layer. Specify the class weights as a vector with three elements corresponding to three classes.

classWeights = [0.1 0.7 0.2];
layer = weightedClassificationLayer(classWeights);

Check that the layer is valid using checkLayer. Set the valid input size to the typical size of a single observation input to the layer. The layer expects a 1-by-1-by-K-by-N array input, where K is the number of classes and N is the number of observations in the mini-batch.

numClasses = numel(classWeights);
validInputSize = [1 1 numClasses];
checkLayer(layer,validInputSize,'ObservationDimension',4);
Skipping GPU tests. No compatible GPU device found.

Running nnet.checklayer.TestOutputLayerWithoutBackward
........
Done nnet.checklayer.TestOutputLayerWithoutBackward
__________

Test Summary:
8 Passed, 0 Failed, 0 Incomplete, 2 Skipped.
Time elapsed: 1.198 seconds.

The test summary reports the number of passed, failed, incomplete, and skipped tests.