Use crosschannelnorm to normalize each observation of a mini-batch using values from adjacent channels.

height = 8;
width = 8;
channels = 6;
observations = 10;

X = rand(height,width,channels,observations);
dlX = dlarray(X,'SSCB');

dlY = crosschannelnorm(dlX,3);

Values at the edges of an array are normalized using contributions from fewer channels, depending on the size of the channel window.

Create the input data as an array of ones with a height and width of two and three channels.

height = 2;
width = 2;
channels = 3;

X = ones(height,width,channels);
dlX = dlarray(X);

Normalize the data using a channel-window size of 3, an $\alpha$ of 1, a $\beta$ of 1, and a $\mathit{K}$ of 1e-5. Specify a data format of 'SSC'.

dlY = crosschannelnorm(dlX,3,'Alpha',1,'Beta',1,'K',1e-5,'DataFormat','SSC');

Compare the values in the original and the normalized data by reshaping the three-channel arrays into 2-D matrices.

dlX = reshape(dlX,2,6)

dlX = 
  2x6 dlarray

     1     1     1     1     1     1
     1     1     1     1     1     1

dlY = reshape(dlY,2,6)

dlY = 
  2x6 dlarray

    1.5000    1.5000    1.0000    1.0000    1.5000    1.5000
    1.5000    1.5000    1.0000    1.0000    1.5000    1.5000

For the first and last channels, the sum of squares is calculated using only two values. For the middle channel, the sum of squares contains the values of all three channels.

Typically, the cross-channel normalization operation follows a ReLU operation. For example, the GoogLeNet architecture contains convolutional operations followed by ReLU and cross-channel normalization operations.

The function modelFunction defined at the end of this example shows how you can use cross-channel normalization in a model. Use modelFunction to find the grouped convolution and ReLU activation of some input data and then normalize the result using cross-channel normalization with a window size of 5.

Create the input data as a single observation of random values with a height and width of ten and four channels.

height = 10;
width = 10;
channels = 4;
observations = 1;

X = rand(height,width,channels,observations);
dlX = dlarray(X,'SSCB');

Create the parameters for the grouped convolution operation. For the weights, use a filter height and width of three, two channels per group, three filters per group, and two groups. Use a value of zero for the bias.

filterSize = [3 3];
numChannelsPerGroup = 2;
numFiltersPerGroup = 3 ;
numGroups = 2;

params = struct;
params.conv.weights = rand(filterSize(1),filterSize(2),numChannelsPerGroup,numFiltersPerGroup,numGroups);
params.conv.bias = 0;

Apply the modelFunction to the data dlX.

dlY = modelFunction(dlX,params);

function dlY = modelFunction(dlX,params)

dlY = dlconv(dlX,params.conv.weights,params.conv.bias);
dlY = relu(dlY);
dlY = crosschannelnorm(dlY,5);

end