Cross channel square-normalize using local responses
The cross-channel normalization operation uses local responses
in different channels to normalize each activation. Cross-channel normalization typically
Cross-channel normalization is also known as local response normalization.
normalizes each element of
dlY = crosschannelnorm(
dlX with respect to local values in the same
position in nearby channels. The normalized elements in
calculated from the elements in
dlX using the following formula.
where y is an element of
x is the corresponding element of
ss is the sum of the squares of the elements in the channel region
windowSize, and α, β,
and K are hyperparameters in the normalization.
crosschannelnorm to normalize each
observation of a mini-batch using values from adjacent channels.
Create the input data as ten observations of random values with a height and width of eight and six channels.
height = 8; width = 8; channels = 6; observations = 10; X = rand(height,width,channels,observations); dlX = dlarray(X,'SSCB');
Compute the cross-channel normalization using a channel window size of three.
dlY = crosschannelnorm(dlX,3);
Each value in each observation of
dlX is normalized using the
element in the previous channel and the element in the next channel.
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 of
1, a of
1, and a of
1e-5. Specify a data format of
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.
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
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;
modelFunction to the data
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
dlX— Input data
Input data, specified as a
dlarray with or without data format.
dlX is an unformatted
dlarray, you must
specify the data format using the
You can specify up to two dimensions in
windowSize— Size of channel window
Size of the channel window, which controls the number of channels that are used for the normalization of each element, specified as a positive integer.
windowSize is even, then the window is asymmetric. The
software looks at the previous
floor((windowSize-1)/2) channels and
floor((windowSize)/2) channels. For example, if
4, then the function normalizes
each element by its neighbor in the previous channel and by its neighbors in the next
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
'Alpha',2e-4,'Beta',0.8sets the multiplicative normalization constant to 0.0002 and the contrast constant exponent to 0.8.
'DataFormat'— Dimension order of unformatted data
Dimension order of unformatted input data, specified as the comma-separated pair
'DataFormat' and a character array or string
FMT that provides a label for each dimension of the data. Each
FMT must be one of the following:
'S' — Spatial
'C' — Channel
'B' — Batch (for example, samples and
'T' — Time (for example, sequences)
'U' — Unspecified
You can specify multiple dimensions labeled
'U'. You can use the labels
'T' at most once.
You must specify
'DataFormat' when the input data
dlX is not a formatted
'Alpha'— Normalization constant (α)
1e-4(default) | numeric scalar
Normalization constant (α) that multiplies the sum of the
squared values, specified as the comma-separated pair consisting of
'Alpha' and a numeric scalar. The default value is
'Beta'— Contrast constant (β)
0.75(default) | numeric scalar greater than or equal to
Contrast constant (β), specified as the comma-separated pair
'Beta' and a numeric scalar greater than or equal to
0.01. The default value is
'K'— Normalization hyperparameter (K)
2(default) | numeric scalar greater than or equal to
Normalization hyperparameter (K) used to avoid singularities in
the normalization, specified as the comma-separated pair consisting of
'K' and a numeric scalar greater than or equal to
1e-5. The default value is
dlY— Normalized data
Normalized data, returned as a
dlarray. The output
dlY has the same underlying data type as the input
If the input data
dlX is a formatted
dlY has the same dimension labels as
dlX. If the
input data is an unformatted
dlY is an
dlarray with the same dimension order as the input data.
Usage notes and limitations:
When the input argument
dlX is a
underlying data of type
gpuArray, this function runs on the
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).